15 Math Shortcuts That Will Speed Up Your Calculations
Mathematics doesn't have to be complicated. With these 15 math shortcuts, you can perform calculations much faster and more efficiently. Whether you're a student, professional, or just someone who wants to improve their mental math skills, these techniques will help you save time and reduce errors.
1. Multiplying by 11
To multiply any two-digit number by 11:
- Add the two digits together
- Place the sum between the two digits
Example: 45 × 11
4 + 5 = 9
Result: 495
2. Squaring Numbers Ending in 5
For numbers ending in 5:
- Take the first digit(s)
- Multiply by the next higher number
- Append 25 to the result
Example: 35²
3 × 4 = 12
Result: 1225
3. Multiplying by 9
To multiply by 9:
- Multiply by 10
- Subtract the original number
Example: 47 × 9 = (47 × 10) - 47 = 470 - 47 = 423
4. Adding Large Numbers
Break numbers into chunks for easier addition:
Example: 648 + 276
= (600 + 200) + (40 + 70) + (8 + 6)
= 800 + 110 + 14 = 924
5. Finding a Percentage of a Number
Percentages can be calculated by breaking them down:
- 10% of a number = divide by 10
- 5% = half of 10%
- 15% = 10% + 5%
Example: 15% of 240
10% of 240 = 24
5% of 240 = 12
15% = 24 + 12 = 36
6. Multiplying by 25
To multiply by 25, divide by 4 and multiply by 100:
Example: 36 × 25 = (36 ÷ 4) × 100 = 9 × 100 = 900
7. Dividing by 5
To divide by 5, multiply by 2 and divide by 10:
Example: 175 ÷ 5 = (175 × 2) ÷ 10 = 350 ÷ 10 = 35
8. Subtracting from 1000
To subtract a number from 1000:
- Subtract each digit from 9
- Subtract the last digit from 10
Example: 1000 - 673 = 327
9-6=3, 9-7=2, 10-3=7
9. Multiplying Two Numbers Between 10 and 19
For numbers between 10 and 19:
- Add the ones digit of one number to the other number
- Multiply by 10
- Multiply the ones digits together
- Add the two results
Example: 14 × 17
= (14 + 7) × 10 + (4 × 7)
= 210 + 28 = 238
10. Converting Fractions to Percentages
To convert a fraction to a percentage:
For 1/8: 1 ÷ 8 = 0.125 = 12.5%
For 3/4: 3 ÷ 4 = 0.75 = 75%
11. Squaring Any Number Between 40 and 50
Let's say we want to square 46:
- Subtract the number from 50: 50 - 46 = 4
- Subtract the result from 25: 25 - 4 = 21
- Append the square of the result: 4² = 16
- Result: 2116
Example: 46² = 2116
12. Multiplying by 10, 100, 1000
- Multiply by 10: Add one zero
- Multiply by 100: Add two zeros
- Multiply by 1000: Add three zeros
Example: 42 × 100 = 4200
13. Finding Cube Roots
Learn the cubes of numbers 1-10 to quickly find cube roots of perfect cubes.
1³=1, 2³=8, 3³=27, 4³=64, 5³=125
6³=216, 7³=343, 8³=512, 9³=729, 10³=1000
Example: ∛343 = 7
14. Multiplying by 101
To multiply a two-digit number by 101, write the number twice:
Example: 53 × 101 = 5353
15. Calculating Tip Quickly
To calculate a tip:
- 10% tip = total ÷ 10
- 15% tip = 10% + half of 10%
- 20% tip = 10% × 2
Example: $68 bill, 15% tip
10% = $6.80
5% = $3.40
Total tip = $6.80 + $3.40 = $10.20
Conclusion
These math shortcuts can significantly improve your calculation speed and mental math abilities. With practice, you'll be able to apply these techniques effortlessly in your daily life, whether you're shopping, budgeting, or solving math problems.
Remember, the key to mastering these shortcuts is practice. Start with a few that seem most useful to you and gradually incorporate more into your daily calculations.