Year 4: Adding, subtracting and money problems
Part of the Year 4 tenths, hundredths and money chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Adding, subtracting and money problems
Adding money. Write the amounts in columns with the decimal points in a straight line, so pounds are under pounds and pence are under pence. Add the pence first, then the pounds. If the pence make 100p or more, carry 1 to the pounds, as you do with any column addition (Chapter 2).
For example, to add £2.75 and £1.86 we write the numbers like this. The decimal points are in a straight line.
| £1 | 10p | 1p | ||
| £ | 2 | . | 7 | 5 |
| + £ | 1 | . | 8 | 6 |
| £ | . | |||
A good check is to estimate: round each amount to the nearest pound. £2.75 is about £3 and £1.86 is about £2, so the total is about £5.
Another way. Add the pounds and the pence separately. £3.85 + £2.47: pounds 3 + 2 = 5. Pence 85 + 47 = 132p = £1.32. Then £5 + £1.32 = £6.32.
Subtracting money is the same as column subtraction: the bigger amount goes on top. If the pence are too small, exchange 1 pound for 100p.
Here is £8.30 − £4.65 set out in columns.
| £1 | 10p | 1p | ||
| £ | 8 | . | 3 | 0 |
| − £ | 4 | . | 6 | 5 |
| £ | . |
Change. The change is the money you get back when you pay with more than the cost. Change = money paid − total cost. You can subtract, or count up from the cost to the money paid: first to the next whole pound, then up in whole pounds.
Multiplying and sharing. For 3 items that cost £1.35 each, multiply the pounds and the pence separately: 3 × £1 = £3 and 3 × 35p = 105p = £1.05. The total is £4.05. To share £7.20 equally between 4 people, change to pence: 720p ÷ 4 = 180p = £1.80 each.
Measures with decimals. You can add and subtract lengths, masses and capacities written as decimals in the same way. Line up the decimal points. 2.5 m has one decimal place and 1.75 m has two, so write 2.5 as 2.50. Then 2.50 + 1.75 = 4.25 m.
Multi-step problems. Draw a bar model. Work out what you need to find first, and do the calculations in order.
Key words. The total is all the amounts added together. Change is the money you get back. To estimate is to find an approximate answer by rounding. Carry and exchange are column-method tricks.
Key ideas
- Line up the decimal points. Pounds under pounds, pence under pence.
- Add or subtract the pence first, then the pounds. Carry or exchange when you need to.
- Change = money paid − total cost. You can also count up from the cost.
- Multiply the pounds and the pence separately. Change 100p into £1.
- To share money equally, change to pence and divide. Change back to pounds.
- Estimate first: round each amount to the nearest pound to check the answer.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 2 . 7 5 + £ 1 . 8 6 £ . - Add the pence. Always start on the right.5 + 6 = 11
11 is 10 or more. Write 1 in the pence column and carry 1 to the tens of pence column. - Add the tens of pence. Now the next column to the left. Add the 1 we carried as well.7 + 8 + 1 = 16
16 is 10 or more. Write 6 in the tens of pence column and carry 1 to the pounds column (across the decimal point). - Add the pounds. Now the next column to the left. Add the 1 we carried as well.2 + 1 + 1 = 4
4 is less than 10, so write 4. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 2 . 7 5 + £ 1 . 8 6 £ 4 . 6 1 1 1
£2.75 + £1.86 = £4.61
Check. Estimate: round to the nearest pound: £3 + £2 = £5. This is close to £4.61. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add the pounds, then add the pence. If the pence make 100p or more, change 100p into another pound.
- Split each amount into pounds and pence. We add the pounds and the pence separately.£3.85 = £3 + 85p
£2.47 = £2 + 47p - Add the pounds. Add the whole pound parts.£3 + £2 = £5
- Add the pence. Add the pence parts.85p + 47p = 132p
- Change 100 pence into a pound. The pence total is 100p or more. Every 100p is £1.132p = £1 and 32p
£5 + £1 = £6 - Put the pounds and pence together. £6 and 32p = £6.32
Check. Estimate: round to the nearest pound: £4 + £2 = £6. This is close to £6.32. ✓
Watch out. If the pence add up to more than 100p, you must change 100p into £1. Do not write £5.113.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 8 . 3 0 − £ 4 . 6 5 £ . - Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
Exchange 1 from the tens of pence column: 3 becomes 2, and the pence column goes from 0 to 10.
10 − 5 = 5 - Exchange, then subtract the tens of pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.2 is not enough to take away 6. We need to exchange.
(There were 3 in this column to start with, but we gave one away in an earlier exchange.)
Exchange 1 from the pounds column: 8 becomes 7, and the tens of pence column goes from 2 to 12. (This crosses the decimal point.)
12 − 6 = 6 - Subtract the pounds. Now the next column to the left.(This digit is 7 now, not 8, because we exchanged from this column.)
7 − 4 = 3 - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 7 8. 12 310 0− £ 4 . 6 5 £ 3 . 6 5
£8.30 − £4.65 = £3.65
Check. Add back: £3.65 + £4.65 = £8.30. ✓
Estimate: £8 − £5 = £3, close to £3.65.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£10 £1 10p 1p £ 1 0 . 0 0 − £ 4 . 3 5 £ . - Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
The columns in between have 0, so we start further left and pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Exchange 1 from the tens of pounds column: 1 becomes 0, and the pounds column goes from 0 to 10.
Exchange 1 from the pounds column: 10 becomes 9, and the tens of pence column goes from 0 to 10. (This crosses the decimal point.)
Exchange 1 from the tens of pence column: 10 becomes 9, and the pence column goes from 0 to 10.
10 − 5 = 5 - Subtract the tens of pence. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 3 = 6 - Subtract the pounds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5 - Bring down the tens of pounds digit. The bottom number has no digit in this column.(This digit is 0 now, not 1, because we exchanged from this column.)
Nothing to take away here, so the digit stays: 0. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£10 £1 10p 1p £ 0 19 0. 9 010 0− £ 4 . 3 5 £ 5 . 6 5
£10.00 − £4.35 = £5.65
Check. Add back: £5.65 + £4.35 = £10.00. ✓
Estimate: £10 − £4 = £6, close to £5.65.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add up the cost of everything. Then take the total cost away from the money that was paid. What is left is the change.
- Draw a bar model. The whole bar is the money we pay with. It is split into the cost of what we buy and the change.
- Step 1: find the total cost. Add all the prices.£1.45 + £0.65 = £2.10
£1 10p 1p £ 1 . 4 5 + £ 0 . 6 5 £ 2 . 1 0 1 1 - Step 2: find the change. Take the cost away from the money paid.£5.00 − £2.10 = £2.90
£1 10p 1p £ 4 5. 10 00 − £ 2 . 1 0 £ 2 . 9 0 - Write the answer. The change is £2.90
Check. Add the change to the cost: £2.10 + £2.90 = £5.00, the money paid. ✓
Watch out. Take away the TOTAL cost, not just one price.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Count up from the cost to the money paid. First jump to the next whole pound, then jump in whole pounds. Add the jumps.
- Start at the cost. We count up from what we spent to the money we paid. The jumps add up to the change.Start at £13.40
- Jump up to the next whole pound. This makes the next jump easier.£13.40 + 60p = £14.00
- Jump up to the money paid. Count on in whole pounds.£14.00 + £6 = £20.00
- Draw the jumps on a number line.
- Add up the jumps. The total of the jumps is the change.60p + £6 = £6.60
Check. Subtract: £20.00 − £13.40 = £6.60. ✓
Watch out. Keep the jumps small and friendly: pence to the next pound, then pounds.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Multiply the pounds and the pence separately. Change any pence over 100p into pounds. Then add the parts.
- Split the price into pounds and pence. It is easier to multiply each part.£1.35 = £1 + 35p
- Multiply the pounds. 3 lots of £1.£1 × 3 = £3
- Multiply the pence. 3 lots of 35p.35p × 3 = 105p
- Change the pence into pounds. 100p = £1.105p = £1 and 5p = £1.05
- Add the parts together. £3 + £1.05 = £4.05
Check. Estimate: £1.35 is about £1, and 3 × £1 = £3, close to £4.05. ✓
Watch out. Write the answer with two decimal places, and change pence over 100p into pounds.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Change the money into pence. Divide by the number of shares. Change the answer back to pounds and pence.
- Change the amount to pence. Pence are whole numbers, so they are easier to divide.£7.20 = 720p
- Divide by 4. Sharing equally into 4 means dividing by 4.720p ÷ 4 = 180p
- Change back to pounds and pence. 100p = £1.180p = £1.80
Check. Go back: £1.80 × 4 = £7.20. ✓
Watch out. Do not divide the pounds and pence as if they were one number. Change to pence first.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Find the cost of each group of items. Add them to find the total. Then take the total away from the money paid to find the change.
- Find the cost of 3 pens. 3 lots of £0.85.3 × £0.85 = £2.55 (85p × 3 = 255p)
- Add the costs to find the total. Use a column method, with the decimal points lined up.£2.55 + £1.50 = £4.05
£1 10p 1p £ 2 . 5 5 + £ 1 . 5 0 £ 4 . 0 5 1 - Take the total cost away from the money paid. What is left is the change.£10.00 − £4.05 = £5.95
£10 £1 10p 1p £ 0 19 0. 9 010 0− £ 4 . 0 5 £ 5 . 9 5 - Write the answer. The change is £5.95
Check. Add the change to the total: £4.05 + £5.95 = £10.00. ✓
Watch out. Multiply first, then add, then subtract from the money paid.
Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.
Method. Line up the decimal points. Add column by column from the right. Carry when a column makes 10 or more. Write the unit.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.2.5 = 2.50
- Line up the amounts in columns. Put the decimal points in a straight line, so tenths are under tenths and ones under ones.
O t h 1 . 7 5 + 2 . 5 0 . - Add the hundredths. Always start on the right.5 + 0 = 5
5 is less than 10, so write 5. There is nothing to carry. - Add the tenths. Now the next column to the left.7 + 5 = 12
12 is 10 or more. Write 2 in the tenths column and carry 1 to the ones column (across the decimal point). - Add the ones. Now the next column to the left. Add the 1 we carried as well.1 + 2 + 1 = 4
4 is less than 10, so write 4. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
O t h 1 . 7 5 + 2 . 5 0 4 . 2 5 1
1.75 kg + 2.50 kg = 4.25 kg
Check. Take away: 4.25 kg − 2.50 kg = 1.75 kg. ✓
Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.
Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.
Method. Line up the decimal points with the bigger number on top. Subtract column by column from the right. Exchange when a top digit is too small. Write the unit.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.3.2 = 3.20
- Line up the amounts in columns. The bigger number goes on top. Put the decimal points in a straight line.
O t h 3 . 2 0 − 1 . 4 5 . - Exchange, then subtract the hundredths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
Exchange 1 from the tenths column: 2 becomes 1, and the hundredths column goes from 0 to 10.
10 − 5 = 5 - Exchange, then subtract the tenths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.1 is not enough to take away 4. We need to exchange.
(There were 2 in this column to start with, but we gave one away in an earlier exchange.)
Exchange 1 from the ones column: 3 becomes 2, and the tenths column goes from 1 to 11. (This crosses the decimal point.)
11 − 4 = 7 - Subtract the ones. Now the next column to the left.(This digit is 2 now, not 3, because we exchanged from this column.)
2 − 1 = 1 - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
O t h 2 3. 11 210 0− 1 . 4 5 1 . 7 5
3.20 m − 1.45 m = 1.75 m
Check. Add back: 1.75 m + 1.45 m = 3.20 m. ✓
Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.
Watch out
Line up the decimal points, not the last digits. £5 + £2.35 must be written £5.00 + £2.35. And if the pence add up to more than 99p, change 100p into £1: £3.65 + £2.48 is £6.13, not £5.113.Exercise 6G Adding, subtracting and change
Non-calculatorKey words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 1 . 3 0 + £ 2 . 4 5 £ . - Add the pence. Always start on the right.0 + 5 = 5
5 is less than 10, so write 5. There is nothing to carry. - Add the tens of pence. Now the next column to the left.3 + 4 = 7
7 is less than 10, so write 7. There is nothing to carry. - Add the pounds. Now the next column to the left.1 + 2 = 3
3 is less than 10, so write 3. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 1 . 3 0 + £ 2 . 4 5 £ 3 . 7 5
£1.30 + £2.45 = £3.75
Check. Estimate: round to the nearest pound: £1 + £2 = £3. This is close to £3.75. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 4 . 2 0 + £ 3 . 5 5 £ . - Add the pence. Always start on the right.0 + 5 = 5
5 is less than 10, so write 5. There is nothing to carry. - Add the tens of pence. Now the next column to the left.2 + 5 = 7
7 is less than 10, so write 7. There is nothing to carry. - Add the pounds. Now the next column to the left.4 + 3 = 7
7 is less than 10, so write 7. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 4 . 2 0 + £ 3 . 5 5 £ 7 . 7 5
£4.20 + £3.55 = £7.75
Check. Estimate: round to the nearest pound: £4 + £4 = £8. This is close to £7.75. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 2 . 7 5 + £ 1 . 2 4 £ . - Add the pence. Always start on the right.5 + 4 = 9
9 is less than 10, so write 9. There is nothing to carry. - Add the tens of pence. Now the next column to the left.7 + 2 = 9
9 is less than 10, so write 9. There is nothing to carry. - Add the pounds. Now the next column to the left.2 + 1 = 3
3 is less than 10, so write 3. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 2 . 7 5 + £ 1 . 2 4 £ 3 . 9 9
£2.75 + £1.24 = £3.99
Check. Estimate: round to the nearest pound: £3 + £1 = £4. This is close to £3.99. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 5 . 6 0 + £ 2 . 1 0 £ . - Add the pence. Always start on the right.0 + 0 = 0
0 is less than 10, so write 0. There is nothing to carry. - Add the tens of pence. Now the next column to the left.6 + 1 = 7
7 is less than 10, so write 7. There is nothing to carry. - Add the pounds. Now the next column to the left.5 + 2 = 7
7 is less than 10, so write 7. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 5 . 6 0 + £ 2 . 1 0 £ 7 . 7 0
£5.60 + £2.10 = £7.70
Check. Estimate: round to the nearest pound: £6 + £2 = £8. This is close to £7.70. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 3 . 6 5 + £ 2 . 4 8 £ . - Add the pence. Always start on the right.5 + 8 = 13
13 is 10 or more. Write 3 in the pence column and carry 1 to the tens of pence column. - Add the tens of pence. Now the next column to the left. Add the 1 we carried as well.6 + 4 + 1 = 11
11 is 10 or more. Write 1 in the tens of pence column and carry 1 to the pounds column (across the decimal point). - Add the pounds. Now the next column to the left. Add the 1 we carried as well.3 + 2 + 1 = 6
6 is less than 10, so write 6. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 3 . 6 5 + £ 2 . 4 8 £ 6 . 1 3 1 1
£3.65 + £2.48 = £6.13
Check. Estimate: round to the nearest pound: £4 + £2 = £6. This is close to £6.13. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 4 . 7 9 + £ 2 . 8 6 £ . - Add the pence. Always start on the right.9 + 6 = 15
15 is 10 or more. Write 5 in the pence column and carry 1 to the tens of pence column. - Add the tens of pence. Now the next column to the left. Add the 1 we carried as well.7 + 8 + 1 = 16
16 is 10 or more. Write 6 in the tens of pence column and carry 1 to the pounds column (across the decimal point). - Add the pounds. Now the next column to the left. Add the 1 we carried as well.4 + 2 + 1 = 7
7 is less than 10, so write 7. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 4 . 7 9 + £ 2 . 8 6 £ 7 . 6 5 1 1
£4.79 + £2.86 = £7.65
Check. Estimate: round to the nearest pound: £5 + £3 = £8. This is close to £7.65. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 5 . 9 5 + £ 1 . 2 7 £ . - Add the pence. Always start on the right.5 + 7 = 12
12 is 10 or more. Write 2 in the pence column and carry 1 to the tens of pence column. - Add the tens of pence. Now the next column to the left. Add the 1 we carried as well.9 + 2 + 1 = 12
12 is 10 or more. Write 2 in the tens of pence column and carry 1 to the pounds column (across the decimal point). - Add the pounds. Now the next column to the left. Add the 1 we carried as well.5 + 1 + 1 = 7
7 is less than 10, so write 7. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 5 . 9 5 + £ 1 . 2 7 £ 7 . 2 2 1 1
£5.95 + £1.27 = £7.22
Check. Estimate: round to the nearest pound: £6 + £1 = £7. This is close to £7.22. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 3 . 5 8 + £ 3 . 6 4 £ . - Add the pence. Always start on the right.8 + 4 = 12
12 is 10 or more. Write 2 in the pence column and carry 1 to the tens of pence column. - Add the tens of pence. Now the next column to the left. Add the 1 we carried as well.5 + 6 + 1 = 12
12 is 10 or more. Write 2 in the tens of pence column and carry 1 to the pounds column (across the decimal point). - Add the pounds. Now the next column to the left. Add the 1 we carried as well.3 + 3 + 1 = 7
7 is less than 10, so write 7. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 3 . 5 8 + £ 3 . 6 4 £ 7 . 2 2 1 1
£3.58 + £3.64 = £7.22
Check. Estimate: round to the nearest pound: £4 + £4 = £8. This is close to £7.22. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add the pounds, then add the pence. If the pence make 100p or more, change 100p into another pound.
- Split each amount into pounds and pence. We add the pounds and the pence separately.£4.65 = £4 + 65p
£2.78 = £2 + 78p - Add the pounds. Add the whole pound parts.£4 + £2 = £6
- Add the pence. Add the pence parts.65p + 78p = 143p
- Change 100 pence into a pound. The pence total is 100p or more. Every 100p is £1.143p = £1 and 43p
£6 + £1 = £7 - Put the pounds and pence together. £7 and 43p = £7.43
Check. Estimate: round to the nearest pound: £5 + £3 = £8. This is close to £7.43. ✓
Watch out. If the pence add up to more than 100p, you must change 100p into £1. Do not write £5.113.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add the pounds, then add the pence. If the pence make 100p or more, change 100p into another pound.
- Split each amount into pounds and pence. We add the pounds and the pence separately.£5.70 = £5 + 70p
£3.55 = £3 + 55p - Add the pounds. Add the whole pound parts.£5 + £3 = £8
- Add the pence. Add the pence parts.70p + 55p = 125p
- Change 100 pence into a pound. The pence total is 100p or more. Every 100p is £1.125p = £1 and 25p
£8 + £1 = £9 - Put the pounds and pence together. £9 and 25p = £9.25
Check. Estimate: round to the nearest pound: £6 + £4 = £10. This is close to £9.25. ✓
Watch out. If the pence add up to more than 100p, you must change 100p into £1. Do not write £5.113.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add the pounds, then add the pence. If the pence make 100p or more, change 100p into another pound.
- Split each amount into pounds and pence. We add the pounds and the pence separately.£2.49 = £2 + 49p
£1.98 = £1 + 98p - Add the pounds. Add the whole pound parts.£2 + £1 = £3
- Add the pence. Add the pence parts.49p + 98p = 147p
- Change 100 pence into a pound. The pence total is 100p or more. Every 100p is £1.147p = £1 and 47p
£3 + £1 = £4 - Put the pounds and pence together. £4 and 47p = £4.47
Check. Estimate: round to the nearest pound: £2 + £2 = £4. This is close to £4.47. ✓
Watch out. If the pence add up to more than 100p, you must change 100p into £1. Do not write £5.113.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 7 . 8 5 − £ 3 . 4 0 £ . - Subtract the pence. Always start on the right.5 − 0 = 5
- Subtract the tens of pence. Now the next column to the left.8 − 4 = 4
- Subtract the pounds. Now the next column to the left.7 − 3 = 4
- Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 7 . 8 5 − £ 3 . 4 0 £ 4 . 4 5
£7.85 − £3.40 = £4.45
Check. Add back: £4.45 + £3.40 = £7.85. ✓
Estimate: £8 − £3 = £5, close to £4.45.
Watch out. Line up the decimal points and work from the right.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 9 . 5 0 − £ 4 . 2 5 £ . - Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
Exchange 1 from the tens of pence column: 5 becomes 4, and the pence column goes from 0 to 10.
10 − 5 = 5 - Subtract the tens of pence. Now the next column to the left.(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 2 = 2 - Subtract the pounds. Now the next column to the left.9 − 4 = 5
- Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 9 . 4 510 0− £ 4 . 2 5 £ 5 . 2 5
£9.50 − £4.25 = £5.25
Check. Add back: £5.25 + £4.25 = £9.50. ✓
Estimate: £10 − £4 = £6, close to £5.25.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 6 . 9 8 − £ 2 . 3 5 £ . - Subtract the pence. Always start on the right.8 − 5 = 3
- Subtract the tens of pence. Now the next column to the left.9 − 3 = 6
- Subtract the pounds. Now the next column to the left.6 − 2 = 4
- Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 6 . 9 8 − £ 2 . 3 5 £ 4 . 6 3
£6.98 − £2.35 = £4.63
Check. Add back: £4.63 + £2.35 = £6.98. ✓
Estimate: £7 − £2 = £5, close to £4.63.
Watch out. Line up the decimal points and work from the right.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 8 . 4 0 − £ 5 . 2 0 £ . - Subtract the pence. Always start on the right.0 − 0 = 0
- Subtract the tens of pence. Now the next column to the left.4 − 2 = 2
- Subtract the pounds. Now the next column to the left.8 − 5 = 3
- Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 8 . 4 0 − £ 5 . 2 0 £ 3 . 2 0
£8.40 − £5.20 = £3.20
Check. Add back: £3.20 + £5.20 = £8.40. ✓
Estimate: £8 − £5 = £3, close to £3.20.
Watch out. Line up the decimal points and work from the right.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 8 . 2 0 − £ 3 . 6 5 £ . - Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
Exchange 1 from the tens of pence column: 2 becomes 1, and the pence column goes from 0 to 10.
10 − 5 = 5 - Exchange, then subtract the tens of pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.1 is not enough to take away 6. We need to exchange.
(There were 2 in this column to start with, but we gave one away in an earlier exchange.)
Exchange 1 from the pounds column: 8 becomes 7, and the tens of pence column goes from 1 to 11. (This crosses the decimal point.)
11 − 6 = 5 - Subtract the pounds. Now the next column to the left.(This digit is 7 now, not 8, because we exchanged from this column.)
7 − 3 = 4 - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 7 8. 11 210 0− £ 3 . 6 5 £ 4 . 5 5
£8.20 − £3.65 = £4.55
Check. Add back: £4.55 + £3.65 = £8.20. ✓
Estimate: £8 − £4 = £4, close to £4.55.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 7 . 0 5 − £ 2 . 3 8 £ . - Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.5 is not enough to take away 8. We need to exchange.
The columns in between have 0, so we start further left and pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Exchange 1 from the pounds column: 7 becomes 6, and the tens of pence column goes from 0 to 10. (This crosses the decimal point.)
Exchange 1 from the tens of pence column: 10 becomes 9, and the pence column goes from 5 to 15.
15 − 8 = 7 - Subtract the tens of pence. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 3 = 6 - Subtract the pounds. Now the next column to the left.(This digit is 6 now, not 7, because we exchanged from this column.)
6 − 2 = 4 - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 6 7. 9 015 5− £ 2 . 3 8 £ 4 . 6 7
£7.05 − £2.38 = £4.67
Check. Add back: £4.67 + £2.38 = £7.05. ✓
Estimate: £7 − £2 = £5, close to £4.67.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 6 . 0 0 − £ 2 . 7 5 £ . - Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
The columns in between have 0, so we start further left and pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Exchange 1 from the pounds column: 6 becomes 5, and the tens of pence column goes from 0 to 10. (This crosses the decimal point.)
Exchange 1 from the tens of pence column: 10 becomes 9, and the pence column goes from 0 to 10.
10 − 5 = 5 - Subtract the tens of pence. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 7 = 2 - Subtract the pounds. Now the next column to the left.(This digit is 5 now, not 6, because we exchanged from this column.)
5 − 2 = 3 - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 5 6. 9 010 0− £ 2 . 7 5 £ 3 . 2 5
£6.00 − £2.75 = £3.25
Check. Add back: £3.25 + £2.75 = £6.00. ✓
Estimate: £6 − £3 = £3, close to £3.25.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the bigger amount on top with the decimal points lined up. Subtract the pence first, then the pounds. Exchange if a top digit is too small.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£10 £1 10p 1p £ 1 2 . 0 0 − £ 8 . 4 5 £ . - Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
The columns in between have 0, so we start further left and pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Exchange 1 from the pounds column: 2 becomes 1, and the tens of pence column goes from 0 to 10. (This crosses the decimal point.)
Exchange 1 from the tens of pence column: 10 becomes 9, and the pence column goes from 0 to 10.
10 − 5 = 5 - Subtract the tens of pence. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5 - Exchange, then subtract the pounds. The top digit is smaller than the bottom digit, so we swap 1 from the next column.1 is not enough to take away 8. We need to exchange.
(There were 2 in this column to start with, but we gave one away in an earlier exchange.)
Exchange 1 from the tens of pounds column: 1 becomes 0, and the pounds column goes from 1 to 11.
11 − 8 = 3 - Bring down the tens of pounds digit. The bottom number has no digit in this column.(This digit is 0 now, not 1, because we exchanged from this column.)
Nothing to take away here, so the digit stays: 0. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£10 £1 10p 1p £ 0 111 2. 9 010 0− £ 8 . 4 5 £ 3 . 5 5
£12.00 − £8.45 = £3.55
Check. Add back: £3.55 + £8.45 = £12.00. ✓
Estimate: £12 − £8 = £4, close to £3.55.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 1 . 4 5 £ 2 . 3 0 + £ 0 . 6 5 £ . - Add the pence. Always start on the right.5 + 0 + 5 = 10
10 is 10 or more. Write 0 in the pence column and carry 1 to the tens of pence column. - Add the tens of pence. Now the next column to the left. Add the 1 we carried as well.4 + 3 + 6 + 1 = 14
14 is 10 or more. Write 4 in the tens of pence column and carry 1 to the pounds column (across the decimal point). - Add the pounds. Now the next column to the left. Add the 1 we carried as well.1 + 2 + 0 + 1 = 4
4 is less than 10, so write 4. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 1 . 4 5 £ 2 . 3 0 + £ 0 . 6 5 £ 4 . 4 0 1 1
£1.45 + £2.30 + £0.65 = £4.40
Check. Estimate: round to the nearest pound: £1 + £2 + £1 = £4. This is close to £4.40. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 3 . 9 9 £ 2 . 5 0 + £ 1 . 9 9 £ . - Add the pence. Always start on the right.9 + 0 + 9 = 18
18 is 10 or more. Write 8 in the pence column and carry 1 to the tens of pence column. - Add the tens of pence. Now the next column to the left. Add the 1 we carried as well.9 + 5 + 9 + 1 = 24
24 is 10 or more. Write 4 in the tens of pence column and carry 2 to the pounds column (across the decimal point). - Add the pounds. Now the next column to the left. Add the 2 we carried as well.3 + 2 + 1 + 2 = 8
8 is less than 10, so write 8. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 3 . 9 9 £ 2 . 5 0 + £ 1 . 9 9 £ 8 . 4 8 2 1
£3.99 + £2.50 + £1.99 = £8.48
Check. Estimate: round to the nearest pound: £4 + £3 + £2 = £9. This is close to £8.48. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. The missing amount is the difference: take the amount you have from the total.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 7 . 0 0 − £ 4 . 5 0 £ . - Subtract the pence. Always start on the right.0 − 0 = 0
- Exchange, then subtract the tens of pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
Exchange 1 from the pounds column: 7 becomes 6, and the tens of pence column goes from 0 to 10. (This crosses the decimal point.)
10 − 5 = 5 - Subtract the pounds. Now the next column to the left.(This digit is 6 now, not 7, because we exchanged from this column.)
6 − 4 = 2 - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 6 7. 10 00 − £ 4 . 5 0 £ 2 . 5 0
£7.00 − £4.50 = £2.50
Check. Add back: £2.50 + £4.50 = £7.00. ✓
Estimate: £7 − £5 = £2, close to £2.50.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. The missing amount is the difference: take the amount you have from the total.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£10 £1 10p 1p £ 1 0 . 0 0 − £ 6 . 7 5 £ . - Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
The columns in between have 0, so we start further left and pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Exchange 1 from the tens of pounds column: 1 becomes 0, and the pounds column goes from 0 to 10.
Exchange 1 from the pounds column: 10 becomes 9, and the tens of pence column goes from 0 to 10. (This crosses the decimal point.)
Exchange 1 from the tens of pence column: 10 becomes 9, and the pence column goes from 0 to 10.
10 − 5 = 5 - Subtract the tens of pence. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 7 = 2 - Subtract the pounds. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 6 = 3 - Bring down the tens of pounds digit. The bottom number has no digit in this column.(This digit is 0 now, not 1, because we exchanged from this column.)
Nothing to take away here, so the digit stays: 0. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£10 £1 10p 1p £ 0 19 0. 9 010 0− £ 6 . 7 5 £ 3 . 2 5
£10.00 − £6.75 = £3.25
Check. Add back: £3.25 + £6.75 = £10.00. ✓
Estimate: £10 − £7 = £3, close to £3.25.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. The missing amount is the difference: take the amount you have from the total.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 5 . 0 0 − £ 3 . 6 5 £ . - Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
The columns in between have 0, so we start further left and pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Exchange 1 from the pounds column: 5 becomes 4, and the tens of pence column goes from 0 to 10. (This crosses the decimal point.)
Exchange 1 from the tens of pence column: 10 becomes 9, and the pence column goes from 0 to 10.
10 − 5 = 5 - Subtract the tens of pence. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 6 = 3 - Subtract the pounds. Now the next column to the left.(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 3 = 1 - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 4 5. 9 010 0− £ 3 . 6 5 £ 1 . 3 5
£5.00 − £3.65 = £1.35
Check. Add back: £1.35 + £3.65 = £5.00. ✓
Estimate: £5 − £4 = £1, close to £1.35.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. The missing amount is the difference: take the amount you have from the total.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£10 £1 10p 1p £ 1 2 . 0 0 − £ 8 . 4 5 £ . - Exchange, then subtract the pence. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
The columns in between have 0, so we start further left and pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Exchange 1 from the pounds column: 2 becomes 1, and the tens of pence column goes from 0 to 10. (This crosses the decimal point.)
Exchange 1 from the tens of pence column: 10 becomes 9, and the pence column goes from 0 to 10.
10 − 5 = 5 - Subtract the tens of pence. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 4 = 5 - Exchange, then subtract the pounds. The top digit is smaller than the bottom digit, so we swap 1 from the next column.1 is not enough to take away 8. We need to exchange.
(There were 2 in this column to start with, but we gave one away in an earlier exchange.)
Exchange 1 from the tens of pounds column: 1 becomes 0, and the pounds column goes from 1 to 11.
11 − 8 = 3 - Bring down the tens of pounds digit. The bottom number has no digit in this column.(This digit is 0 now, not 1, because we exchanged from this column.)
Nothing to take away here, so the digit stays: 0. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£10 £1 10p 1p £ 0 111 2. 9 010 0− £ 8 . 4 5 £ 3 . 5 5
£12.00 − £8.45 = £3.55
Check. Add back: £3.55 + £8.45 = £12.00. ✓
Estimate: £12 − £8 = £4, close to £3.55.
Watch out. Take the bottom number from the top number. Exchange 1 pound for 100p when the pence are not enough.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add up the cost of everything. Then take the total cost away from the money that was paid. What is left is the change.
- Draw a bar model. The whole bar is the money we pay with. It is split into the cost of what we buy and the change.
- Step 1: find the change. Take the cost away from the money paid.£5.00 − £3.65 = £1.35
£1 10p 1p £ 4 5. 9 010 0− £ 3 . 6 5 £ 1 . 3 5 - Write the answer. The change is £1.35
Check. Add the change to the cost: £3.65 + £1.35 = £5.00, the money paid. ✓
Watch out. Take the cost away from the money paid, not the other way round.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add up the cost of everything. Then take the total cost away from the money that was paid. What is left is the change.
- Draw a bar model. The whole bar is the money we pay with. It is split into the cost of what we buy and the change.
- Step 1: find the change. Take the cost away from the money paid.£10.00 − £7.45 = £2.55
£10 £1 10p 1p £ 0 19 0. 9 010 0− £ 7 . 4 5 £ 2 . 5 5 - Write the answer. The change is £2.55
Check. Add the change to the cost: £7.45 + £2.55 = £10.00, the money paid. ✓
Watch out. Take the cost away from the money paid, not the other way round.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add up the cost of everything. Then take the total cost away from the money that was paid. What is left is the change.
- Draw a bar model. The whole bar is the money we pay with. It is split into the cost of what we buy and the change.
- Step 1: find the change. Take the cost away from the money paid.£20.00 − £12.50 = £7.50
£10 £1 10p 1p £ 1 29 0. 10 00 − £ 1 2 . 5 0 £ 7 . 5 0 - Write the answer. The change is £7.50
Check. Add the change to the cost: £12.50 + £7.50 = £20.00, the money paid. ✓
Watch out. Take the cost away from the money paid, not the other way round.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add up the cost of everything. Then take the total cost away from the money that was paid. What is left is the change.
- Draw a bar model. The whole bar is the money we pay with. It is split into the cost of what we buy and the change.
- Step 1: find the change. Take the cost away from the money paid.£5.00 − £1.99 = £3.01
£1 10p 1p £ 4 5. 9 010 0− £ 1 . 9 9 £ 3 . 0 1 - Write the answer. The change is £3.01
Check. Add the change to the cost: £1.99 + £3.01 = £5.00, the money paid. ✓
Watch out. Take the cost away from the money paid, not the other way round.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add up the cost of everything. Then take the total cost away from the money that was paid. What is left is the change.
- Draw a bar model. The whole bar is the money we pay with. It is split into the cost of what we buy and the change.
- Step 1: find the total cost. Add all the prices.£2.85 + £0.95 = £3.80
£1 10p 1p £ 2 . 8 5 + £ 0 . 9 5 £ 3 . 8 0 1 1 - Step 2: find the change. Take the cost away from the money paid.£10.00 − £3.80 = £6.20
£10 £1 10p 1p £ 0 19 0. 10 00 − £ 3 . 8 0 £ 6 . 2 0 - Write the answer. The change is £6.20
Check. Add the change to the cost: £3.80 + £6.20 = £10.00, the money paid. ✓
Watch out. Take away the TOTAL cost, not just one price.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add up the cost of everything. Then take the total cost away from the money that was paid. What is left is the change.
- Draw a bar model. The whole bar is the money we pay with. It is split into the cost of what we buy and the change.
- Step 1: find the total cost. Add all the prices.£4.50 + £6.75 = £11.25
£10 £1 10p 1p £ 4 . 5 0 + £ 6 . 7 5 £ 1 1 . 2 5 1 1 - Step 2: find the change. Take the cost away from the money paid.£12.00 − £11.25 = £0.75
£10 £1 10p 1p £ 1 1 2. 9 010 0− £ 1 1 . 2 5 £ 0 . 7 5 - Write the answer. The change is £0.75
Check. Add the change to the cost: £11.25 + £0.75 = £12.00, the money paid. ✓
Watch out. Take away the TOTAL cost, not just one price.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Round each price to the nearest pound. Then add.
- Round each price. 50p or more rounds up to the next pound. Less than 50p rounds down.£3.95 ≈ £4 (95p rounds up)
£2.10 ≈ £2 (10p rounds down) - Add the rounded prices. £4 + £2 = £6
Check. The exact total is a bit more than this. ✓
Watch out. Round each amount first, then add.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 3 . 9 5 + £ 2 . 1 0 £ . - Add the pence. Always start on the right.5 + 0 = 5
5 is less than 10, so write 5. There is nothing to carry. - Add the tens of pence. Now the next column to the left.9 + 1 = 10
10 is 10 or more. Write 0 in the tens of pence column and carry 1 to the pounds column (across the decimal point). - Add the pounds. Now the next column to the left. Add the 1 we carried as well.3 + 2 + 1 = 6
6 is less than 10, so write 6. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 3 . 9 5 + £ 2 . 1 0 £ 6 . 0 5 1
£3.95 + £2.10 = £6.05
Check. Estimate: round to the nearest pound: £4 + £2 = £6. This is close to £6.05. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Subtract the estimate from the exact total to see how close they are.
- Line up the amounts in columns. The bigger amount goes on top. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 6 . 0 5 − £ 6 . 0 0 £ . - Subtract the pence. Always start on the right.5 − 0 = 5
- Subtract the tens of pence. Now the next column to the left.0 − 0 = 0
- Subtract the pounds. Now the next column to the left.6 − 6 = 0
- Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 6 . 0 5 − £ 6 . 0 0 £ 0 . 0 5
£6.05 − £6.00 = £0.05
Check. Add back: £0.05 + £6.00 = £6.05. ✓
Estimate: £6 − £6 = £0, close to £0.05.
Watch out. Line up the decimal points and work from the right.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add the pounds and add the pence again. Check whether the pence are more than 100p.
- Look at what Jack did. Jack added the pounds and added the pence.£3 + £2 = £5 and 65p + 48p = 113p, so Jack wrote £5.113.
- Find the mistake. 113p is more than 100p. Only two digits can go after the decimal point, so 100p must be changed into £1.113p = £1 and 13p
- Work out the correct answer. Add the extra pound to the pounds.£5 + £1 = £6, so the total is £6.13
Check. Estimate: £4 + £2 = £6, so £6.13 is sensible and £5.113 is not. ✓
Watch out. Money has only two digits after the decimal point. If the pence reach 100 or more, change 100p into £1.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Add every possible pair of prices. Look for the pair that makes exactly £5.
- List every pair. There are 5 prices, so there are 10 different pairs. Work through them in order.£1.35 + £2.20 = £3.55
£1.35 + £2.80 = £4.15
£1.35 + £3.15 = £4.50
£1.35 + £1.95 = £3.30
£2.20 + £2.80 = £5.00 ✓
£2.20 + £3.15 = £5.35
£2.20 + £1.95 = £4.15
£2.80 + £3.15 = £5.95
£2.80 + £1.95 = £4.75
£3.15 + £1.95 = £5.10 - Find the pair that makes £5.00. Only one total is exactly £5.00.£2.20 and £2.80
Check. £2.20 + £2.80 = £5.00. ✓
Watch out. Look at the pence first: 20p + 80p = 100p makes the pence a whole pound. It saves time.
Exercise 6H Multiplying, sharing and measures
Non-calculatorKey words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Multiply the pounds and the pence separately. Change any pence over 100p into pounds. Then add the parts.
- Split the price into pounds and pence. It is easier to multiply each part.£1.20 = £1 + 20p
- Multiply the pounds. 3 lots of £1.£1 × 3 = £3
- Multiply the pence. 3 lots of 20p.20p × 3 = 60p
- Add the parts together. £3 + £0.60 = £3.60
Check. Estimate: £1.20 is about £1, and 3 × £1 = £3, close to £3.60. ✓
Watch out. Write the answer with two decimal places, and change pence over 100p into pounds.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Multiply the pounds and the pence separately. Change any pence over 100p into pounds. Then add the parts.
- Split the price into pounds and pence. It is easier to multiply each part.£2.50 = £2 + 50p
- Multiply the pounds. 4 lots of £2.£2 × 4 = £8
- Multiply the pence. 4 lots of 50p.50p × 4 = 200p
- Change the pence into pounds. 100p = £1.200p = £2 and 0p = £2.00
- Add the parts together. £8 + £2.00 = £10.00
Check. Estimate: £2.50 is about £3, and 4 × £3 = £12, close to £10.00. ✓
Watch out. Write the answer with two decimal places, and change pence over 100p into pounds.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Multiply the pounds and the pence separately. Change any pence over 100p into pounds. Then add the parts.
- Split the price into pounds and pence. It is easier to multiply each part.£3.45 = £3 + 45p
- Multiply the pounds. 2 lots of £3.£3 × 2 = £6
- Multiply the pence. 2 lots of 45p.45p × 2 = 90p
- Add the parts together. £6 + £0.90 = £6.90
Check. Estimate: £3.45 is about £3, and 2 × £3 = £6, close to £6.90. ✓
Watch out. Write the answer with two decimal places, and change pence over 100p into pounds.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Multiply the pounds and the pence separately. Change any pence over 100p into pounds. Then add the parts.
- Multiply the pence. 5 lots of 65p.65p × 5 = 325p
- Change the pence into pounds. 100p = £1.325p = £3 and 25p = £3.25
- Add the parts together. 325p = £3.25
Check. Estimate: £0.65 is about £1, and 5 × £1 = £5, close to £3.25. ✓
Watch out. Write the answer with two decimal places, and change pence over 100p into pounds.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Change the money into pence. Divide by the number of shares. Change the answer back to pounds and pence.
- Change the amount to pence. Pence are whole numbers, so they are easier to divide.£6.80 = 680p
- Divide by 2. Sharing equally into 2 means dividing by 2.680p ÷ 2 = 340p
- Change back to pounds and pence. 100p = £1.340p = £3.40
Check. Go back: £3.40 × 2 = £6.80. ✓
Watch out. Do not divide the pounds and pence as if they were one number. Change to pence first.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Change the money into pence. Divide by the number of shares. Change the answer back to pounds and pence.
- Change the amount to pence. Pence are whole numbers, so they are easier to divide.£9.60 = 960p
- Divide by 4. Sharing equally into 4 means dividing by 4.960p ÷ 4 = 240p
- Change back to pounds and pence. 100p = £1.240p = £2.40
Check. Go back: £2.40 × 4 = £9.60. ✓
Watch out. Do not divide the pounds and pence as if they were one number. Change to pence first.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Change the money into pence. Divide by the number of shares. Change the answer back to pounds and pence.
- Change the amount to pence. Pence are whole numbers, so they are easier to divide.£8.40 = 840p
- Divide by 3. Sharing equally into 3 means dividing by 3.840p ÷ 3 = 280p
- Change back to pounds and pence. 100p = £1.280p = £2.80
Check. Go back: £2.80 × 3 = £8.40. ✓
Watch out. Do not divide the pounds and pence as if they were one number. Change to pence first.
Key words. Pence (p) are small amounts of money. 100 pence make 1 pound.
Method. Change the money into pence. Find a fraction of it: divide by the bottom number, then multiply by the top number. Change back to pounds.
- Change the pounds into pence. 1 pound is 100 pence, so we can divide the pence exactly.£8 = 8 × 100 = 800p
- Find one part: divide by the bottom number, 2. The bottom number says how many equal parts.800p ÷ 2 = 400p
- Change back to pounds and pence. 100p = £1, so divide by 100. Always show two decimal places.400p = £4.00
Check. 400p × 2 = 800p, so 2 parts make the whole amount. ✓
Watch out. Write money with two decimal places: £3.50, not £3.5.
Key words. Pence (p) are small amounts of money. 100 pence make 1 pound.
Method. Change the money into pence. Find a fraction of it: divide by the bottom number, then multiply by the top number. Change back to pounds.
- Change the pounds into pence. 1 pound is 100 pence, so we can divide the pence exactly.£10 = 10 × 100 = 1000p
- Find one part: divide by the bottom number, 4. The bottom number says how many equal parts.1000p ÷ 4 = 250p
- Change back to pounds and pence. 100p = £1, so divide by 100. Always show two decimal places.250p = £2.50
Check. 250p × 4 = 1000p, so 4 parts make the whole amount. ✓
Watch out. Write money with two decimal places: £3.50, not £3.5.
Key words. Pence (p) are small amounts of money. 100 pence make 1 pound.
Method. Change the money into pence. Find a fraction of it: divide by the bottom number, then multiply by the top number. Change back to pounds.
- Change the pounds into pence. 1 pound is 100 pence, so we can divide the pence exactly.£6 = 6 × 100 = 600p
- Find one part: divide by the bottom number, 4. The bottom number says how many equal parts.600p ÷ 4 = 150p
- Multiply by the top number, 3. The top number says how many parts we take.150p × 3 = 450p
- Change back to pounds and pence. 100p = £1, so divide by 100. Always show two decimal places.450p = £4.50
Check. 150p × 4 = 600p, so 4 parts make the whole amount. ✓
Watch out. Write money with two decimal places: £3.50, not £3.5.
Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.
Method. Line up the decimal points. Add column by column from the right. Carry when a column makes 10 or more. Write the unit.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.1.5 = 1.50
- Line up the amounts in columns. Put the decimal points in a straight line, so tenths are under tenths and ones under ones.
O t h 1 . 5 0 + 2 . 2 5 . - Add the hundredths. Always start on the right.0 + 5 = 5
5 is less than 10, so write 5. There is nothing to carry. - Add the tenths. Now the next column to the left.5 + 2 = 7
7 is less than 10, so write 7. There is nothing to carry. - Add the ones. Now the next column to the left.1 + 2 = 3
3 is less than 10, so write 3. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
O t h 1 . 5 0 + 2 . 2 5 3 . 7 5
1.50 kg + 2.25 kg = 3.75 kg
Check. Take away: 3.75 kg − 2.25 kg = 1.50 kg. ✓
Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.
Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.
Method. Line up the decimal points. Add column by column from the right. Carry when a column makes 10 or more. Write the unit.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.1.5 = 1.50
- Line up the amounts in columns. Put the decimal points in a straight line, so tenths are under tenths and ones under ones.
O t h 0 . 7 5 + 1 . 5 0 . - Add the hundredths. Always start on the right.5 + 0 = 5
5 is less than 10, so write 5. There is nothing to carry. - Add the tenths. Now the next column to the left.7 + 5 = 12
12 is 10 or more. Write 2 in the tenths column and carry 1 to the ones column (across the decimal point). - Add the ones. Now the next column to the left. Add the 1 we carried as well.0 + 1 + 1 = 2
2 is less than 10, so write 2. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
O t h 0 . 7 5 + 1 . 5 0 2 . 2 5 1
0.75 m + 1.50 m = 2.25 m
Check. Take away: 2.25 m − 1.50 m = 0.75 m. ✓
Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.
Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.
Method. Line up the decimal points. Add column by column from the right. Carry when a column makes 10 or more. Write the unit.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.2.4 = 2.40
- Line up the amounts in columns. Put the decimal points in a straight line, so tenths are under tenths and ones under ones.
O t h 2 . 4 0 + 1 . 3 5 . - Add the hundredths. Always start on the right.0 + 5 = 5
5 is less than 10, so write 5. There is nothing to carry. - Add the tenths. Now the next column to the left.4 + 3 = 7
7 is less than 10, so write 7. There is nothing to carry. - Add the ones. Now the next column to the left.2 + 1 = 3
3 is less than 10, so write 3. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
O t h 2 . 4 0 + 1 . 3 5 3 . 7 5
2.40 litres + 1.35 litres = 3.75 litres
Check. Take away: 3.75 litres − 1.35 litres = 2.40 litres. ✓
Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.
Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.
Method. Line up the decimal points with the bigger number on top. Subtract column by column from the right. Exchange when a top digit is too small. Write the unit.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.4.5 = 4.50
- Line up the amounts in columns. The bigger number goes on top. Put the decimal points in a straight line.
O t h 4 . 5 0 − 1 . 2 5 . - Exchange, then subtract the hundredths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
Exchange 1 from the tenths column: 5 becomes 4, and the hundredths column goes from 0 to 10.
10 − 5 = 5 - Subtract the tenths. Now the next column to the left.(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 2 = 2 - Subtract the ones. Now the next column to the left.4 − 1 = 3
- Read the answer. Put the decimal point in the answer, directly under the other decimal points.
O t h 4 . 4 510 0− 1 . 2 5 3 . 2 5
4.50 m − 1.25 m = 3.25 m
Check. Add back: 3.25 m + 1.25 m = 4.50 m. ✓
Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.
Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.
Method. Line up the decimal points with the bigger number on top. Subtract column by column from the right. Exchange when a top digit is too small. Write the unit.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.5 = 5.00
- Line up the amounts in columns. The bigger number goes on top. Put the decimal points in a straight line.
O t h 5 . 0 0 − 2 . 7 5 . - Exchange, then subtract the hundredths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
The columns in between have 0, so we start further left and pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Exchange 1 from the ones column: 5 becomes 4, and the tenths column goes from 0 to 10. (This crosses the decimal point.)
Exchange 1 from the tenths column: 10 becomes 9, and the hundredths column goes from 0 to 10.
10 − 5 = 5 - Subtract the tenths. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 7 = 2 - Subtract the ones. Now the next column to the left.(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 2 = 2 - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
O t h 4 5. 9 010 0− 2 . 7 5 2 . 2 5
5.00 kg − 2.75 kg = 2.25 kg
Check. Add back: 2.25 kg + 2.75 kg = 5.00 kg. ✓
Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.
Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.
Method. Line up the decimal points with the bigger number on top. Subtract column by column from the right. Exchange when a top digit is too small. Write the unit.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.2.1 = 2.10
- Line up the amounts in columns. The bigger number goes on top. Put the decimal points in a straight line.
O t h 2 . 1 0 − 0 . 8 5 . - Exchange, then subtract the hundredths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
Exchange 1 from the tenths column: 1 becomes 0, and the hundredths column goes from 0 to 10.
10 − 5 = 5 - Exchange, then subtract the tenths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 8. We need to exchange.
(There were 1 in this column to start with, but we gave one away in an earlier exchange.)
Exchange 1 from the ones column: 2 becomes 1, and the tenths column goes from 0 to 10. (This crosses the decimal point.)
10 − 8 = 2 - Subtract the ones. Now the next column to the left.(This digit is 1 now, not 2, because we exchanged from this column.)
1 − 0 = 1 - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
O t h 1 2. 10 110 0− 0 . 8 5 1 . 2 5
2.10 litres − 0.85 litres = 1.25 litres
Check. Add back: 1.25 litres + 0.85 litres = 2.10 litres. ✓
Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Find the cost of each group of items. Add them to find the total. Then take the total away from the money paid to find the change.
- Find the cost of 4 stickers. 4 lots of £0.35.4 × £0.35 = £1.40 (35p × 4 = 140p)
- Add the costs to find the total. Use a column method, with the decimal points lined up.£1.40 + £2.20 = £3.60
£1 10p 1p £ 1 . 4 0 + £ 2 . 2 0 £ 3 . 6 0 - Take the total cost away from the money paid. What is left is the change.£5.00 − £3.60 = £1.40
£1 10p 1p £ 4 5. 10 00 − £ 3 . 6 0 £ 1 . 4 0 - Write the answer. The change is £1.40
Check. Add the change to the total: £3.60 + £1.40 = £5.00. ✓
Watch out. Multiply first, then add, then subtract from the money paid.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Find the cost of each group of items. Then add the costs together.
- Find the cost of 4 tickets. 4 lots of £4.75.4 × £4.75 = £19.00 (£16 + 300p)
- Write the answer. The total is £19.00
Check. Estimate: £19 = £19, close to £19.00. ✓
Watch out. Multiply first when there is more than one of an item, then add.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Find how much more money is needed. Then find how many weeks of saving give that amount.
- Find how much more money is needed. Take the money already saved away from the cost.£12.60 − £4.20 = £8.40
- Find how many weeks it takes. Each week adds £2.10. We ask how many lots of £2.10 make £8.40. Change to pence to divide.840p ÷ 210p = 4 weeks
- Write the answer. 4 weeks
Check. 4 × £2.10 = £8.40, and £4.20 + £8.40 = £12.60. ✓
Watch out. First find what is still needed. Do not divide the whole price.
Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.
Method. Line up the decimal points. Add column by column from the right. Carry when a column makes 10 or more. Write the unit.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.2.5 = 2.50
- Line up the amounts in columns. Put the decimal points in a straight line, so tenths are under tenths and ones under ones.
O t h 1 . 7 5 + 2 . 5 0 . - Add the hundredths. Always start on the right.5 + 0 = 5
5 is less than 10, so write 5. There is nothing to carry. - Add the tenths. Now the next column to the left.7 + 5 = 12
12 is 10 or more. Write 2 in the tenths column and carry 1 to the ones column (across the decimal point). - Add the ones. Now the next column to the left. Add the 1 we carried as well.1 + 2 + 1 = 4
4 is less than 10, so write 4. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
O t h 1 . 7 5 + 2 . 5 0 4 . 2 5 1
1.75 m + 2.50 m = 4.25 m
Check. Take away: 4.25 m − 2.50 m = 1.75 m. ✓
Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.
Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.
Method. Line up the decimal points with the bigger number on top. Subtract column by column from the right. Exchange when a top digit is too small. Write the unit.
- Give both numbers the same number of decimal places. Adding a 0 on the end of a decimal does not change its value. It helps the digits line up.5 = 5.00
- Line up the amounts in columns. The bigger number goes on top. Put the decimal points in a straight line.
O t h 5 . 0 0 − 4 . 2 5 . - Exchange, then subtract the hundredths. The top digit is smaller than the bottom digit, so we swap 1 from the next column.0 is not enough to take away 5. We need to exchange.
The columns in between have 0, so we start further left and pass the exchange along one column at a time. Each 0 in the middle becomes 9.
Exchange 1 from the ones column: 5 becomes 4, and the tenths column goes from 0 to 10. (This crosses the decimal point.)
Exchange 1 from the tenths column: 10 becomes 9, and the hundredths column goes from 0 to 10.
10 − 5 = 5 - Subtract the tenths. Now the next column to the left.(This digit is 9 now, not 0, because we exchanged from this column.)
9 − 2 = 7 - Subtract the ones. Now the next column to the left.(This digit is 4 now, not 5, because we exchanged from this column.)
4 − 4 = 0 - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
O t h 4 5. 9 010 0− 4 . 2 5 0 . 7 5
5.00 m − 4.25 m = 0.75 m
Check. Add back: 0.75 m + 4.25 m = 5.00 m. ✓
Watch out. Line up the decimal points, not the right-hand digits: 2.5 has fewer digits than 1.75, so write 2.50.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Change the money into pence. Divide by the number of shares. Change the answer back to pounds and pence.
- Change the amount to pence. Pence are whole numbers, so they are easier to divide.£9.60 = 960p
- Divide by 4. Sharing equally into 4 means dividing by 4.960p ÷ 4 = 240p
- Change back to pounds and pence. 100p = £1.240p = £2.40
Check. Go back: £2.40 × 4 = £9.60. ✓
Watch out. Do not divide the pounds and pence as if they were one number. Change to pence first.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Write the amounts in columns with the decimal points lined up. Add the pence first, then the pounds. Carry when a column makes 10 or more.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 2 . 4 0 + £ 1 . 3 5 £ . - Add the pence. Always start on the right.0 + 5 = 5
5 is less than 10, so write 5. There is nothing to carry. - Add the tens of pence. Now the next column to the left.4 + 3 = 7
7 is less than 10, so write 7. There is nothing to carry. - Add the pounds. Now the next column to the left.2 + 1 = 3
3 is less than 10, so write 3. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 2 . 4 0 + £ 1 . 3 5 £ 3 . 7 5
£2.40 + £1.35 = £3.75
Check. Estimate: round to the nearest pound: £2 + £1 = £3. This is close to £3.75. ✓
Watch out. Line up the decimal points. Write £5.00 for a whole number of pounds, so the digits line up.
Key words. In column addition and column subtraction you write the numbers one under the other with the decimal points in a straight line, and work one column at a time from the right. To carry is to move 10 of one column to the next column. To exchange is to swap 1 of the next column for 10 of this one.
Method. Add the three prices to find the total. Then compare the total with £10.
- Line up the amounts in columns. Pounds under pounds and pence under pence, with the decimal points in a straight line.
£1 10p 1p £ 2 . 9 5 £ 3 . 2 0 + £ 3 . 5 5 £ . - Add the pence. Always start on the right.5 + 0 + 5 = 10
10 is 10 or more. Write 0 in the pence column and carry 1 to the tens of pence column. - Add the tens of pence. Now the next column to the left. Add the 1 we carried as well.9 + 2 + 5 + 1 = 17
17 is 10 or more. Write 7 in the tens of pence column and carry 1 to the pounds column (across the decimal point). - Add the pounds. Now the next column to the left. Add the 1 we carried as well.2 + 3 + 3 + 1 = 9
9 is less than 10, so write 9. There is nothing to carry. - Read the answer. Put the decimal point in the answer, directly under the other decimal points.
£1 10p 1p £ 2 . 9 5 £ 3 . 2 0 + £ 3 . 5 5 £ 9 . 7 0 1 1
£2.95 + £3.20 + £3.55 = £9.70 - Compare the total with £10. The total must not be more than the money she has.£9.70 is less than £10.00, so yes. She has £0.30 left.
Check. Estimate: £3 + £3 + £4 = £10, and the exact total is a little less. ✓
Watch out. Line up the decimal points and carry the pence into the pounds.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Try every way to split the coins into the two kinds. Work out the total of each way and look for the one that matches.
- List every possible way. There are 7 coins altogether. If there are 0, 1, 2 ... 50p coins, the rest are 20p coins.
- Work out the total for each way. Multiply each number of coins by its value, then add.
50p coins 20p coins Total 0 7 140p 1 6 170p 2 5 200p 3 4 230p 4 3 260p 5 2 290p 6 1 320p 7 0 350p - Find the total 260p. Only one row matches.4 coins of 50p and 3 coins of 20p
Check. 4 × 50p + 3 × 20p = 200p + 60p = 260p = £2.60. ✓
Watch out. Work in pence and be systematic: start with 0 of one coin and count up.
Key words. Pence (p) are small amounts of money: 100p = £1. Change is the money you get back when you pay with more than the cost. The total is all the amounts added together.
Method. Work out the cost again, step by step, and compare with Leo’s answer.
- Look at what Leo did. Leo multiplied the pounds (3 × £1 = £3) and the pence (3 × 45p = 135p). Then he wrote the pence after the point.He wrote £3.135.
- Find the mistake. 135p is more than 100p. Only two digits can go after the decimal point, so 100p must be changed into £1.135p = £1 and 35p
- Work out the correct answer. Add the extra pound to the 3 pounds.£3 + £1.35 = £4.35
Check. Estimate: 3 × £1.45 is about 3 × £1 = £3, and a bit more: £4.35 is sensible but £3.135 is not. ✓
Watch out. Pence over 99 must be changed into pounds.