Subtraction

What is Subtraction?

Subtraction finds the difference between two numbers, or what remains after taking one amount away from another.

Symbol: − | Result: difference

In a subtraction: minuend − subtrahend = difference

• Minuend: the number you start with
• Subtrahend: the number you take away
• Difference: the result

Example: 742 − 385 = 357 (742 is the minuend, 385 is the subtrahend, 357 is the difference)

Column Subtraction

Column subtraction lines up digits by place value (hundreds, tens, ones) and subtracts column by column from right to left.

Example: 742 − 385

  742
- 385
-----

Ones column: 2 − 5. Cannot do this, so borrow from the tens. The 4 in the tens becomes 3, and the 2 becomes 12. 12 − 5 = 7

Tens column: 3 (after borrowing) − 8. Cannot do this, so borrow from the hundreds. The 7 in the hundreds becomes 6, and the 3 becomes 13. 13 − 8 = 5

Hundreds column: 6 (after borrowing) − 3 = 3

Result: 357

Borrowing (Regrouping)

Borrowing (also called regrouping) is needed when a digit in the minuend is smaller than the digit below it.

When you borrow:

1. Take 1 from the column to the left
2. Add 10 to the current column
3. Then subtract

Example: 1,000 − 364

There are zeros in every column — you must borrow through each one:

• Borrow from the thousands: 1,000 becomes 0 thousands, 9 hundreds, 9 tens, 10 ones
• Ones: 10 − 4 = 6
• Tens: 9 − 6 = 3
• Hundreds: 9 − 3 = 6

Result: 636

A quick trick: 1,000 − 364. Subtract from 999 first (999 − 364 = 635), then add 1. Result: 636.

Subtracting from Round Numbers

When subtracting from numbers ending in zeros, the borrowing chain can be long. A useful shortcut:

5,000 − 1,847: Think of 4,999 − 1,847 = 3,152, then add 1 → 3,153

Or just borrow carefully column by column.

Mental Subtraction Strategies

Count up (complementary addition): To find 83 − 47, count up from 47 to 83: 47 → 50 (+3) → 80 (+30) → 83 (+3) = 36

This is often faster than column subtraction for two-digit numbers.

Round and adjust: 75 − 29: round 29 up to 30, subtract, then add 1 back 75 − 30 = 45, then 45 + 1 = 46

84 − 39: round 39 up to 40, subtract, then add 1 back 84 − 40 = 44, then 44 + 1 = 45

Breaking apart: 83 − 47 = 83 − 40 − 7 = 43 − 7 = 36

Checking Your Answer

Always check subtraction by adding back:

If 742 − 385 = 357, then 357 + 385 should equal 742.

357 + 385 = 742 ✓

This works because subtraction and addition are inverse operations.

Word Problem Clue Words

Look for these words to know subtraction is needed:

difference, less than, fewer, remain, left over, how many more, how much change, decreased by, reduced by, took away

Example: "A shop has 1,200 items. 463 are sold. How many remain?" 1,200 − 463 = 737

Example: "Jo has 85 stickers. Sam has 48. How many more does Jo have?" 85 − 48 = 37

Multi-Step Problems

Some problems require more than one subtraction, or a mix of operations.

Example: A baker makes 300 loaves. 127 are sold in the morning and 94 in the afternoon. How many are left?

Step 1: 127 + 94 = 221 total sold Step 2: 300 − 221 = 79 loaves remaining

Common Mistakes

• Forgetting to reduce the borrowed column by 1
• Subtracting the larger digit from the smaller without borrowing (e.g. writing 5 − 9 = 4 instead of borrowing)
• Losing track of the borrow when there are multiple zeros in the minuend
• Subtracting in the wrong order (subtrahend from minuend, not the other way round)

Tips and Tricks

• Always work right to left in column subtraction (ones first, then tens, then hundreds)
• Use the count-up method when the numbers are close together
• Use round-and-adjust when the subtrahend ends in 8 or 9
• Always check your answer by adding back — it takes seconds and catches errors
• Estimate first: 742 − 385 ≈ 740 − 390 = 350, so 357 is a reasonable answer