Mental math tricks that actually work

Fast mental arithmetic is not a talent; it is a handful of techniques used often enough that they become automatic. The idea behind all of them is the same: instead of copying the slow written method into your head, rearrange the problem into steps that are easy to hold in memory. Here are ten that pay off the most, each with examples and the reason it works — understanding why is what makes a trick stick.

1. Multiply by 5: multiply by 10, then halve

Because 5 = 10 ÷ 2, multiplying by 5 is the same as multiplying by 10 and halving.

• 48 × 5 → 480 ÷ 2 = 240
• 136 × 5 → 1360 ÷ 2 = 680
• Dividing by 5 works in reverse: double, then divide by 10. 370 ÷ 5 → 740 ÷ 10 = 74

2. Multiply by 9: multiply by 10, then subtract

9 × n = 10 × n − n. One easy multiplication and one subtraction.

• 9 × 47 → 470 − 47 = 423
• 9 × 86 → 860 − 86 = 774

The same idea gives × 99 (multiply by 100, subtract once): 99 × 23 = 2300 − 23 = 2277.

3. Multiply a two-digit number by 11: add the digits

Write the two digits apart and put their sum in the middle. If the sum is 10 or more, carry the 1 to the first digit.

• 11 × 34 → 3 _ 4, 3 + 4 = 7 → 374
• 11 × 72 → 7 _ 2, 7 + 2 = 9 → 792
• 11 × 68 → 6 _ 8, 6 + 8 = 14 → 6+1, 4, 8 → 748

It works because 11 × (10a + b) = 100a + 10(a + b) + b.

4. Square a number ending in 5

Take the tens part, multiply it by the next whole number, and write 25 after it.

• 35² → 3 × 4 = 12 → 1225
• 65² → 6 × 7 = 42 → 4225
• 95² → 9 × 10 = 90 → 9025

Algebra: (10a + 5)² = 100a(a + 1) + 25.

5. Percentages can be swapped

x% of y is the same as y% of x, because both equal x × y ÷ 100. Pick the direction that is easier.

• 8% of 50 = 50% of 8 = 4
• 16% of 25 = 25% of 16 = 4
• For other percentages, build from 10% and 1%: 15% of 240 = 24 + 12 = 36 (10% + 5%).

6. Round, then compensate

Numbers near a round number are easier to handle as “round number minus a little”.

• 398 + 247 → 400 + 247 − 2 = 645
• 7 × 49 → 7 × 50 − 7 = 343
• 1000 − 386 → think “what makes 386 up to 1000”: 14 to 400, 600 more → 614

7. Double and halve

In a product you can double one number and halve the other without changing the result. Keep going until one side is easy.

• 16 × 25 → 8 × 50 → 4 × 100 = 400
• 14 × 35 → 7 × 70 = 490
• 4.5 × 18 → 9 × 9 = 81

8. Split one number to multiply

Break the harder number into easy parts and add the pieces (the distributive law).

• 6 × 47 → 6 × 40 + 6 × 7 = 240 + 42 = 282
• 13 × 12 → 13 × 10 + 13 × 2 = 130 + 26 = 156

9. Add left to right

School taught us to add from the right because of carrying on paper. In your head, adding from the left keeps the size of the answer in view and needs less to remember.

• 456 + 378 → 400 + 300 = 700, 50 + 70 = 120 → 820, 6 + 8 = 14 → 834

10. Check with a quick estimate

Before you commit, ask whether the answer is the right size. 48 × 21 must be close to 50 × 20 = 1000, so an answer of 1008 is plausible and 108 is not. In BRINXO this rule alone removes most wrong answers, because the wrong choices are often the right digits in the wrong size.

Another fast check: the last digit. 37 × 23 must end in 1 (because 7 × 3 = 21), so any option ending in another digit is wrong before you calculate anything.

How to make these automatic

1. Learn one trick at a time. Try it on ten examples of your own on paper.
2. Use it under light pressure: play a round of Blitz and look for questions where it applies.
3. Keep a short daily habit. The Daily Challenge takes about two minutes and keeps the skills fresh.

After a week or two, you will notice you no longer “use a trick” — you simply see 9 × 47 as 470 − 47. That is the point where mental math becomes fast.