Mental Math Strategies for Subtraction

Core Idea

Mental math strategies for subtraction include counting on, counting back, using tens, and relating subtraction to addition. For example, 45 - 18 can be solved by counting up from 18 to 45 (18 → 20 → 45 is 2 + 25 = 27).

Explainer

Mental subtraction feels harder than mental addition, but there is a secret: you do not have to subtract at all. You already know from your work on number relationships that subtraction and addition are inverses — 45 − 18 asks the same question as "what do I add to 18 to reach 45?" This reframe, called counting on, turns a subtraction problem into a more natural addition problem.

Here is counting on in action for 45 − 18. Start at 18. The nearest friendly ten is 20, so first add 2 to get there (18 → 20). Now jump by tens: 20 → 30 → 40 is two jumps of 10. One more jump of 5 lands on 45. Add up your jumps: 2 + 10 + 10 + 5 = 27. You never subtracted; you collected small additions. Each hop targeted a ten, which you can hold in memory easily.

The use-tens strategy works differently, but also leans on landmark numbers. To compute 45 − 18, round the number being subtracted to the nearest ten: 18 rounds up to 20. Subtracting 20 from 45 is easy: 25. But you subtracted 2 too many (you subtracted 20 instead of 18), so add them back: 25 + 2 = 27. This adjust-and-correct pattern — overshoot a friendly number, then compensate — is a theme that appears throughout arithmetic and algebra. The adjustment is always the difference between the rounded number and the original.

Choosing which strategy to use is itself a skill. Counting on works best when the two numbers are close together (e.g., 62 − 57 is 5 hops). Using-tens works best when one number is close to a multiple of ten (e.g., 71 − 29 rounds 29 to 30, subtract to get 41, add 1 back). With practice, you will start recognizing which approach fits a given problem in a few seconds — the hallmark of number sense, the ability to see numbers flexibly rather than mechanically.