Subtraction
Subtraction finds the difference between two numbers by taking away a smaller quantity from a larger one. The operation answers questions like "How many are left?" or "How much more is needed?" This fundamental arithmetic skill appears in CCSS.1.OA and CCSS.2.NBT standards, beginning with simple take-away problems and progressing to multi-digit calculations requiring regrouping.
Why it matters
Subtraction drives countless daily calculations, from determining change at a store ($20 - $12.50 = $7.50) to measuring time differences (3:45 PM - 2:15 PM = 1 hour 30 minutes). Financial literacy depends on subtraction when tracking expenses against budgets or calculating loan balances. In construction and engineering, subtraction determines material needs and tolerances. The skill forms the foundation for more advanced mathematical concepts including negative numbers, algebraic equations, and calculus derivatives. Students encounter subtraction in word problems involving comparisons, such as finding how many more votes one candidate received than another (Sara: 347 votes, Mike: 289 votes, difference: 58 votes). Without solid subtraction skills, learners struggle with multi-step problems and higher-level mathematics that require breaking down complex calculations into component parts.
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
5 - _______ = 2
Answer: 3
- Read the problem → 5 - ? = 2 — We know the start (5) and end (2). We need the missing piece.
- Find the gap → 5 - 2 = 3 — How far is it from 2 to 5? It is 3. That is the missing number.
- Check → 5 - 3 = 2 ✓ — Put it back: 5 - 3 = 2. Correct!
There are 16 people in a queue. 7 leave. How many remain?
Answer: 9
- Look at what we are taking away → 16 - 7 — We start with 16 and need to take away 7. Imagine you have 16 candies and eat 7 of them.
- Count back from the bigger number → 16 - 7 = 9 — Start at 16 and subtract 7. We get 9.
- Check: add back to verify → 9 + 7 = 16 ✓ — To check subtraction, add the answer back: 9 + 7 = 16. It matches what we started with, so we are correct!
Solve: 56 - 28 -----
Answer: 28
- Look at what we are subtracting → 56 - 28 — We need to take 28 away from 56. We will do this column by column, starting from the ones (right side), just like you unstack blocks.
- Ones column: we need to borrow! → 6 < 8 → borrow 10 from tens — We cannot take 8 from 6 (that would go below zero). So we borrow 1 ten (which is 10 ones) from the tens column. Now we have 16 ones and 4 tens.
- Subtract the ones → 16 - 8 = 8 — Now 16 - 8 = 8. That is the ones digit of our answer.
- Subtract the tens → 4 - 2 = 2 — Remember we borrowed, so the tens are now 4 - 2 = 2.
- Put the digits together → 56 - 28 = 28 — Tens digit 2 and ones digit 8 give us 28.
- Check: add back to verify → 28 + 28 = 56 ✓ — Adding 28 + 28 gives 56. Our subtraction is correct!
Common mistakes
- When borrowing in problems like 43 - 17, writing 46 instead of 26 by forgetting to reduce the tens digit after borrowing from it
- Subtracting the smaller digit from the larger digit regardless of position, producing 64 - 29 = 45 instead of 35 by calculating 9 - 4 = 5 in the ones place
- In vertical subtraction like 80 - 23, writing 63 instead of 57 by subtracting 8 - 2 = 6 and 0 - 3 = 3 without proper borrowing