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How to Improve Your Calculations

It is important to have a good calculation speed to perform well in exam. Learn some useful tricks to improve your calculations.

Improve Your Calculations

Do you have the tendency of leaving Quant and Data Interpretation questions involving intense calculations without even solving them? Now you don't need to be scared of such questions.

Through this article, we are going to learn some important tricks and shortcuts to improve calculations. By using these tricks, you'll be able to solve intense calculations within seconds and invest the time saved in questions which demand more time.

The first step in improving your calculations is to learn tables, squares, cubes and fractions by heart. This helps you recognize numbers which you generally do not encounter in normal routine. By learning these numbers through tables, squares and cubes you get to know their factors and multiples which also help you in solving problems.

Knowing all the tables till 25 is a must. Talking about squares, squares from 1 to 35 should be on your tips. You must also know cubes of at least first 25 numbers. Remembering these can surely help you in competitive exams.


Base Multiplication Trick
For multiplying numbers like 107 & 109, you can use the technique of base multiplication.

Step 1: To multiply 107 and 109, take the base as 100. These numbers are 7 and 9 more than the base.
Step 2: In order to get the answer add 9 and 7 in the numbers to the base and get the number as 116 (100 + 7 + 9). This becomes the left hand side.
Step 3: Take the product of the two earlier numbers i.e. 9 & 7 and get the product as 63. Now just attach this at the end of the earlier result i.e. 11663.
You can use this trick to multiply numbers with any base.


Example: What is 506*512?
Solution:
Step 1: To multiply 506 and 512, take the base as 500. These numbers are 6 and 12 more than the base.
Step 2: In order to get the answer add 6 and 12 in the numbers to the base and get the number as 518 (500 + 6 + 12). Now, multiply 518 with 5(as the base is 5 times 100). We get 2590. Take the 1st three digits. This becomes the left hand side.
Step 3: Take the product of the two earlier numbers i.e. 6 & 12 and get the product as 72. This will form the last three digits of the answer.
Step 4: Now just attach this at the end of the earlier result i.e. 259072.
Note: The base for both numbers should be same. Otherwise, we cannot use this method.


Now let's proceed to another trick.
You must be aware of the algebraic expression (a2-b2) = (a-b)*(a+b). We'll use this expression to simplify calculations. Let us see how.

Example: What is 87*113?
Solution:
Step 1: We take the base as 100. 87 is 13 less than 100 and 113 is 13 more than 100.
Step 2: Think of 87*113 as (100-13)*(100+13)
Step 3: Apply the above discussed expression i.e. (a2-b2) = (a-b)*(a+b).
Step 4: Answer= 1002-132 = 10000-169= 9831.
This trick too can be used to multiply numbers with any base. For practice, try calculating 517*483.


Fraction to Percentage Conversion Technique

We can use knowledge of standard fractions to reduce calculation time. Say you want to find 91.67% of 2400. Now finding this will be really tough, if you take the actual numbers into consideration, but knowing that 91.66% is actually 11/12 of a number, you can just divide 2400 by 12 and then multiply by 11 and find the answer as 2200. Similarly, calculating 42.85% of 700 will be quite time consuming process. But knowing that 42.85% is 3/7 of a number, you can answer this within 5 seconds that the answer will be 300. To use this technique effectively and efficiently, you must be well versed with the following fraction table:

Fraction Decimal Percent
1/2 0.5 50%
1/3 0.333... 33.333...%
2/3 0.666... 66.666...%
1/4 0.25 25%
3/4 0.75 75%
1/5 0.2 20%
2/5 0.4 40%
3/5 0.6 60%
4/5 0.8 80%
1/6 0.1666... 16.666...%
5/6 0.8333... 83.333...%
1/8 0.125 12.5%
3/8 0.375 37.5%
5/8 0.625 62.5%
7/8 0.875 87.5%
1/9 0.111... 11.111...%
2/9 0.222... 22.222...%
4/9 0.444... 44.444...%
5/9 0.555... 55.555...%
7/9 0.777... 77.777...%
8/9 0.888 88.888...%
1/10 0.1 10%
1/12 0.08333... 8.333...%
1/16 0.0625 6.25%
1/32 0.03125 3.125%

Tip: Start applying these tricks in questions.

To conclude, memorize the decimal equivalents of fractions starting from 1/2, 1/3, 2/3, 1/4, 2/4, 3/4...11/12. It will help you save a lot of time which you can use to solve more questions. Hence, it will significantly improve your percentile.


    Key Learning:
  • Memorizing squares, cubes and tables till 25 will help you improve your approximations and the better the approximations, the closer will be your answer to the exact answer.
  • Having knowledge of the fraction to percentage conversion and vice versa will help you simplify your calculations and get answers within less time. Hence, it is advisable to learn the table given in this article.

For doubts, post your comments below and our experts will provide you with the solutions.
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