How to subtract in your head without losing track
Three ways to make subtraction easier, and how to choose between them.
The trick is to change the route, not the answer
To subtract in your head, try one of three routes: break the number into parts, round it and adjust, or count up to find the gap. For 83 − 29, rounding is convenient: subtract 30 to get 53, then add 1 back to get 54. You subtracted one too many. That last adjustment is what keeps the answer correct.
Method 1: subtract tens, then ones
For 76 − 34, split 34 into 30 and 4. First, 76 − 30 = 46. Then, 46 − 4 = 42. You only need to hold one running total in mind. This method is useful when the number you are taking away is not especially close to a round number. For 92 − 47, subtract 40 to get 52, then subtract 7 to get 45. You can break that last 7 into 2 and 5 if crossing a ten feels awkward: 52 − 2 = 50, then 50 − 5 = 45.
Method 2: round, then put the extra back
Numbers ending in 8 or 9 often invite rounding. For 145 − 98, take away 100 to get 45, then restore the extra 2: the answer is 47. Check the direction of the adjustment by asking what you actually did. Taking away 100 instead of 98 made the result too small, so add 2. For 63 − 21, you might round down instead: subtract 20 to get 43, then take away the remaining 1 to get 42. Rounding up and rounding down need opposite adjustments.
Method 3: count the distance between the numbers
Subtraction also asks how far apart two numbers are. To find 102 − 87, count from 87 to 90: that is 3. From 90 to 100 is 10 more, and from 100 to 102 is another 2. Add the jumps: 3 + 10 + 2 = 15. This is particularly convenient when the numbers are close together. It also works for decimal amounts: from 8.75 to 9 is 0.25, and from 9 to 10 is 1, so 10 − 8.75 = 1.25. Keep the place values aligned when you add those jumps.
Choose the easiest route for this particular problem
There is no need to use the same method every time. Try tens and ones for 76 − 34, rounding for 145 − 98, and counting up for 102 − 87. If a method makes you hold too many steps in memory, write them down while learning it. The goal is to understand why each step works before trying to make it fast.
Check by adding back
Your answer plus the amount subtracted should give the starting number. For 145 − 98 = 47, check 98 + 47 = 145. A rough estimate can catch larger slips too: 145 − 98 should be near 145 − 100, so an answer around 45 is plausible. An estimate is a useful warning light, while adding back checks the exact calculation.
Try these before opening the answers
Work out 84 − 32, 156 − 99, and 203 − 188. Choose the method that needs the fewest comfortable steps. Then compare your reasoning with the worked answers below.
Check your answers
84 − 32
52. Subtract 30 to get 54, then subtract 2.
156 − 99
57. Subtract 100 to get 56, then add 1 back.
203 − 188
15. Count up 12 to 200, then another 3 to 203.
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