Quick Mental Math Tricks

Multiplying by 11

To multiply any two-digit number by 11, split the digits and place their sum in the middle. For example:

• 36 × 11: Split 3 and 6, place (3+6) = 9 in the middle. Answer: 396
• 72 × 11: Split 7 and 2, place (7+2) = 9 in the middle. Answer: 792
• 85 × 11: 8+5 = 13, carry the 1. Answer: 935

Percentage Shortcuts

Finding percentages mentally becomes easy if you start from 10% and adjust:

• 10%: Just move the decimal point one place left. 10% of 85 = 8.5
• 5%: Find 10% and halve it. 5% of 85 = 4.25
• 15%: Find 10% + 5%. 15% of 85 = 8.5 + 4.25 = 12.75
• 20%: Find 10% and double it. 20% of 85 = 17

Also remember: X% of Y equals Y% of X. So 8% of 50 is the same as 50% of 8, which is 4.

Squaring Numbers Ending in 5

Take the tens digit, multiply it by itself plus one, and append 25:

• 35²: 3 × 4 = 12, append 25. Answer: 1,225
• 75²: 7 × 8 = 56, append 25. Answer: 5,625

The 9s Multiplication Trick

For 9 × any single digit (1-10): the tens digit is one less than the multiplier, and the digits sum to 9.

• 9 × 7: One less than 7 is 6, and 6 + ? = 9, so the answer is 63
• 9 × 4: One less than 4 is 3, and 3 + ? = 9, so the answer is 36