Techniques

🧠 15 Mental Math Tricks to Solve Operations in Seconds

10 de enero de 20268 min
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Este artículo está en inglés. Leer la versión en español: 15 Trucos de Cálculo Mental para Resolver Operaciones en Segundos

Calculate like a genius

Techniques used by math champions

Mental math isn't magic, it's technique. The tricks you'll learn here are the same ones used by mental calculation champions and math teachers around the world. With practice, you'll be able to solve operations that seem impossible in just seconds.

📚 Scientific basis:Research in cognitive neuroscience (Dehaene, 2011) shows that mental calculation activates the intraparietal sulcus, a brain region that develops with practice. Children who regularly practice mental math show greater activation in this area and better performance in standardized tests.

✖️Multiplication Tricks

1

Multiply by 11 (2-digit numbers)

basic

The most impressive trick: separate the digits and add in the middle.

How to do it:

  1. 1Separate the two digits: 36 → 3_6
  2. 2Add both digits: 3 + 6 = 9
  3. 3Place the result in the middle: 3(9)6 = 396
  4. 4If sum is ≥10, carry 1 to the first digit (see special case)

Try it:

36 × 11

⚠️ Special case:

47 × 11 = 517

4+7=11 → The 1 carries: (4+1)(1)7 = 517. Not 4(11)7.

2

9 times table with fingers

basic

A visual trick that never fails for the 9 times table.

How to do it:

  1. 1Extend your 10 fingers in front of you (numbered 1-10)
  2. 2For 9×7, lower finger number 7
  3. 3Count fingers to the left of the lowered one: 6 (tens)
  4. 4Count fingers to the right: 3 (ones)
  5. 5Result: 63

Try it:

9 × 7
3

Multiply by 5

basic

Divide by 2 and multiply by 10. Much easier than multiplying directly.

How to do it:

  1. 1Divide the number by 2: 48 ÷ 2 = 24
  2. 2Multiply the result by 10 (add a 0): 24 × 10 = 240
  3. 3Done! 48 × 5 = 240

Try it:

48 × 5

Ready to practice multiplication?

Test these tricks with interactive exercises on MatesRetos

➗Division Tricks

4

Divide by 5

basic

Multiply by 2 and divide by 10. The inverse of multiplying by 5.

How to do it:

  1. 1Multiply the number by 2: 135 × 2 = 270
  2. 2Divide by 10 (remove a zero or move decimal): 27

Try it:

135 ÷ 5
5

Divisibility by 3

intermediate

A number is divisible by 3 if the sum of its digits is divisible by 3.

How to do it:

  1. 1Add all the digits: 1 + 4 + 7 = 12
  2. 2Check if the sum is divisible by 3: 12 ÷ 3 = 4
  3. 3If yes, the original number is divisible by 3

Try it:

Is 147 divisible by 3?

%Percentage Tricks

6

Calculate 10%

basic

Simply move the decimal point one place to the left.

How to do it:

  1. 1Take the number: 85
  2. 2Move the decimal one place left: 8.5
  3. 3That's your 10%

Try it:

10% of 85
7

Calculate 15% (tips)

intermediate

Calculate 10%, then add half of that (5%).

How to do it:

  1. 1Calculate 10%: 80 → 8
  2. 2Calculate 5% (half of 10%): 8 ÷ 2 = 4
  3. 3Add them: 8 + 4 = 12

Try it:

15% of 80

Ready to practice percentages?

Test these tricks with interactive exercises on MatesRetos

The Key is Practice

These tricks only become automatic with regular practice. Start with the easiest ones and add more as you master them. In a few weeks, you'll be calculating faster than most people with a calculator.

📚 References

  • • Dehaene, S. (2011). The Number Sense. Oxford University Press.
  • • 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. (Origin of the Nikhilam method for multiplication)
  • • Sowder, J. (1988). Mental computation and number comparison. In M. Behr & J. Hiebert (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.
  • • Sowder, J. (1992). Estimation and number sense. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning.
  • • Trachtenberg, J. (1960/2013). The Trachtenberg Speed System of Basic Mathematics.
  • • Benjamin, A. (2006). Secrets of Mental Math. Three Rivers Press.

Note: These strategies derive from fundamental properties of the decimal system (distributive, associative, commutative). Understanding the "why" is as important as the "how".

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