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How to : How to Improve Mental Math Skills

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1

Break addition and subtraction problems into parts.

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    Add the hundreds, tens, and ones places separately. Treat each group as a separate problem:

    • 712 + 281 → “700 + 200,” “10 + 80,” and “2 + 1”
    • 700 + 200 = 900, then 10 + 80 = 90, then 2 + 1 = 3
    • 900 + 90 + 3 = 993.
    • Thinking in “hundreds” or “tens” instead of single digits will make it easier to keep track when digits sum to more than ten. For example, for 37 + 45, think “30 + 40 = 70” and “7 + 5 = 12”. Then add 70 + 12 to get 82.

2

Change the problem to make round numbers.

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    Adjust to get round numbers, then correct after the problem is done. Round numbers are much faster for most of us to work with. Keep a mental note of the changes you made so you can adjust to get the exact answer at the end.[1]
3

Learn to add many numbers at once.

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    Reorder the numbers to make convenient sums. An addition problem is the same no matter what order you solve it in. Look for numbers that add up to 10 or other nice, round numbers:

    • For example, 7 + 4 + 9 + 13 + 6 + 51 can be reorganized to (7 + 13) + (9 + 51) + (6 + 4) = 20 + 60 + 10 = 90.

4

Multiply from left to right.

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    Keep track of the hundreds, tens, and ones places. On paper, most people multiply the ones place first, going from right to left. But in your head, it’s easier to go the other way:

    • For 453 x 4, start with 400 x 4 = 1600, then 50 x 4 = 200, then 3 x 4 = 12. Add them all together to get 1812.
    • If both numbers have more than one digit, you can break it into parts. Each digit has to multiply with each other digit, so it can be tough to keep track of it all. 34 x 12 = (34 x 10) + (34 x 2), which you can break down further into (30 x 10) + (4 x 10) + (30 x 2) + (4 x 2) = 300 + 40 + 60 + 8 = 408.
5

Try a fast multiplication trick best for numbers 11 through 19.

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    Try this method of turning one hard problem into two easier ones. This is another way of breaking a problem into parts. It can be a little tricky to remember at first, but once you have it down it can make multiplication much faster. This is easiest when multiplying two numbers that are both in the range of 11 to 19, but you can learn to use it for other problems:[2]

6

Simplify problems with numbers ending in zero.

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    If the numbers end in zeroes, you can ignore them until the end:

    • Addition: If all numbers have zeroes at the end, you can ignore the zeroes they have in common and restore them at the end. 850 + 120 → 85 + 12 = 97, then restore the shared zero: 970.
    • Subtraction works the same way: 1000 – 700 → 10 – 7 = 3, then restore the two shared zeroes to get 300. Notice that you can only remove the two zeroes the numbers have in common, and must keep the third zero in 1000.
    • Multiplication: ignore all the zeroes, then restore each one individually. 3000 x 50 → 3 x 5 = 15, then restore all four zeroes to get 150,000.
    • Division: you can remove all shared zeroes and the answer will be the same. 60,000 ÷ 12,000 = 60 ÷ 12 = 5. Don’t add any zeroes back on.
7

Easily multiply by 4, 5, 8, or 16.

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    You can convert these problems so they only use 2s and 10s. Here’s how:

    • To multiply by 5, instead multiply by 10, then divide by 2.
    • To multiply by 4, instead double the number, then double it again.
    • For 8, 16, 32, or even higher powers of two, just keep doubling. For example, 13 x 8 = 13 x 2 x 2 x 2, so double 13 three times: 13 → 26 → 52 → 104.

8

Memorize the 11s trick.

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    You can multiply a two-digit number by 11 with barely any math. Add the two digits together, then put the result in between the original digits:[4]
9

Turn percentages into easier problems.

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    Know which percentages are easier to calculate in your head. There are a couple useful tricks to know:[5]

10

Memorize advanced multiplication shortcuts for specific problems.

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    These tricks are powerful, but narrow. They can turn a seemingly impossible mental math task into a quick task, but will only work on a very small percentage of problems. Learn these if you are already pretty good at mental math and want to approach “mathemagician” levels of speed:

    • For problems like 84 x 86, where the tens place is the same and the ones place digits sum to exactly 10, the first digits of the answer are (8 + 1) x 8 = 72 and the last digits are 4 x 6 = 24, for an answer of 7224. That is, for a problem AB x AC, if B + C = 10, the answer starts with A(A+1) and ends with BC. This also works for larger numbers if all digits besides the ones place are identical.[6]
    • You can rewrite the powers of five (5, 25, 125, 625, …) as powers of 10 divided by an integer (10 / 2, 100 / 4, 1000 / 8, 10000 / 16, …).[7]
11

Memorize squares charts.

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    Squares charts give you a new way to multiply. Memorizing your multiplication tables from 1 to 9 makes single-digit multiplication automatic. But for larger numbers, instead of trying to memorize hundreds of answers, it’s more efficient to memorize just the squares instead (each number times itself). With a little extra work, you can use these squares to find the answer to other problems:[8]

12

Find useful ways to practice your mental math.

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    Daily practice will make a huge difference.[9]

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Tips

  • Some people find it easier to think in money than abstract numbers. Instead of 100 – 55, try thinking of a dollar minus a 50¢ coin and a 5¢ coin.

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  • In the real world, you don’t always need to know the exact answer. If you’re at the grocery store and trying to add 7.07 + 8.95 + 10.09, you could round to the closest whole numbers and estimate that the total is roughly 7 + 9 + 10 = 26.

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