Quick Mental Math Tricks – Each With a Timed Drill

How it works

These quick mental math tricks come one to a drill. Read a trick and its worked example in the list further down, then run it against the clock. Every answer is whole, and the score is correct answers a minute.

Read the full guide

Why the tricks near 100 work

(100 + a) × (100 + b) is 100 × (100 + a + b) plus a × b. The first part is one number plus the other's extra, with two zeros after it, and a × b fills the zeros. Under 100 an extra is a gap and counts as minus.

Why a square comes from its neighbour

One step up, a square grows by the number plus the next one: 61² is 3,600 + 60 + 61 = 3,721. One step down it shrinks the same way: 59² is 3,600 − 60 − 59 = 3,481.

Mental math tricks training

Take one trick at a time: work its example on paper, then run its drill until the score stops rising. Then move to a mix.

Check the last digit before you type: 104 × 107 must end in 8, because 4 × 7 does.
Say the big part first. For 96 × 107, hold 10,300 in your head, then take off 28.

Questions and answers

What are the best tricks to do mental math fast?

The ones that swap a hard sum for an easy one. Go through a round number, lean on a square you already know, or turn a multiplication into a division: 64 × 125 is an eighth of 64, which is 8, counted in thousands.

What are some cool mental math tricks?

12 × 37 is 444 and 21 × 37 is 777, because 3 × 37 is 111. 45 × 111 is 4,995: the two digits with their sum written twice between them. And 96² is 9,216: 96 less 4, then 4² as two digits.

How does the mental math trick for squaring numbers in the teens work?

A teen's square is 100, plus twenty times its ones digit, plus the digit squared. The first two parts are the number plus the digit, times ten. For 14²: 14 + 4 is 18, so 180, plus 16: 196.

Are these mental math trick games?

Each drill plays like one: a single trick, a clock, and a score to beat on the next run. There are no levels, lives or leaderboards, and a score is only ever compared with your own earlier runs.

Where are the other mental math tips and tricks, like times 11 and times 99?

On the pages that already drill them. Mental math multiplication has times 4, 8, 15 and 99 and teens times teens. Mental math practice has times 11, squares ending in 5 and change from 1,000.

All 16 drills

Near 100 3

One under 100, one over Take the smaller number's gap from the larger number, write two zeros, then subtract the two gaps multiplied: 97 × 104 is 101 with two zeros, 10,100, less 3 × 4 = 12, so 10,088.
Squares near 100 Move the number its own gap further from 100, then write the gap squared as two digits: 97² is 94 and 09, so 9,409, and 104² is 108 and 16, so 10,816.
Two numbers just over 100 Add the extra of one number to the other, then write the two extras multiplied as two digits: 103 × 106 is 109, then 3 × 6 = 18, so 10,918.

Squares 4

Squares ending in 1 Square the round number just below, then add that number and the next one: 31² is 900 + 30 + 31 = 961.
Squares ending in 4 or 6 Start from the square ending in 5 next door and add or take away the two numbers: 36² is 35² = 1,225 plus 35 + 36, so 1,296, and 34² is 1,225 − 35 − 34 = 1,156.
Squares ending in 9 Square the round number just above, then take away that number and the one below it: 29² is 900 − 30 − 29 = 841.
Squares of the teens Add the ones digit to the number, multiply by ten, then add the ones digit squared: 17² is 17 + 7 = 24, so 240, plus 49 = 289.

Handy numbers 5

Divide by 125: eight to the thousand Every 1,000 holds eight 125s and every 500 holds four: 3,625 ÷ 125 is 24 for the 3,000, 4 for the 500 and 1 more, so 29.
Times 16: double four times Keep doubling until you have done it four times: 35 × 16 runs 70, 140, 280, 560.
Times 37: multiples of 3 3 × 37 is 111, so take a third of the other number and count in 111s: 27 × 37 is nine of them, 999, and 36 × 37 is twelve, 1,332.
Times 75: three quarters of a hundred Take a quarter of the other number, multiply it by 3 and write two zeros: 36 × 75 is 9, then 27, so 2,700.
Times 125: an eighth of a thousand 125 is 1,000 ÷ 8, so take an eighth of the other number and count it in thousands: 48 × 125 is 6 thousands, 6,000, and 12 × 125 is one and a half, 1,500.

Elevens 2

Three digits times 11 Keep the first and last digits and write the sum of each pair of neighbours between them: 342 × 11 is 3, then 3 + 4, then 4 + 2, then 2, so 3,762. A sum of ten or more carries one to the left.
Times 111: digits that add to 9 or less Write the first digit, the sum of the two digits twice, then the last digit: 34 × 111 is 3, 7, 7, 4, so 3,774.

Mixed 2

Near 100 mix Two numbers just over 100, one under and one over, and squares near 100 in one run, so you have to pick the right trick each time.
Quick tricks warm-up The four gentlest tricks shuffled together: squares of the teens, times 111, times 125 and times 75.