Subtraction (Core Skills)
Find the difference between quantities using borrowing and regrouping — the core skill behind budgeting, change-making, and tracking what's left.
Subtraction tells you what's left. After paying bills, after giving change, after making a purchase — subtraction shows your remaining balance. Borrow incorrectly, and your numbers are off from the very first step.
- Subtract multi-digit numbers using the column method
- Apply regrouping (borrowing) when a top digit is smaller than the bottom digit
- Subtract across zeros without losing your place
Subtraction finds the difference between two quantities. Like addition, you work right to left. When the top digit is smaller than the bottom digit in a column, you borrow — take 1 ten from the column to the left, which adds 10 to your current column.
\[ \text{Minuend} - \text{Subtrahend} = \text{Difference} \]The Borrowing Process
When you can't subtract because the top digit is smaller, borrow from the next column to the left:
Example: 403 − 167 — borrowing across a zero
| adjusted → | 3 | 9 | 13 |
| 4 | 0 | 3 | |
| − | 1 | 6 | 7 |
| 2 | 3 | 6 | |
Calculate: \(52 - 38\)
- Ones: \(2 - 8\) — can't do it. Borrow from tens: 5 becomes 4, ones become 12.
- Ones: \(12 - 8 = 4\)
- Tens: \(4 - 3 = 1\)
Calculate: \(403 - 167\)
- Ones: \(3 - 7\) — can't. Tens column is 0, so skip to hundreds.
- Borrow from hundreds: 4 → 3. Give to tens: 0 → 10. Borrow from tens: 10 → 9. Give to ones: 3 → 13.
- Ones: \(13 - 7 = 6\). Tens: \(9 - 6 = 3\). Hundreds: \(3 - 1 = 2\).
You start the month with $1,500. You spend $387 on rent deposit and $428 on furniture. How much is left?
- Total spent: \(387 + 428 = 815\)
- Remaining: \(1{,}500 - 815 = 685\)
You have $685 remaining for the rest of the month.
Try these:
- Calculate: \(84 - 47\)
- Calculate: \(600 - 253\)
- Your paycheck is $2,340. After rent of $950, what's left?
▶ Show Answers
- 37 — borrow from 8: ones become 14, 14−7=7; tens 7−4=3.
- 347 — borrow across two zeros: 600 → 599+10 in ones column.
- $1,390 — 2,340 − 950 = 1,390.
- Subtracting the larger from the smaller: 3 − 7 is not 4. You must borrow — never flip the digits.
- Forgetting to reduce the borrowed column: When you borrow from a digit, that digit decreases by 1. Skip this step and your answer will be off by 10 or more.
- Borrowing across a zero: You can't borrow from zero — you must skip to the next non-zero column and cascade the borrow back. This is the most common error.
- Subtract right to left — start at the ones column.
- Borrow when top < bottom — take 1 from the next column left, adding 10 to the current column.
- Zeros need a chain borrow — skip to the nearest non-zero column, then cascade back.
- Subtraction is not commutative — \(10 - 3 \neq 3 - 10\). Order always matters.
Retail cashiers calculate change by subtracting the purchase from the amount tendered. Warehouse managers subtract consumed inventory from starting stock to track what remains. In both cases, a borrowing error produces a wrong answer that directly affects customers or operations.
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Subtraction (Core Skills) — Quiz
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