Mathematics questions can often be tedious to solve, not only due to the number of steps required to arrive at the solution but also due to the arduous calculations involved. Here are some ways you can make the calculation portion of the solution more manageable.
Multiplying Large Numbers Easily
Here is a simple trick to multiply two numbers that are close to 100, you can use the following method:
- Identify how much each number is less than 100. For example, to multiply 98 and 97:
- 98 is 2 less than 100.
- 97 is 3 less than 100.
- Subtract the sum of these differences from 100.
- 100 − (2 + 3) = 95
- Multiply the differences together.
- 2 × 3=62
- Combine these results.
- The final answer is 9500 + 6 = 9506
The Magic of 11
Multiplying any number by 11 can be done quickly using a simple trick. Let’s multiply 54 by 11:
- Write the original number with a space between its digits.
- 5 _ 4
- Add the original digits together and place the result in the space.
- 5 + 4 = 9, so 5 _ 4 becomes 594
Therefore, 54×11=594
This trick can be very helpful while having to multiply a number by π, first multiply the number by 11 then 2 and finally divide by 7.
Squaring Numbers Ending in 5
Squaring numbers that end in 5 is another trick that can save you time. Here’s how you can square a number like 75:
- Multiply the first digit(s) by the next higher number.
- 7×8=56
- Add 25 to the end of this product.
- The answer is 5625.
Thus, 752 = 5625.
The Rule of 9 for Division
When you need to check if a number is divisible by 9, you can use the rule of 9. A number is divisible by 9 if the sum of its digits is also divisible by 9. For example, check if 738 is divisible by 9:
- Add the digits of the number together.
- 7 + 3 + 8 = 18
- Check if the sum is divisible by 9.
- Since 18 is divisible by 9, 738 is also divisible by 9.
Quick Percentages
Calculating percentages in your head can be much easier if you break down the percentage into smaller more manageable parts. To find 17.5% of a number, say 480, you can break it down:
- Find 10% of the number.
- 10% of 480=48
- Find 5% of the number (which is half of 10%).
- 5% of 480=24
- Find 2.5% of the number (which is half of 5%).
- 2.5% of 480=12
- Add these results together.
- 48+24+12=84
So, 17.5% of 480 is 84.
Tricks like these can make calculations in mathematics a lot less overwhelming and can save a significant amount of time in competitive exams such as the JEE where every second matters.
