🧠 15 Mental Math Tricks to Solve Operations in Seconds
Why learn mental math?
It's technique, not magic
Mental math is a practical skill we use every day: tips, discounts, splitting a bill... Each of the 15 strategies below comes from a property of our number system, and each one includes why it works, its limits and the most common mistake. Understanding the "why" matters as much as the "how".
✖️Multiplication Strategies
Multiply by 11 (2-digit numbers)
basicSeparate the digits and put their sum in the middle.
How to do it:
- 1Separate the two digits: 36 → 3_6
- 2Add them: 3 + 6 = 9
- 3Put the sum in the middle: 3(9)6 = 396
- 4If the sum is 10 or more, carry 1 to the first digit (see special case)
Try it:
⚠️ Special case:
4 + 7 = 11 → carry the 1: (4+1)(1)7 = 517. Not 4(11)7.
Multiply by 5
basicHalve the number and multiply by 10.
How to do it:
- 1Halve the number: 48 ÷ 2 = 24
- 2Multiply by 10 (add a 0): 24 × 10 = 240
- 3Done! 48 × 5 = 240
Try it:
9 times table with your fingers
basicA visual trick for the 9 times table.
How to do it:
- 1Hold up your 10 fingers (numbered 1-10 from the left)
- 2For 9 × 7, fold down finger number 7
- 3Fingers to the left of it: 6 (tens)
- 4Fingers to the right of it: 3 (ones)
- 5Result: 63
Try it:
Multiply by 25
intermediateDivide by 4 and multiply by 100.
How to do it:
- 1Divide by 4: 48 ÷ 4 = 12
- 2Multiply by 100 (add two zeros): 12 × 100 = 1200
- 3Done! 48 × 25 = 1200
Try it:
⚠️ Special case:
87 ÷ 4 = 21.75 → 21.75 × 100 = 2175. A whole number divided by 4 has at most two decimals, and × 100 removes them.
Squaring numbers that end in 5
intermediateRemove the 5, multiply what is left by the next number and write 25 at the end.
How to do it:
- 1Remove the final 5: 35 leaves 3 (115 would leave 11)
- 2Multiply it by the next number: 3 × 4 = 12
- 3Write 25 at the end: 12|25 = 1225
Try it:
⚠️ Special case:
7 × 8 = 56, then 25 → 5625
➗Division Strategies
Divide by 5
basicMultiply by 2 and divide by 10. The inverse of trick 2.
How to do it:
- 1Multiply by 2: 135 × 2 = 270
- 2Divide by 10 (remove a zero or move the decimal point): 270 ÷ 10 = 27
Try it:
Divisibility by 3
basicIf the sum of the digits is divisible by 3, so is the number.
How to do it:
- 1Add all the digits
- 2If the sum is divisible by 3, the number is too
- 3If the sum is large, repeat the process
Try it:
Divisibility by 9
basicSame idea: if the digits add up to a multiple of 9, the number is divisible by 9.
How to do it:
- 1Add all the digits
- 2If the sum is a multiple of 9, the number is divisible by 9
- 3Bonus: keep adding digits until one digit is left and you get the remainder when dividing by 9 (if it's 9, the remainder is 0). E.g. 89 → 17 → 8, and 89 = 9 × 9 + 8
Try it:
%Percentage Strategies
The swap trick
basicX% of Y = Y% of X. Pick the easier one.
How to do it:
- 1Asked for 8% of 50? Ask yourself which is easier
- 250% of 8 = 4 (half of 8)
- 3It's the same result!
Try it:
15% (tips)
basicFind 10% and add half of it.
How to do it:
- 110%: move the decimal point one place left: 10% of 80 = 8
- 25% is half of that: 8 ÷ 2 = 4
- 3Add them: 8 + 4 = 12
Try it:
20%
basicDivide by 5.
How to do it:
- 1Divide the number by 5
- 2That's 20%!
Try it:
➕Add, Subtract and Multiply Near 100
Add from left to right
intermediateStart with the digits that are worth most and keep a running total.
How to do it:
- 1Hundreds first: 300 + 200 = 500
- 2Then tens: 40 + 80 = 120 → 500 + 120 = 620
- 3Then ones: 7 + 5 = 12 → 620 + 12 = 632
Try it:
Round and adjust
basicRound one number to an easy one, then correct.
How to do it:
- 1Round one number: 198 → 200
- 2Do the easy sum: 200 + 347 = 547
- 3Undo the rounding: 547 − 2 = 545
Try it:
Subtract from 1000
intermediateSubtract each digit from 9, except the last non-zero digit, which you subtract from 10. Trailing zeros stay.
How to do it:
- 1For 1000 − 648:
- 2First digit: 9 − 6 = 3
- 3Second digit: 9 − 4 = 5
- 4Last non-zero digit: 10 − 8 = 2
- 5Result: 352
Try it:
⚠️ Special case:
It ends in 0: the 0 stays, the 4 (last non-zero digit) comes off 10 and the 6 off 9 → 360. With 2-digit numbers, think of 45 as 045: 1000 − 45 = 955.
Multiply numbers close to 100
advancedFor numbers like 97 × 96, use their distance from 100.
How to do it:
- 1Distance from 100: 97 → 3, 96 → 4
- 2Subtract one distance from the OTHER number: 97 − 4 = 93 (or 96 − 3 = 93)
- 3That gives the first digits: 93__
- 4Multiply the distances: 3 × 4 = 12
- 5That gives the last two digits: __12 (always two: 6 is written 06)
- 6Result: 9312
Try it:
⚠️ Special case:
Distances 2 and 7. First digits: 98 − 7 = 91. Last: 2 × 7 = 14. Result: 9114.
🧠Reasoning Exercises (Not Just Speed)
Focusing only on speed can increase math anxiety (Boaler, 2015). These exercises build understanding:
- Solve 47 × 11 two ways (digit trick and 47 × 10 + 47). Why do both give the same result?
- If × 11 is × (10 + 1), how would you multiply by 101? Try 23 × 101.
- Before working out 48 × 25: is it more or less than 1000? Closer to 1000 or 1500?
- If 35² = 1225, what is √1225? What clue does the ending 25 give?
- Invent a strategy to multiply by 15 (hint: 15 = 10 + 5).
⚠️ Speed vs understanding
Memorizing tricks is not the same as understanding mathematics. Make sure you know why each one works, practice without a timer if timing makes you anxious, and add tricks one at a time, starting with the simplest (× 5, × 10).
📚 References
- • Dehaene, S. (2011). The Number Sense (rev. ed.). Oxford University Press.
- • Willingham, D. T. (2009). Why Don't Students Like School? Jossey-Bass.
- • Boaler, J. (2015). Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts. Youcubed, Stanford University.
- • Tirthaji, B. K. (1965). Vedic Mathematics. Motilal Banarsidass. (Source of the Nikhilam method)
- • Sowder, J. (1988). Mental computation and number comparison. In J. Hiebert & M. Behr (Eds.), Number Concepts and Operations in the Middle Grades. NCTM.
- • NCTM (2014). Principles to Actions: Ensuring Mathematical Success for All. National Council of Teachers of Mathematics.
- • Benjamin, A., & Shermer, M. (2006). Secrets of Mental Math. Three Rivers Press.
Note: These strategies derive from properties of the decimal system (distributive, associative, commutative). Understanding the "why" is as important as the "how".
⭐ Was this article helpful?
Your feedback helps us improve