Year 5: Adding, subtracting and solving problems
Part of the Year 5 decimals and percentages chapter. Chapter overview · whole chapter on one page
Adding, subtracting and solving problems
Adding and subtracting decimals uses the same column method as whole numbers, with one rule: line up the decimal points. Write zeros at the end of the shorter number so that every column has a digit. Then work from the right.
Key ideas
- Line up the decimal points, one under the other.
- Fill empty places with zeros so that each number has the same number of decimal places.
- Work column by column from the right, and exchange (carry) when a column is more than 9 or less than 0.
- Put the decimal point in the answer straight down, under the others. Check with the opposite operation.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
3.45 + 1.728 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
3.450 + 1.728 -------
- Add column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
3.450 + 1.728 ------- 5.178
- Write the decimal point in the answer. Bring the point straight down, under the others.5.178
Check. Check with the opposite operation: 5.178 − 1.728 = 3.45. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
4.6 − 2.375 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
4.600 − 2.375 -------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
4.600 − 2.375 ------- 2.225
- Write the decimal point in the answer. Bring the point straight down, under the others.2.225
Check. Check with the opposite operation: 2.225 + 2.375 = 4.6. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Choose the operation. Some water was poured out, so we subtract the amount that was poured out.1.5 litres − 0.275 litres
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
1.5 − 0.275 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
1.500 − 0.275 -------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
1.500 − 0.275 ------- 1.225
- Write the decimal point in the answer. Bring the point straight down, under the others.1.225 litres
Check. Check with the opposite operation: 1.225 + 0.275 = 1.5. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Watch out
The most common mistake is to line up the last digits instead of the decimal points. When you work out 4.6 − 2.375, write 4.6 as 4.600 first, so that the 6 sits in the tenths column above the 3 of 2.375.Exercise 7D Adding and subtracting decimals
Non-calculatorKey words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
2.6 + 0.35 ------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
2.60 + 0.35 ------
- Add column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
2.60 + 0.35 ------ 2.95
- Write the decimal point in the answer. Bring the point straight down, under the others.2.95
Check. Check with the opposite operation: 2.95 − 0.35 = 2.6. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
4.25 + 1.8 ------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
4.25 + 1.80 ------
- Add column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
4.25 + 1.80 ------ 6.05
- Write the decimal point in the answer. Bring the point straight down, under the others.6.05
Check. Check with the opposite operation: 6.05 − 1.8 = 4.25. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
0.125 + 0.4 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
0.125 + 0.400 -------
- Add column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
0.125 + 0.400 ------- 0.525
- Write the decimal point in the answer. Bring the point straight down, under the others.0.525
Check. Check with the opposite operation: 0.525 − 0.4 = 0.125. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
3.007 + 1.993 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
3.007 + 1.993 -------
- Add column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
3.007 + 1.993 ------- 5.000
- Write the decimal point in the answer. Bring the point straight down, under the others.5
Check. Check with the opposite operation: 5 − 1.993 = 3.007. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
5.3 − 2.14 ------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
5.30 − 2.14 ------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
5.30 − 2.14 ------ 3.16
- Write the decimal point in the answer. Bring the point straight down, under the others.3.16
Check. Check with the opposite operation: 3.16 + 2.14 = 5.3. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
7.5 − 0.625 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
7.500 − 0.625 -------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
7.500 − 0.625 ------- 6.875
- Write the decimal point in the answer. Bring the point straight down, under the others.6.875
Check. Check with the opposite operation: 6.875 + 0.625 = 7.5. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
10. − 3.45 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
10.00 − 3.45 -------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
10.00 − 3.45 ------- 6.55
- Write the decimal point in the answer. Bring the point straight down, under the others.6.55
Check. Check with the opposite operation: 6.55 + 3.45 = 10. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
2.04 − 0.4 ------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
2.04 − 0.40 ------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
2.04 − 0.40 ------ 1.64
- Write the decimal point in the answer. Bring the point straight down, under the others.1.64
Check. Check with the opposite operation: 1.64 + 0.4 = 2.04. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
0.5 + 0.25 ------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
0.50 + 0.25 ------
- Add column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
0.50 + 0.25 ------ 0.75
- Write the decimal point in the answer. Bring the point straight down, under the others.0.75
Check. Check with the opposite operation: 0.75 − 0.25 = 0.5. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
1.2 − 0.7 -----
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
1.2 − 0.7 -----
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
1.2 − 0.7 ----- 0.5
- Write the decimal point in the answer. Bring the point straight down, under the others.0.5
Check. Check with the opposite operation: 0.5 + 0.7 = 1.2. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
0.75 + 0.05 ------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
0.75 + 0.05 ------
- Add column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
0.75 + 0.05 ------ 0.80
- Write the decimal point in the answer. Bring the point straight down, under the others.0.8
Check. Check with the opposite operation: 0.8 − 0.05 = 0.75. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
3.9 − 0.09 ------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
3.90 − 0.09 ------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
3.90 − 0.09 ------ 3.81
- Write the decimal point in the answer. Bring the point straight down, under the others.3.81
Check. Check with the opposite operation: 3.81 + 0.09 = 3.9. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Look at the sentence. The box is the number we need to find.0.6 + ? = 1.15
- Use the opposite operation. The missing number was added to 0.6 to make 1.15. To undo an addition, subtract.1.15 − 0.6 = ?
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
1.15 − 0.6 ------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
1.15 − 0.60 ------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
1.15 − 0.60 ------ 0.55
- Write the decimal point in the answer. Bring the point straight down, under the others.0.55
Check. Check with the opposite operation: 0.55 + 0.6 = 1.15. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Look at the sentence. The box is the number we need to find.? − 0.375 = 0.8
- Use the opposite operation. The missing number had 0.375 taken away to leave 0.8. To undo a subtraction, add.0.8 + 0.375 = ?
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
0.8 + 0.375 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
0.800 + 0.375 -------
- Add column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
0.800 + 0.375 ------- 1.175
- Write the decimal point in the answer. Bring the point straight down, under the others.1.175
Check. Check with the opposite operation: 1.175 − 0.375 = 0.8. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Look at the sentence. The box is the number we need to find.2.4 − ? = 1.875
- Use the opposite operation. 2.4 had some taken away to leave 1.875. The missing number is the amount taken away, so subtract 1.875 from 2.4.2.4 − 1.875 = ?
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
2.4 − 1.875 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
2.400 − 1.875 -------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
2.400 − 1.875 ------- 0.525
- Write the decimal point in the answer. Bring the point straight down, under the others.0.525
Check. Check with the opposite operation: 0.525 + 1.875 = 2.4. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Choose the operation. Maya pays for two things, so we add the two prices.£1.45 + £2.80
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
1.45 + 2.8 ------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
1.45 + 2.80 ------
- Add column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
1.45 + 2.80 ------ 4.25
- Write the decimal point in the answer. Bring the point straight down, under the others.£4.25
Check. Check with the opposite operation: 4.25 − 2.8 = 1.45. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Choose the operation. Some of the ribbon was cut off, so we subtract the length cut off.2.45 m − 0.8 m
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
2.45 − 0.8 ------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
2.45 − 0.80 ------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
2.45 − 0.80 ------ 1.65
- Write the decimal point in the answer. Bring the point straight down, under the others.1.65 m
Check. Check with the opposite operation: 1.65 + 0.8 = 2.45. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Add the first two jugs. Line up the decimal points: 0.75 + 1.20 = 1.95.0.75 + 1.20 = 1.95 litres
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
1.95 + 0.365 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
1.950 + 0.365 -------
- Add column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
1.950 + 0.365 ------- 2.315
- Write the decimal point in the answer. Bring the point straight down, under the others.2.315 litres
Check. Check with the opposite operation: 2.315 − 0.365 = 1.95. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Choose the operation. The jug holds 2.5 litres and Ben has poured in 0.725 litres, so subtract to find how much more is needed.2.5 litres − 0.725 litres
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
2.5 − 0.725 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
2.500 − 0.725 -------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
2.500 − 0.725 ------- 1.775
- Write the decimal point in the answer. Bring the point straight down, under the others.1.775 litres
Check. Check with the opposite operation: 1.775 + 0.725 = 2.5. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
6.035 − 5.9 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
6.035 − 5.900 -------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
6.035 − 5.900 ------- 0.135
- Write the decimal point in the answer. Bring the point straight down, under the others.0.135
Check. Check with the opposite operation: 0.135 + 5.9 = 6.035. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
12.5 − 12.46 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
12.50 − 12.46 -------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
12.50 − 12.46 ------- 0.04
- Write the decimal point in the answer. Bring the point straight down, under the others.0.04 seconds
Check. Check with the opposite operation: 0.04 + 12.46 = 12.5. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Find the mistake by working out the correct answer yourself, then compare.
- Work out the correct answer. Do the calculation one step at a time.
2.40 + 1.37 ------ 3.77
- Compare with the pupil’s answer. Sam wrote 3.61.His answer is too small. He did not line up the decimal points, so some digits were added in the wrong columns.
- Write the correct answer. 3.77. Sam is not correct.
Check. 3.77 − 1.37 = 2.40. ✓
Watch out. Write 2.4 as 2.40 before you add, so the hundredths column is in the right place.
Key words. The column method lines up the decimal points, so that each place value is in the same column. A zero written at the end of a decimal does not change its value.
Method. Line up the decimal points, fill the empty places with zeros, then work column by column from the right.
- Line up the decimal points. Write one number under the other so that the digits with the same place value are in the same column.
5.5 − 2.375 -------
- Fill the empty places with zeros. Zeros on the right do not change the value. They make both numbers have the same number of decimal places.
5.500 − 2.375 -------
- Subtract column by column, from the right. Start with the smallest place value. Exchange or carry when you need to.
5.500 − 2.375 ------- 3.125
- Write the decimal point in the answer. Bring the point straight down, under the others.3.125
Check. Check with the opposite operation: 3.125 + 2.375 = 5.5. ✓
Watch out. Line up the decimal POINTS, not the last digits. Add zeros so that every number has the same number of decimal places, then each column has one place value.