Subtraction
Get to grips with subtraction using these Foundation GCSE Maths practice questions. The worksheet focuses on column subtraction, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Borrow from the next column when the top digit is smaller than the bottom one.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Challenge / Extension
Stretch yourself beyond the basics.
Topic overview
Column subtraction works like column addition but in reverse, taking the bottom number from the top. When a digit on top is too small, you exchange from the column to its left.
Exchanging is often called borrowing. Taking one from the tens column adds ten to the units, so the total value of the number is unchanged — you have simply rewritten it in a more useful form.
With decimals, align the decimal points and pad with trailing zeros first. Subtracting \(4.7\) from \(9\) is much clearer once you write \(9.0\) above \(4.7\), because the columns then match.
Revision notes
Setting out and exchanging
Align the place values and work from the right. If the top digit is smaller than the bottom one, take one from the column to the left and add ten to the current column.
In \(52 - 27\), you cannot take \(7\) from \(2\), so exchange a ten: the \(5\) becomes \(4\) and the \(2\) becomes \(12\). Then \(12 - 7 = 5\) and \(4 - 2 = 2\), giving \(25\).
Exchanging across a zero
When the column to the left is a zero, you must exchange from further along. Take one from the first non-zero column and pass it down.
For \(300 - 148\), the tens column is zero, so exchange from the hundreds: \(300\) becomes \(2\) hundreds, \(9\) tens and \(10\) units, and the subtraction proceeds normally.
Checking by adding back
Subtraction is undone by addition, so add your answer to the number you subtracted. If you get the original, the answer is right.
For \(52 - 27 = 25\), check \(25 + 27 = 52\). This takes seconds and catches most errors.
Key points
- Align place values and decimal points.
- Work from right to left.
- Exchange from the left when the top digit is too small.
- Exchanging keeps the value of the number the same.
- Pad decimals with trailing zeros first.
- Check by adding the answer back to the number subtracted.
Worked examples
Example 1
Work out \(83 - 47\).
Working
Example 2
Work out \(9 - 4.7\).
Working
Example 3
Check that \(500 - 236 = 264\).
Working
Common mistakes
Subtracting the smaller digit from the larger regardless of position.
In 52 − 27 the units give 2 − 7, not 7 − 2. You must exchange rather than swap.
Forgetting to reduce the column you exchanged from.
If the units gain ten, the tens must lose one, or the value changes.
Struggling to exchange across a zero.
Go to the first non-zero column to the left and pass the exchange down through the zeros.
Not padding decimals.
Writing 9 above 4.7 misaligns the columns. Write 9.0 first.
Exam tips
- Cross out and rewrite digits clearly when exchanging.
- Always pad decimals so both numbers have the same number of decimal places.
- Check by adding your answer back to the number you subtracted.
- Estimate first so you know roughly what the answer should be.
Key terms
- Exchange
- Taking one from the column to the left and adding ten to the current column.
- Difference
- The result of a subtraction.
- Minuend
- The number being subtracted from.
- Inverse
- The opposite operation, so addition is the inverse of subtraction.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.