50 Math Tricks That Will Change Your Life

Here’s a list of 50 math tricks that can help make everyday calculations faster and easier:

### 1. **Multiplying by 9**:
To multiply any number by 9, multiply the number by 10 and subtract the number itself.
Example: 9 × 6 = (10 × 6) – 6 = 60 – 6 = 54.

### 2. **Multiplying by 11**:
To multiply any two-digit number by 11, add the digits together and place the sum between them.
Example: 23 × 11 = 2 + 3 = 5 → 253.

### 3. **Multiplying by 5**:
Multiply the number by 10 and then divide by 2.
Example: 5 × 24 = (10 × 24) ÷ 2 = 240 ÷ 2 = 120.

### 4. **Squaring Numbers Ending in 5**:
For numbers ending in 5, square the number by multiplying the first digit(s) by the next higher number and appending 25.
Example: 25² = 2 × 3 = 6 → 625.

### 5. **Multiplying by 4**:
Double the number twice.
Example: 4 × 6 = (2 × 6) × 2 = 12 × 2 = 24.

### 6. **Square of a Binomial**:
Use the formula: (a + b)² = a² + 2ab + b².
Example: (5 + 3)² = 5² + 2(5)(3) + 3² = 25 + 30 + 9 = 64.

### 7. **Multiplying by Powers of 2**:
Double the number the number of times indicated by the exponent.
Example: 16 × 2 = 32, 16 × 4 = 64.

### 8. **Dividing by 5**:
Multiply by 2 and then divide by 10.
Example: 15 ÷ 5 = (15 × 2) ÷ 10 = 30 ÷ 10 = 3.

### 9. **Finding Percentages**:
To find 10% of a number, move the decimal point one place to the left.
Example: 10% of 150 = 15.

### 10. **Multiplying by 12**:
Multiply by 10 and then add double the number.
Example: 12 × 15 = (10 × 15) + (2 × 15) = 150 + 30 = 180.

### 11. **Adding Large Numbers Quickly**:
Round up each number to the nearest ten, add them, and then subtract the rounding differences.
Example: 78 + 59 = (80 + 60) – 3 = 140 – 3 = 137.

### 12. **Finding 20%**:
Find 10%, then double it.
Example: 20% of 150 = (10% of 150) × 2 = 15 × 2 = 30.

### 13. **Multiplying by 25**:
Multiply by 100 and divide by 4.
Example: 25 × 16 = (100 × 16) ÷ 4 = 1600 ÷ 4 = 400.

### 14. **Using the Rule of 72**:
To find how long it takes for an investment to double at a given interest rate, divide 72 by the interest rate percentage.
Example: If interest rate = 6%, it will take 72 ÷ 6 = 12 years to double.

### 15. **Multiplying by 15**:
Multiply by 10 and add half of that number.
Example: 15 × 16 = (10 × 16) + (5 × 16) = 160 + 80 = 240.

### 16. **Multiplying by 1000**:
Simply add three zeros to the number.
Example: 67 × 1000 = 67000.

### 17. **Doubling and Halving**:
If one number is doubled and the other is halved, the product remains the same.
Example: 16 × 25 = 8 × 50 = 400.

### 18. **Adding Fractions**:
If the denominators are the same, add the numerators and keep the denominator the same.
Example: 3/5 + 1/5 = 4/5.

### 19. **Multiplying by 2-digit Numbers**:
Split the number into tens and ones, then apply distributive property.
Example: 23 × 14 = (20 × 14) + (3 × 14) = 280 + 42 = 322.

### 20. **Multiplying by 19**:
Multiply by 20 and subtract the number.
Example: 19 × 25 = (20 × 25) – 25 = 500 – 25 = 475.

### 21. **Multiplying by 6**:
Multiply by 3 and double the result.
Example: 6 × 8 = (3 × 8) × 2 = 24 × 2 = 48.

### 22. **Multiplying by 7**:
Multiply by 10 and subtract 3 times the original number.
Example: 7 × 12 = (10 × 12) – (3 × 12) = 120 – 36 = 84.

### 23. **Squaring Any Two-Digit Number Close to 50**:
Subtract the number from 50, square the result, and add it to 2500.
Example: 52² = (52 – 50)² = 2² = 4 → 2500 + 4 = 2504.

### 24. **Subtracting from 1000**:
Subtract each digit from 9, except the last digit which is subtracted from 10.
Example: 1000 – 689 = 311.

### 25. **Finding Half of a Number**:
Divide by 2 or simply take half.
Example: Half of 30 = 15.

### 26. **Multiplying by 100**:
Just add two zeros to the number.
Example: 67 × 100 = 6700.

### 27. **Multiplying by 8**:
Double the number three times.
Example: 8 × 7 = (2 × 7) × 2 × 2 = 14 × 4 = 56.

### 28. **Multiplying by 3**:
Multiply by 2 and add the original number.
Example: 3 × 15 = (2 × 15) + 15 = 30 + 15 = 45.

### 29. **Multiplying by 99**:
Multiply by 100 and subtract the original number.
Example: 99 × 12 = (100 × 12) – 12 = 1200 – 12 = 1188.

### 30. **Square Numbers Ending in 1**:
For numbers like 21, 31, 41, etc., square the tens digit, multiply it by 2, and add 1.
Example: 21² = (2 × 2) + 1 = 4 + 1 = 41 → 441.

### 31. **Using Cross Multiplication**:
Cross-multiply when solving proportions.
Example: For x/4 = 10/5, cross-multiply: x = (4 × 10) ÷ 5 = 40 ÷ 5 = 8.

### 32. **Squaring a Number Ending in 5**:
Square the tens digit, multiply it by 2, and add 25.
Example: 35² = (3 × 4) + 25 = 12 + 25 = 1225.

### 33. **Multiplying by 13**:
Multiply by 10 and add three times the original number.
Example: 13 × 6 = (10 × 6) + (3 × 6) = 60 + 18 = 78.

### 34. **Finding Square Roots of Perfect Squares**:
List squares for common numbers and find the root.
Example: The square root of 81 is 9 because 9² = 81.

### 35. **Multiplying by 30**:
Multiply by 3 and add a zero.
Example: 30 × 6 = (3 × 6) × 10 = 18 × 10 = 180.

### 36. **Doubling a Number with Even Digits**:
Simply double each digit and add them.
Example: 24 × 2 = 4 + 8 = 48.

### 37. **Multiplying by 14**:
Multiply by 10 and add four times the original number.
Example: 14 × 15 = (10 × 15) + (4 × 15) = 150 + 60 = 210.

### 38. **Multiplying by 17**:
Multiply by 10 and add seven times the original number.
Example: 17 × 5 = (10 × 5) + (7 × 5) = 50 + 35 = 85.

### 39. **Multiplying by 33**:
Multiply by 30 and add three times the original number.
Example: 33 × 6 = (30 × 6) + (3 × 6) = 180 + 18 = 198.

### 40. **Multiplying by 50**:
Multiply by 100 and divide by 2.
Example: 50 × 24 = (100 × 24) ÷ 2 = 2400 ÷ 2 = 1200.

### 41. **Find the Missing Number in Sequences**:
Use the difference between the numbers to calculate the missing term.
Example: 2, 4, ?, 8 → The difference is 2, so the missing number is 6.

### 42. **Estimate Fractions**:
Convert fractions into decimal equivalents for quicker approximations.
Example: 2/3 ≈ 0.666.

### 43. **Converting Fractions to Percentages**:
Multiply by 100 and add a percent sign.
Example: 1/2 = (1 ÷ 2) × 100 = 50%.

### 44. **Rounding to the Nearest 10**:
Round numbers to the nearest 10 to simplify mental math.
Example: 57 ≈ 60.

### 45. **Squaring Even Numbers**:
For even numbers, subtract 1 from the number, square it, and add the square of 2.
Example: 6² = (5²) + 2² = 25 + 4 = 36.

### 46. **Counting Money Quickly**:
Use mental math to quickly add up coins or bills based on their denominations.

### 47. **Simplifying Ratios**:
Divide both terms by their greatest common divisor.
Example: 8:12 = 2:3.

### 48. **Adding Large Numbers Using Rounding**:
Round numbers to the nearest hundred, add them, then adjust by the rounding difference.

### 49. **Multiplying by 20**:
Double the number and add a zero.
Example: 20 × 16 = (2 × 16) × 10 = 32 × 10 = 320.

### 50. **Fast Square of Large Numbers**:
Use the formula (a + b)² = a² + 2ab + b² for quick squaring.

These tricks can help save time and simplify many tasks!