Cool Math Shortcuts and Tricks for Simplified Calculations
Mathematics can often seem daunting, but with the right set of shortcuts and tricks, you can make complex problems easier to solve. This article introduces some of the most useful math shortcuts and tricks that can help you perform calculations faster and with greater confidence.
Multiplying by 9
One of the simplest tricks to multiply any number by 9 is to multiply the number by 10 and then subtract the original number. This method can help you calculate 9 times any number quickly and efficiently.
Example:
7 times 9:
- 7 times 10 70
- 70 - 7 63
Squaring Numbers Ending in 5
When squaring any two-digit number ending in 5, you can use this formula: Multiply the first digit by itself plus one, then append 25.
Example:
35 squared:
- 3 times 3 1 12
- 35 squared 1225
Multiplying by 11
Multiplying a two-digit number by 11 can be done by adding the two digits together and placing the result in between the original digits.
Example:
34 times 11:
- 3 4 7
- So 34 times 11 374
Divisibility Rules
Understanding divisibility rules can help you quickly determine if a number can be divided by 2, 3, 5, or 9. Here are the rules:
Divisible by 2: The last digit is even. Divisible by 3: The sum of the digits is divisible by 3. Divisible by 5: The last digit is 0 or 5. Divisible by 9: The sum of the digits is divisible by 9.Calculating Percentages
Several mental math techniques can help you quickly calculate percentages. For example, to find 10% of a number, divide it by 10. To find 5%, divide by 20 or by half the 10%. This method can be extended for other percentages.
Example:
To find 15% of 80:
- 10% of 80 8
- 5% of 80 4
- So 15% 8 4 12
Using the Distributive Property
The distributive property can simplify multiplication. By breaking down a problem into smaller, more manageable parts, you can multiply more efficiently.
Example:
6 times 47:
- 6 times 40 6 times 7 240 42 282
Finding the Average
To quickly find the average of two numbers, simply add them together and divide by 2.
Example:
Average of 8 and 12:
- 8 12 20
- 20 divided by 2 10
The Finger Trick for 9s
For multiplying by 9, you can use your fingers to help. Hold out both hands and for 9 times n, fold down the nth finger. The fingers to the left represent tens, and those to the right represent units.
Example:
9 times 3:
- Fold down the third finger
- You have 2 fingers up on the left (20) and 7 fingers up on the right (7)
- So 9 times 3 27
Mental Math with Squares
For quickly calculating squares of numbers near to 10, 20, or 30, use the formula: a b^2 a^2 2ab b^2.
Example:
23 squared:
- 20 3^2 20^2 2 * 20 * 3 3^2 400 120 9 529
Estimation Techniques
Estimation can be a valuable tool in mental math. Round numbers to make calculations easier and then adjust as needed.
Example:
Estimating 198 times 47:
- Round to 200 times 50 10000 for a quick estimate.
Certainly, these tricks can help you perform calculations faster and with greater confidence. They are particularly useful in situations where quick mental math is required, such as in business or everyday life.