Subtraction

You have 8 candies and eat 3. How many are left? $8 - 3 = 5$ . Where addition combines two groups, subtraction runs backwards: it takes away one group from another. But subtraction has a second job too — comparing.

Two meanings: take away or compare

Take away: eat 3 of 8 candies and $8 - 3 = 5$ remain;
Compare: a brother is 12, his sister is 9, and the gap is $12 - 9 = 3$ years. Nobody took years away from anyone — subtraction here just measures the distance between two points.

The same sentence $12 - 9 = 3$ tells both stories. The result of subtraction is called the difference.

InteractiveSubtraction Drill

16 − 6 = ?

🔥 0 · ★ 0

Column subtraction: borrow when short

Line the digits up and start from the ones; when a column is too small, borrow 1 from the next place and treat it as 10. Watch the classic troublemaker $803 - 567$ :

	Hundreds	Tens	Ones
	7	9	13
	8	0	3
−	5	6	7
	2	3	6

The top row shows the numbers after borrowing. Step by step:

Ones: 3 cannot cover 7, so it borrows from the tens — but the tens is 0! The hundreds must step in: 8 becomes 7, the tens receives 10, lends 1 to the ones and keeps 9, and the ones becomes 13;
Ones $13 - 7 = 6$ , tens $9 - 6 = 3$ , hundreds $7 - 5 = 2$ — the answer is 236.

Check by adding back

Subtraction and addition are inverse operations: difference + subtracted number = the starting number. $236 + 567 = 803$ — the check passes.

Common trap

Borrowing across a 0 is the risky move: the 0 has nothing to lend and must fetch from the place above. With numbers like 803 or 9006, slow down.

Subtraction is not commutative

$8 - 3 = 5$ , but $3 - 8 = -5$ — swap the order and the story changes completely. Subtraction does not allow swapping: $a - b$ and $b - a$ are equal only when $a = b$ .

Two special cases are easy to love: subtracting 0 changes nothing ( $7 - 0 = 7$ ), and subtracting a number from itself gives 0 ( $7 - 7 = 0$ ).

Subtraction words in word problems

Left, remain, spent, ate, change (money), difference, "how many more", "how many fewer".

"A book costs 45 dollars and you pay with 100 — how much change?" — $100 - 45 = 55$ . "Ming has 34 cards and Amy has 42 — how many more does Amy have?" — $42 - 34 = 8$ : to compare, subtract the smaller from the larger. That is the "compare" subtraction from the first section.

Check yourself

Quick quiz

1. 803 − 567 = ?
2. Which statement is always true?
3. Ming has 34 cards and Amy has 42. Which expression finds how many more Amy has?