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Subtracting Decimals
Here we will learn about subtracting decimals including how to solve problems that involve the subtraction of decimal numbers.
There are also subtracting decimals worksheets with word problems and problem solving questions based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
What is subtracting decimals?
Subtracting decimals involves using column addition to subtract decimal numbers by lining up the digits so that they have the same place value.
The ones, decimal points, tenths, hundredths etc. should be lined up. This is particularly important to do if the values we are adding have been given to a different number of decimal places.
This column method of subtraction only works if the number we are subtracting is smaller than the one we are subtracting it from. If we know our answer will be negative, we must switch the numbers around, find the positive difference and then make our answer negative.
What is subtracting decimals?
How to subtract decimals
In order to subtract decimals:
- Set up a column subtraction, writing the larger number above the other. Make sure the decimal points line up to ensure numbers in each column have the correct place value. Fill in any gaps with zeros.
- Subtract each column from right to left remembering to exchange (or borrow) from the left if required.
- Read off your answer, remembering to include the decimal point. If the original subtraction would have given a negative answer, remember to include the negative sign.
How to subtract decimals
Subtracting decimals worksheet
Get your free subtracting decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREE Subtracting decimals worksheet
Get your free subtracting decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREERelated lessons on decimals
Subtracting decimals is part of our series of lessons to support revision on decimals. You may find it helpful to start with the main decimals lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
Subtracting decimals examples
Example 1: Subtracting numbers with one decimal place
Work out
- Set up a column subtraction, writing the larger number above the other. Make sure the decimal points line up to ensure numbers in each column have the correct place value. Fill in any gaps with zeros.
2Subtract each column from right to left remembering to exchange (or borrow) from the left if required.
3Read off your answer, remembering to include the decimal point. If the original subtraction would have given a negative answer, remember to include the negative sign.
The answer is
Example 2: subtracting numbers with two decimal places
Work out
Set up a column subtraction, writing the larger number above the other. Make sure the decimal points line up to ensure numbers in each column have the correct place value. Fill in any gaps with zeros.
Subtract each column from right to left remembering to exchange (or borrow) from the left if required.
Read off your answer, remembering to include the decimal point. If the original subtraction would have given a negative answer, remember to include the negative sign.
The answer is
Example 3: subtracting numbers with different amounts of decimals places
Work out
Set up a column subtraction, writing the larger number above the other. Make sure the decimal points line up to ensure numbers in each column have the correct place value. Fill in any gaps with zeros.
Subtract each column from right to left remembering to exchange (or borrow) from the left if required.
Read off your answer, remembering to include the decimal point. If the original subtraction would have given a negative answer, remember to include the negative sign.
The answer is
Example 4: subtracting larger decimal numbers from smaller decimal numbers
Work out
Set up a column subtraction, writing the larger number above the other. Make sure the decimal points line up to ensure numbers in each column have the correct place value. Fill in any gaps with zeros.
This subtraction will give a negative answer. We will need to swap the order to make the column subtraction method work. So we will work out
Subtract each column from right to left remembering to exchange (or borrow) from the left if required.
Read off your answer, remembering to include the decimal point. If the original subtraction would have given a negative answer, remember to include the negative sign.
We swapped the order of the numbers in our subtraction so we need to make our answer negative.
The answer is −
Example 5: subtracting more than one decimal number from another
Find the change from £
Set up a column subtraction, writing the larger number above the other. Make sure the decimal points line up to ensure numbers in each column have the correct place value. Fill in any gaps with zeros.
We could do two separate subtractions or add the two items to be subtracted and subtract the total from £
Here we will add the two items and then set up one subtraction.
Subtract each column from right to left remembering to exchange (or borrow) from the left if required.
Read off your answer, remembering to include the decimal point. If the original subtraction would have given a negative answer, remember to include the negative sign.
The answer is £
Common misconceptions
- Not lining up the decimal point
A common error when subtracting decimals occurs when the decimal points are not lined up but instead the last digits are lined up.
E.g.
- Not swapping the order when taking a larger number from a smaller number
It is important to remember that the column subtraction method does not give the correct answer if it is used with a smaller number above a larger number. If it is clear that the answer will be negative, we must remember to swap the order of the numbers for the subtraction and then make the answer negative.
Practice subtracting decimals questions
1. Work out 12.5 − 7.8
You must remember to line up the decimal points carefully and exchange (or borrow) from the left if required.
2. Work out 56.29 − 2.47
3.159
You must remember to line up the decimal points carefully and exchange (or borrow) from the left if required.
3. Work out 23.4 − 16.573
You must remember to line up the decimal points carefully, filling in any gaps with zeros. Exchange (or borrow) from the left if required.
4. Work out 3.51 − 8.29
You must remember to swap the order of the numbers to perform column subtraction, then put a negative sign on the answer.
5. Work out 8.5 − 1.4 − 5.9
Either add 1.4 and 5.9 together first and then subtract from 8.5 , or subtract 1.4 from 8.5 and then 5.9 from the answer.
6. Work out 11.2 − 3.6 − 2.01
Either add 3.6 and 2.01 together first and then subtract from 11.2 , or subtract 3.6 from 11.2 and then 2.01 from the answer.
Subtracting decimals GCSE questions
1.
a) Work out 12.79 − 5.82
b) Work out 44.6 – 23.39 – 8.42
(3 marks)
a)
Correct answer of 6.97
(1)
b)
21.21 or 36.18 or 31.81 seen
(1)
Correct answer of 12.79
(1)
2. Complete the following calculations:
a)
b)
(5 marks)
a)
9 in the top row.
(1)
3 in the second row.
(1)
b)
9 in first box in top row.
(1)
4 in second box in top row.
(1)
8 in second row.
(1)
3. Mark went to a clothes shop and bought 2 t-shirts costing £8.99 each, a hat costing £6.50 and a pair of shoes costing £22.90.
He paid for the items with a £50 note.
What change should he receive?
(3 marks)
£8.99 + £8.99 + £6.50 + £22.90
(1)
£50 – £47.38.
(1)
Correct answer of £2.62.
(1)
Learning checklist
You have now learned how to:
- Understand and use place value for decimals, measures and integers of any size
- Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
The next lessons are
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