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Mental Math Shortcuts & Tricks

47 cards · 🇺🇸 English

Fast calculation tricks: squaring, multiplying near round numbers, percentages.

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Mental calculation

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1Mental calculation
Arithmetical calculations made by the mind, with no help from supplies (pencil/paper) or devices (calculator)
2Quickly multiply any number by 10
Add a zero to the end (or move decimal point right one place): 37 × 10 = 370
3Quickly multiply any number by 5
Multiply by 10 and divide by 2: 28 × 5 = (28 × 10) ÷ 2 = 280 ÷ 2 = 140
4Quickly multiply any number by 9
Multiply by 10 and subtract the original number: 47 × 9 = (47 × 10) - 47 = 470 - 47 = 423
5Quickly multiply any number by 11 (2 digits)
Add the two digits and put the sum in the middle: 54 × 11 = 5[5+4]4 = 594
6What if the sum exceeds 9 when multiplying by 11?
Carry the tens digit: 78 × 11 = 7[7+8]8 = 7[15]8 = (7+1)[5]8 = 858
7Square a number ending in 5 (2 digits)
First digit × (first digit + 1), then append 25: 35² = 3×4|25 = 1225
8Quickly multiply by 25
Divide by 4 (or multiply by 100 and divide by 4): 16 × 25 = 16 ÷ 4 × 100 = 400
9Quickly multiply by 50
Divide by 2 and multiply by 100: 28 × 50 = (28 ÷ 2) × 100 = 1400
10Quickly multiply by 99
Multiply by 100 and subtract the original: 53 × 99 = (53 × 100) - 53 = 5300 - 53 = 5247
11Add numbers close to multiples of 10
Round to 10s, add, then adjust: 28 + 47 = (30 + 50) - 2 - 3 = 80 - 5 = 75
12Quickly find 10% of a number
Move decimal point left one place: 10% of 850 = 85.0
13Quickly find 5% of a number
Find 10% then divide by 2: 5% of 200 = (10% = 20) ÷ 2 = 10
14Quickly find 15% (for tips)
Find 10% + 5%: 15% of 80 = 8 + 4 = 12
15Quickly find 20% of a number
Divide by 5 (or multiply by 2 then divide by 10): 20% of 150 = 150 ÷ 5 = 30
16Square numbers ending in 1 (mental trick)
Use (n-1)² + 2n - 1: 41² = 40² + 82 - 1 = 1600 + 81 = 1681
17Multiply two numbers close to each other
Use (a+b)(a-b) = a² - b²: 23 × 17 = 20² - 3² = 400 - 9 = 391
18Quickly check divisibility by 3
Sum the digits; if divisible by 3, the number is: 123 → 1+2+3=6, divisible by 3
19Quickly check divisibility by 9
Sum the digits; if divisible by 9, the number is: 729 → 7+2+9=18, divisible by 9
20Quickly check divisibility by 6
Must be even AND divisible by 3: 48 is even, 4+8=12 (divisible by 3), so 48÷6 works
21Quickly check divisibility by 4
Last two digits divisible by 4: 1324, check 24÷4=6, so yes
22Quickly check divisibility by 8
Last three digits divisible by 8: 5024, check 024÷8=3, so yes
23Multiply numbers near 100
Use (100-a)(100-b) = 10000 - 100(a+b) + ab: 97×94 = 100(97-6) + (-3)(-6) = 9100+18 = 9118
24Left-to-right addition method
Add from left to right (largest place first): 345+278 = (300+200)+(40+70)+(5+8) = 500+110+13 = 623
25Compensation method for addition
Round one number, add, then compensate: 567+298 = 567+300-2 = 865
26Multiply by doubling and halving
If one number is even, double it and halve the other: 16×35 = 32×17.5 = 64×8.75... (or 8×70=560)
27Russian peasant multiplication method
Repeatedly double one, halve the other, sum odds: 23×17: double 17 (34,68,136,272), halve 23 (11,5,2,1), sum odd rows
28Quickly multiply by 12
Multiply by 10, then add 2x the original: 34×12 = 340+68 = 408
29Square numbers near 50
Use 50² ± (difference)² formula: 47² = 2500 - (3×100) + 9 = 2209
30Subitizing in mental math
The ability to instantly recognize small quantities (1-4) without counting