Mental math shortcuts
Most arithmetic on the test has a faster route than writing it out.
Times 5
Multiply by 10, then halve.
68 × 5 → 680 ÷ 2 = 340
Times 25
Multiply by 100, then divide by 4.
36 × 25 → 3,600 ÷ 4 = 900
Times 9
Multiply by 10, then take away the number once.
47 × 9 → 470 − 47 = 423
Times 11, two digits
Spread the digits apart and put their sum in the middle. If the sum is 10 or more, carry the 1.
53 × 11 → 5 _ 3 with 5 + 3 = 8 in the middle = 583
Squaring a number ending in 5
Multiply the front part by one more than itself, then write 25 after it.
→ 6 × 7 = 42, then 25 = 4,225
Two numbers the same distance from a round one
Use (a + b)(a − b) = a² − b².
48 × 52 → = 2,500 − 4 = 2,496
Halve one, double the other
The product stays the same. Keep going until it is easy.
16 × 35 → 8 × 70 = 560
Percents swap
x% of y is the same as y% of x. Pick whichever is easier.
8% of 50 → 50% of 8 = 4
Build a percent from 10% and 1%
10% moves the decimal one place left, 1% moves it two. Add up the pieces.
15% of 240 → 10% is 24, 5% is 12, together 36 = 36
AFOQT questions on this: Order of operations · Percent of a number · Signed numbers