GCSE Maths: Adding and subtracting decimals (Foundation)
Part of the GCSE Maths decimals, rounding and estimation chapter (Foundation). Chapter overview · Higher version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Adding and subtracting decimals
You can only add or subtract things that are the same kind. Hundreds are added to hundreds, tens to tens, and so on. This is also true for decimals: tenths are added to tenths and hundredths to hundredths. That is why the decimal points must be lined up in a vertical line: it puts every column of the same value under each other.
The method is called a formal written method (also called column addition and column subtraction):
- Write the numbers one under the other with the decimal points in a vertical line.
- If one number has fewer decimal places, fill the gaps with zeros. This does not change its value.
- Work from the right (the smallest column) to the left, adding or subtracting one column at a time.
- Put the decimal point in the answer straight down, in line with the others.
A whole number has a decimal point that you cannot see, after the units digit: 7 is the same as 7.0 or 7.00. When the question has a whole number, write the point and the zeros yourself.
Layout for 2.4 + 1.75 (a zero is added so both numbers have 2 decimal places):
2.40 + 1.75 ---- 4.15
Adding. If a column adds to 10 or more, write the units digit and carry the ten to the next column on the left. Subtracting. If the top digit is smaller than the bottom digit, you cannot take away. Exchange one from the next column on the left: that one becomes ten in the column you are working on. Always subtract the smaller number from the larger number. After you finish, check by doing the opposite: add to check a subtraction, or subtract to check an addition.
Key ideas
- Write the numbers with the decimal points in a vertical line.
- Fill empty places with zeros, e.g. 5 = 5.00.
- Work from the right, one column at a time. Carry when adding, exchange when subtracting.
- The decimal point in the answer goes straight down.
- Check with the opposite operation.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To add decimals, write the numbers in columns with the decimal points in a vertical line, then add column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.45.30 + 28.75 -----
- Add column by column, starting at the right (the smallest column). When a column adds to 10 or more, write the units digit and carry the 10 to the next column to the left.hundredths: 0 + 5 = 5
tenths: 3 + 7 = 10, write 0 and carry 1
Put the decimal point straight down, directly under the other decimal points.
units: 5 + 8 + 1 (carried) = 14, write 4 and carry 1
tens: 4 + 2 + 1 (carried) = 7 - Read the answer. Write the digits, with the decimal point where you put it.45.3 + 28.75 = 74.05
Check. Use the opposite operation: 74.05 − 28.75 = 45.3. ✓
Estimate: 50 + 30 = 80, close to 74.05. ✓
Watch out. Line up the decimal points, not the right-hand ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths), not above the 7.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.9.040 − 3.576 -----
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.thousandths: 0 is smaller than 6, so exchange 1 from the next column on the left: 10 − 6 = 4
hundredths: the 4 gave 1 to the column on its right, so it is now 3: 3 is smaller than 7, so exchange 1 from the next column on the left: 13 − 7 = 6
tenths: the top digit is 0, but the column to its right needs 1 from it. So it takes 1 from the next column on the left (making 10) and then gives 1 away, leaving 9. 9 − 5 = 4
Put the decimal point straight down, directly under the other decimal points.
units: the 9 gave 1 to the column on its right, so it is now 8: 8 − 3 = 5 - Read the answer. Write the digits, with the decimal point where you put it.9.04 − 3.576 = 5.464
Check. Use the opposite operation: 5.464 + 3.576 = 9.04. ✓
Estimate: 9 − 4 = 5, close to 5.464. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.100.00 − 7.95 ------
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.hundredths: 0 is smaller than 5, so exchange 1 from the next column on the left: 10 − 5 = 5
tenths: the top digit is 0, but the column to its right needs 1 from it. So it takes 1 from the next column on the left (making 10) and then gives 1 away, leaving 9. 9 − 9 = 0
Put the decimal point straight down, directly under the other decimal points.
units: the top digit is 0, but the column to its right needs 1 from it. So it takes 1 from the next column on the left (making 10) and then gives 1 away, leaving 9. 9 − 7 = 2
tens: the top digit is 0, but the column to its right needs 1 from it. So it takes 1 from the next column on the left (making 10) and then gives 1 away, leaving 9. 9 − 0 = 9
hundreds: the 1 gave 1 to the column on its right, so it is now 0: 0 − 0 = 0 - Read the answer. Write the digits, with the decimal point where you put it.100 − 7.95 = 92.05
Check. Use the opposite operation: 92.05 + 7.95 = 100. ✓
Estimate: 100 − 8 = 92, close to 92.05. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Method. Add the prices to find the total cost, then subtract the total from the money paid.
- Write down what we know. A book costs £4.85 and a magazine costs £12.50. Rasha pays with a £20 note.£4.85, £12.50 and £20
- Add the two prices. Line up the decimal points, fill the gaps with zeros, and add column by column from the right.4.85 + 12.50 ----- 17.35
- Subtract the total from £20 to find the change. Line up the decimal points, fill the gaps with zeros, and subtract column by column from the right.20.00 − 17.35 ----- 2.65
- Write the answer as money. Amounts of money are written with two decimal places.£2.65
Check. Add the change to the total: £17.35 + £2.65 = £20. ✓
Watch out. Write the £ sign in the answer, and give amounts of money with two decimal places (£2.65, not £2.6).
Watch out
Line up the decimal points, not the ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths). If you line up the right-hand ends you will add tenths to hundredths and get the wrong answer.Exercise 4B Adding and subtracting decimals
Non-calculatorKey words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To add decimals, write the numbers in columns with the decimal points in a vertical line, then add column by column.
- Write the numbers in columns, with the decimal points directly under each other. Each digit must sit in the right column (units under units, tenths under tenths...). Then every column can be added or subtracted separately.1.2 + 3.5 ---
- Add column by column, starting at the right (the smallest column). When a column adds to 10 or more, write the units digit and carry the 10 to the next column to the left.tenths: 2 + 5 = 7
Put the decimal point straight down, directly under the other decimal points.
units: 1 + 3 = 4 - Read the answer. Write the digits, with the decimal point where you put it.1.2 + 3.5 = 4.7
Check. Use the opposite operation: 4.7 − 3.5 = 1.2. ✓
Estimate: 1 + 4 = 5, close to 4.7. ✓
Watch out. Line up the decimal points, not the right-hand ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths), not above the 7.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To add decimals, write the numbers in columns with the decimal points in a vertical line, then add column by column.
- Write the numbers in columns, with the decimal points directly under each other. Each digit must sit in the right column (units under units, tenths under tenths...). Then every column can be added or subtracted separately.2.7 + 1.6 ---
- Add column by column, starting at the right (the smallest column). When a column adds to 10 or more, write the units digit and carry the 10 to the next column to the left.tenths: 7 + 6 = 13, write 3 and carry 1
Put the decimal point straight down, directly under the other decimal points.
units: 2 + 1 + 1 (carried) = 4 - Read the answer. Write the digits, with the decimal point where you put it.2.7 + 1.6 = 4.3
Check. Use the opposite operation: 4.3 − 1.6 = 2.7. ✓
Estimate: 3 + 2 = 5, close to 4.3. ✓
Watch out. Line up the decimal points, not the right-hand ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths), not above the 7.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To add decimals, write the numbers in columns with the decimal points in a vertical line, then add column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.0.50 + 0.25 ----
- Add column by column, starting at the right (the smallest column). When a column adds to 10 or more, write the units digit and carry the 10 to the next column to the left.hundredths: 0 + 5 = 5
tenths: 5 + 2 = 7
Put the decimal point straight down, directly under the other decimal points.
units: 0 + 0 = 0 - Read the answer. Write the digits, with the decimal point where you put it.0.5 + 0.25 = 0.75
Check. Use the opposite operation: 0.75 − 0.25 = 0.5. ✓
Estimate: 0.5 + 0.3 = 0.8, close to 0.75. ✓
Watch out. Line up the decimal points, not the right-hand ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths), not above the 7.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To add decimals, write the numbers in columns with the decimal points in a vertical line, then add column by column.
- Write the numbers in columns, with the decimal points directly under each other. Each digit must sit in the right column (units under units, tenths under tenths...). Then every column can be added or subtracted separately.3.4 + 2.5 ---
- Add column by column, starting at the right (the smallest column). When a column adds to 10 or more, write the units digit and carry the 10 to the next column to the left.tenths: 4 + 5 = 9
Put the decimal point straight down, directly under the other decimal points.
units: 3 + 2 = 5 - Read the answer. Write the digits, with the decimal point where you put it.3.4 + 2.5 = 5.9
Check. Use the opposite operation: 5.9 − 2.5 = 3.4. ✓
Estimate: 3 + 3 = 6, close to 5.9. ✓
Watch out. Line up the decimal points, not the right-hand ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths), not above the 7.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To add decimals, write the numbers in columns with the decimal points in a vertical line, then add column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.0.60 + 0.27 ----
- Add column by column, starting at the right (the smallest column). When a column adds to 10 or more, write the units digit and carry the 10 to the next column to the left.hundredths: 0 + 7 = 7
tenths: 6 + 2 = 8
Put the decimal point straight down, directly under the other decimal points.
units: 0 + 0 = 0 - Read the answer. Write the digits, with the decimal point where you put it.0.6 + 0.27 = 0.87
Check. Use the opposite operation: 0.87 − 0.27 = 0.6. ✓
Estimate: 0.6 + 0.3 = 0.9, close to 0.87. ✓
Watch out. Line up the decimal points, not the right-hand ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths), not above the 7.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To add decimals, write the numbers in columns with the decimal points in a vertical line, then add column by column.
- Write the numbers in columns, with the decimal points directly under each other. Each digit must sit in the right column (units under units, tenths under tenths...). Then every column can be added or subtracted separately.12.7 + 8.5 ----
- Add column by column, starting at the right (the smallest column). When a column adds to 10 or more, write the units digit and carry the 10 to the next column to the left.tenths: 7 + 5 = 12, write 2 and carry 1
Put the decimal point straight down, directly under the other decimal points.
units: 2 + 8 + 1 (carried) = 11, write 1 and carry 1
tens: 1 + 0 + 1 (carried) = 2 - Read the answer. Write the digits, with the decimal point where you put it.12.7 + 8.5 = 21.2
Check. Use the opposite operation: 21.2 − 8.5 = 12.7. ✓
Estimate: 10 + 9 = 19, close to 21.2. ✓
Watch out. Line up the decimal points, not the right-hand ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths), not above the 7.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To add decimals, write the numbers in columns with the decimal points in a vertical line, then add column by column.
- Write the numbers in columns, with the decimal points directly under each other. Each digit must sit in the right column (units under units, tenths under tenths...). Then every column can be added or subtracted separately.4.56 + 3.78 ----
- Add column by column, starting at the right (the smallest column). When a column adds to 10 or more, write the units digit and carry the 10 to the next column to the left.hundredths: 6 + 8 = 14, write 4 and carry 1
tenths: 5 + 7 + 1 (carried) = 13, write 3 and carry 1
Put the decimal point straight down, directly under the other decimal points.
units: 4 + 3 + 1 (carried) = 8 - Read the answer. Write the digits, with the decimal point where you put it.4.56 + 3.78 = 8.34
Check. Use the opposite operation: 8.34 − 3.78 = 4.56. ✓
Estimate: 5 + 4 = 9, close to 8.34. ✓
Watch out. Line up the decimal points, not the right-hand ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths), not above the 7.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To add decimals, write the numbers in columns with the decimal points in a vertical line, then add column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.0.907 + 0.850 -----
- Add column by column, starting at the right (the smallest column). When a column adds to 10 or more, write the units digit and carry the 10 to the next column to the left.thousandths: 7 + 0 = 7
hundredths: 0 + 5 = 5
tenths: 9 + 8 = 17, write 7 and carry 1
Put the decimal point straight down, directly under the other decimal points.
units: 0 + 0 + 1 (carried) = 1 - Read the answer. Write the digits, with the decimal point where you put it.0.907 + 0.85 = 1.757
Check. Use the opposite operation: 1.757 − 0.85 = 0.907. ✓
Estimate: 0.9 + 0.9 = 1.8, close to 1.757. ✓
Watch out. Line up the decimal points, not the right-hand ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths), not above the 7.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To add decimals, write the numbers in columns with the decimal points in a vertical line, then add column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.25.00 + 3.64 -----
- Add column by column, starting at the right (the smallest column). When a column adds to 10 or more, write the units digit and carry the 10 to the next column to the left.hundredths: 0 + 4 = 4
tenths: 0 + 6 = 6
Put the decimal point straight down, directly under the other decimal points.
units: 5 + 3 = 8
tens: 2 + 0 = 2 - Read the answer. Write the digits, with the decimal point where you put it.25 + 3.64 = 28.64
Check. Use the opposite operation: 28.64 − 3.64 = 25. ✓
Estimate: 30 + 4 = 34, close to 28.64. ✓
Watch out. Line up the decimal points, not the right-hand ends of the numbers. In 3.5 + 0.27 the 5 (tenths) goes above the 2 (tenths), not above the 7.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Each digit must sit in the right column (units under units, tenths under tenths...). Then every column can be added or subtracted separately.7.9 − 3.4 ---
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.tenths: 9 − 4 = 5
Put the decimal point straight down, directly under the other decimal points.
units: 7 − 3 = 4 - Read the answer. Write the digits, with the decimal point where you put it.7.9 − 3.4 = 4.5
Check. Use the opposite operation: 4.5 + 3.4 = 7.9. ✓
Estimate: 8 − 3 = 5, close to 4.5. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Each digit must sit in the right column (units under units, tenths under tenths...). Then every column can be added or subtracted separately.6.5 − 2.8 ---
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.tenths: 5 is smaller than 8, so exchange 1 from the next column on the left: 15 − 8 = 7
Put the decimal point straight down, directly under the other decimal points.
units: the 6 gave 1 to the column on its right, so it is now 5: 5 − 2 = 3 - Read the answer. Write the digits, with the decimal point where you put it.6.5 − 2.8 = 3.7
Check. Use the opposite operation: 3.7 + 2.8 = 6.5. ✓
Estimate: 7 − 3 = 4, close to 3.7. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.12.40 − 5.67 -----
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.hundredths: 0 is smaller than 7, so exchange 1 from the next column on the left: 10 − 7 = 3
tenths: the 4 gave 1 to the column on its right, so it is now 3: 3 is smaller than 6, so exchange 1 from the next column on the left: 13 − 6 = 7
Put the decimal point straight down, directly under the other decimal points.
units: the 2 gave 1 to the column on its right, so it is now 1: 1 is smaller than 5, so exchange 1 from the next column on the left: 11 − 5 = 6
tens: the 1 gave 1 to the column on its right, so it is now 0: 0 − 0 = 0 - Read the answer. Write the digits, with the decimal point where you put it.12.4 − 5.67 = 6.73
Check. Use the opposite operation: 6.73 + 5.67 = 12.4. ✓
Estimate: 10 − 6 = 4, close to 6.73. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.10.00 − 3.45 -----
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.hundredths: 0 is smaller than 5, so exchange 1 from the next column on the left: 10 − 5 = 5
tenths: the top digit is 0, but the column to its right needs 1 from it. So it takes 1 from the next column on the left (making 10) and then gives 1 away, leaving 9. 9 − 4 = 5
Put the decimal point straight down, directly under the other decimal points.
units: the top digit is 0, but the column to its right needs 1 from it. So it takes 1 from the next column on the left (making 10) and then gives 1 away, leaving 9. 9 − 3 = 6
tens: the 1 gave 1 to the column on its right, so it is now 0: 0 − 0 = 0 - Read the answer. Write the digits, with the decimal point where you put it.10 − 3.45 = 6.55
Check. Use the opposite operation: 6.55 + 3.45 = 10. ✓
Estimate: 10 − 3 = 7, close to 6.55. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.8.003 − 2.900 -----
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.thousandths: 3 − 0 = 3
hundredths: 0 − 0 = 0
tenths: 0 is smaller than 9, so exchange 1 from the next column on the left: 10 − 9 = 1
Put the decimal point straight down, directly under the other decimal points.
units: the 8 gave 1 to the column on its right, so it is now 7: 7 − 2 = 5 - Read the answer. Write the digits, with the decimal point where you put it.8.003 − 2.9 = 5.103
Check. Use the opposite operation: 5.103 + 2.9 = 8.003. ✓
Estimate: 8 − 3 = 5, close to 5.103. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.0.500 − 0.347 -----
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.thousandths: 0 is smaller than 7, so exchange 1 from the next column on the left: 10 − 7 = 3
hundredths: the top digit is 0, but the column to its right needs 1 from it. So it takes 1 from the next column on the left (making 10) and then gives 1 away, leaving 9. 9 − 4 = 5
tenths: the 5 gave 1 to the column on its right, so it is now 4: 4 − 3 = 1
Put the decimal point straight down, directly under the other decimal points.
units: 0 − 0 = 0 - Read the answer. Write the digits, with the decimal point where you put it.0.5 − 0.347 = 0.153
Check. Use the opposite operation: 0.153 + 0.347 = 0.5. ✓
Estimate: 0.5 − 0.3 = 0.2, close to 0.153. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Each digit must sit in the right column (units under units, tenths under tenths...). Then every column can be added or subtracted separately.5.6 − 2.3 ---
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.tenths: 6 − 3 = 3
Put the decimal point straight down, directly under the other decimal points.
units: 5 − 2 = 3 - Read the answer. Write the digits, with the decimal point where you put it.5.6 − 2.3 = 3.3
Check. Use the opposite operation: 3.3 + 2.3 = 5.6. ✓
Estimate: 6 − 2 = 4, close to 3.3. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Each digit must sit in the right column (units under units, tenths under tenths...). Then every column can be added or subtracted separately.4.8 − 1.9 ---
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.tenths: 8 is smaller than 9, so exchange 1 from the next column on the left: 18 − 9 = 9
Put the decimal point straight down, directly under the other decimal points.
units: the 4 gave 1 to the column on its right, so it is now 3: 3 − 1 = 2 - Read the answer. Write the digits, with the decimal point where you put it.4.8 − 1.9 = 2.9
Check. Use the opposite operation: 2.9 + 1.9 = 4.8. ✓
Estimate: 5 − 2 = 3, close to 2.9. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Key words. A column holds digits of the same place value. Carrying moves ten of one column into one of the next column to the left. Exchanging (borrowing) moves one of the next column on the left into ten of this column.
Method. To subtract decimals, write the numbers in columns with the decimal points in a vertical line, then subtract column by column.
- Write the numbers in columns, with the decimal points directly under each other. Fill the gaps with zeros. Each digit must sit in the right column (units under units, tenths under tenths...). A zero on the end of a decimal does not change its value, so writing 4.5 as 4.50 is allowed.3.00 − 1.25 ----
- Subtract column by column, starting at the right (the smallest column). When the top digit is smaller than the bottom digit, exchange 1 from the next column on the left. That 1 is worth 10 in this column, so add 10 to the top digit.hundredths: 0 is smaller than 5, so exchange 1 from the next column on the left: 10 − 5 = 5
tenths: the top digit is 0, but the column to its right needs 1 from it. So it takes 1 from the next column on the left (making 10) and then gives 1 away, leaving 9. 9 − 2 = 7
Put the decimal point straight down, directly under the other decimal points.
units: the 3 gave 1 to the column on its right, so it is now 2: 2 − 1 = 1 - Read the answer. Write the digits, with the decimal point where you put it.3 − 1.25 = 1.75
Check. Use the opposite operation: 1.75 + 1.25 = 3. ✓
Estimate: 3 − 1 = 2, close to 1.75. ✓
Watch out. Line up the decimal points, and fill gaps with zeros first: 5 − 2.37 needs 5.00 − 2.37. Subtract the smaller number from the bigger one.
Method. Find the total cost first, then subtract it from the money Tom paid.
- Add the price of the drink and the sandwich. Line up the decimal points, fill the gaps with zeros, and add column by column from the right.1.85 + 3.60 ---- 5.45
- Subtract from £10 to find the change. Line up the decimal points, fill the gaps with zeros, and subtract column by column from the right.10.00 − 5.45 ----- 4.55
- Write the answer as money. Amounts of money are written with two decimal places.£4.55
Check. £5.45 + £4.55 = £10.00. ✓
Watch out. Do not subtract each item from £10 separately and then add: find the total first.
Method. Add the three masses to find the total, then subtract the total from the limit.
- Add the first two masses. Line up the decimal points, fill the gaps with zeros, and add column by column from the right.2.35 + 4.80 ---- 7.15
- Add the third mass. Line up the decimal points, fill the gaps with zeros, and add column by column from the right.7.150 + 0.975 ----- 8.125
- Subtract from the 10 kg limit. Line up the decimal points, fill the gaps with zeros, and subtract column by column from the right.10.000 − 8.125 ------ 1.875
- Answer the question. The question asks how much more can be added before the limit is reached.1.875 kg
Check. 8.125 + 1.875 = 10. ✓
Watch out. Keep the units (kg) in your answer.
Method. Subtract the length that was cut off from the original length.
- Write the sum. The ribbon starts at 3 m and 1.85 m is cut off.3 − 1.85
- Subtract the length cut off from 3 m. Write 3 as 3.00 so the decimal places line up, then subtract column by column.3.00 − 1.85 ---- 1.15
- Write the answer with units. 1.15 m
Check. 1.15 + 1.85 = 3. ✓
Watch out. A whole number needs its zeros: 3 = 3.00.
Method. The missing number is what you add to 4.6 to reach 9.1, so subtract: 9.1 − 4.6.
- Choose the operation. The opposite of adding is subtracting.? = 9.1 − 4.6
- Subtract. Line up the decimal points, fill the gaps with zeros, and subtract column by column from the right.9.1 − 4.6 --- 4.5
Check. 4.6 + 4.5 = 9.1. ✓
Method. The missing number is the total take away the number we know.
- Choose the operation. The opposite of adding is subtracting.? = 6 − 2.75
- Subtract (write 6 as 6.00). Line up the decimal points, fill the gaps with zeros, and subtract column by column from the right.6.00 − 2.75 ---- 3.25
Check. 3.25 + 2.75 = 6. ✓
Method. The missing number is the amount taken away. Take the answer from the starting number.
- Choose the operation. If 12 − ? = 7.4 then 12 − 7.4 = ?? = 12 − 7.4
- Subtract (write 12 as 12.0). Line up the decimal points, fill the gaps with zeros, and subtract column by column from the right.12.0 − 7.4 ---- 4.6
Check. 12 − 4.6 = 7.4. ✓
Watch out. Here you subtract again, not add.
Method. Check that the digits are in the correct columns. Her answer is smaller than 3.5, which cannot be right when you add something to 3.5.
- Look for the mistake. Sara probably lined up the right-hand ends: 5 above 7 and nothing above 2. That adds tenths to hundredths.The 5 is in the tenths column but the 7 is in the hundredths column.
- Line up the decimal points and add correctly. Write 3.5 as 3.50 so that tenths are under tenths and hundredths are under hundredths.3.50 + 0.27 ---- 3.77
- Write the answer. 3.5 + 0.27 = 3.77
Check. Estimate: 3.5 + 0.3 = 3.8, close to 3.77. ✓
Watch out. If you add a positive number, the answer must be bigger than the number you started with.
Method. Add the four times one at a time, using the column method each time.
- Add the first two times. Line up the decimal points, fill the gaps with zeros, and add column by column from the right.11.43 + 10.98 ----- 22.41
- Add the third time. Line up the decimal points, fill the gaps with zeros, and add column by column from the right.22.41 + 11.07 ----- 33.48
- Add the fourth time. Line up the decimal points, fill the gaps with zeros, and add column by column from the right.33.48 + 11.52 ----- 45.00
- Write the total with units. 45 seconds
Check. Round each time and estimate: 11 + 11 + 11 + 12 = 45, so 45.00 is sensible. ✓
Watch out. Take care when the total is a whole number: 45.00 = 45.
Method. The perimeter is the distance all the way round. A rectangle has two lengths and two widths.
- Add the length and the width. Half the perimeter is one length plus one width.5.40 + 3.65 ---- 9.05
- Double it. There are two of each side, so the perimeter is twice this.9.05 × 2 = 18.10
- Write the answer with units. The last zero can be dropped.18.1 cm
Check. 5.4 + 3.65 + 5.4 + 3.65 = 18.1. ✓
Watch out. Perimeter is a length, so the units are cm, not cm².
Method. A rise means going up the number line. Go up to 0 first, then see how much of the rise is left.
- Rise from −3.4 to 0. You need to go up 3.4 to reach 0.−3.4 + 3.4 = 0
- Work out how much of the rise is left. The total rise is 5.7, and 3.4 of it has been used.5.7 − 3.4 --- 2.3
- Write the final temperature. The remaining 2.3 takes us above 0.2.3°C
Check. −3.4 + 5.7 = 5.7 − 3.4 = 2.3. ✓
Watch out. When the rise is bigger than the negative number, the answer is positive.
Method. Work out the left-hand side step by step and show it equals 8.
- Add the first two numbers. Line up the decimal points, fill the gaps with zeros, and add column by column from the right.2.4 + 3.7 --- 6.1
- Add the third number. Line up the decimal points, fill the gaps with zeros, and add column by column from the right.6.1 + 1.9 --- 8.0
- Write the conclusion. The total is 8.0, which is 8.2.4 + 3.7 + 1.9 = 6.1 + 1.9 = 8.0 = 8
Check. Pair 3.7 + 1.9 = 5.6 and 2.4 + 5.6 = 8. ✓
Watch out. In a “show that” question, write down every step and finish with the result.
Method. The bigger number is the smaller number plus 0.3. Remove the 0.3 from the total, share the rest equally, then add the 0.3 back to find the bigger number.
- Take away the difference from the total. If the bigger number were reduced by 0.3 the two numbers would be equal.1.0 − 0.3 --- 0.7
- Share what is left equally. Two equal numbers add to 0.7, so each is half of it.0.7 ÷ 2 = 0.35
- Find the bigger number. Add the difference back on.0.35 + 0.30 ---- 0.65
- Write the two numbers. 0.65 and 0.35
Check. 0.65 + 0.35 = 1 and 0.65 − 0.35 = 0.3. ✓
Watch out. Check both conditions: the total and the difference.