Subtraction
Subtraction is one of the four fundamental arithmetic operations, representing the process of taking away one number from another. The operation uses the minus sign (−) and produces a result called the difference. When subtracting 8 from 15, written as 15 − 8 = 7, the number 7 represents what remains after removing 8 from the original 15.
Why it matters
Subtraction appears constantly in everyday situations, from calculating change when buying items to determining time remaining until an event. A shopper with £20 who spends £12.50 uses subtraction to find they have £7.50 left. In sport, subtracting a team's goals conceded (18) from goals scored (25) gives their goal difference (+7). The operation forms the foundation for more advanced mathematics, including negative numbers in Year 7, algebraic equations in KS3, and calculus in A-levels. Financial literacy depends heavily on subtraction — calculating mortgage payments, comparing prices, or working out savings require this fundamental skill. Even young children use subtraction when sharing toys or counting down to special events.
How to solve subtraction
Subtraction — how to
- Line up digits by place value, larger number on top.
- Subtract column by column from the right.
- If the top digit is smaller, borrow 10 from the next column.
Example: 52 − 27: 2 < 7, borrow. 12−7=5. 4−2=2. Answer: 25.
Worked examples
There are 5 coins. 3 roll away. How many are left?
Answer: 2
- Look at what we are taking away → 5 - 3 — We start with 5 and need to take away 3. Imagine you have 5 candies and eat 3 of them.
- Count back from the bigger number → 5 - 3 = 2 — Start at 5 and count back 3: 4, 3, 2. We land on 2!
- Check: add back to verify → 2 + 3 = 5 ✓ — To check subtraction, add the answer back: 2 + 3 = 5. It matches what we started with, so we are correct!
Start at 12. Count back 5. Where do you land?
Answer: 7
- Look at what we are taking away → 12 - 5 — We start with 12 and need to take away 5. Imagine you have 12 candies and eat 5 of them.
- Count back from the bigger number → 12 - 5 = 7 — Start at 12 and count back 5: 11, 10, 9, 8, 7. We land on 7!
- Check: add back to verify → 7 + 5 = 12 ✓ — To check subtraction, add the answer back: 7 + 5 = 12. It matches what we started with, so we are correct!
You saved £87.00 and spent £34.00 on a gift. How much is left?
Answer: 53
- Look at what we are subtracting → 87 - 34 — We need to take 34 away from 87. We will do this column by column, starting from the ones (right side), just like you unstack blocks.
- Subtract the ones column → 7 - 4 = 3 — Start with the ones: 7 - 4 = 3. No borrowing needed!
- Subtract the tens column → 8 - 3 = 5 — Now the tens: 8 - 3 = 5.
- Put the digits together → 87 - 34 = 53 — Tens digit 5 and ones digit 3 give us 53.
- Check: add back to verify → 53 + 34 = 87 ✓ — Adding 53 + 34 gives 87. Our subtraction is correct!
Common mistakes
- Subtracting digits in the wrong order when borrowing is needed. For 63 − 47, incorrectly calculating 7 − 3 = 4 in the ones column instead of borrowing to get 13 − 7 = 6.
- Forgetting to reduce the tens digit after borrowing. In 52 − 27, taking 12 − 7 = 5 correctly but then calculating 5 − 2 = 3 instead of 4 − 2 = 2, giving 35 instead of 25.
- Placing the smaller number on top regardless of the subtraction order. Writing 25 − 43 as 25 on top and 43 below, leading to impossible calculations instead of recognising this produces a negative result.