Simplification and Approximation
Last Updated : 30 Oct, 2024
Simplification and approximation questions are crucial in the Quantitative Aptitude section of government exams, testing candidates' abilities to solve complex problems quickly. Mastering these topics can significantly boost scores in exams like SBI Clerk Mains, UPSC, and Railways.
This article will highlight the rules, tips, and tricks of simplification and approximation questions.
Simplification Rules
Several simplification rules can be applied to solve quantitative aptitude questions efficiently. Some of the most commonly used simplification rules are:
| V | Vinculum |
| B | Remove Brackets The order is: ( ), { }, [ ] |
| O | Of |
| D | Division |
| M | Multiplication |
| A | Addition |
| S | Subtraction |
Tips and Tricks to Solve Simplification Questions
- When attempting to solve questions that involve, simplification, it is important to remember the VBODMAS rule.
- Keep in mind the following formulas to solve the questions accurately:
- (a+b)2 = a2 + b2 + 2ab
- (a-b)2 = a2 + b2 – 2ab
- a2 – b2 = (a+b) (a-b)
- a3 + b3 = (a+b) (a2 – ab + b2)
- (a+b)3 = a3 + b3 + 3ab (a+b)
- (a-b)3 = a3 – b3 – 3ab (a-b)
- Always put on a timer while solving questions so that you can solve questions on time.
Rules to Solve the Mathematical Expressions by Approximation:
Rule 1:
To solve complex problems, take the closest value of the number given in the expression. for example, 77.8 is round off to 78;
33.02 is round off to 33 etc.
Example 1: 19% of (399.88/20 × 400) + 30 =?
20/100 × (400/20 × 400) + 30 =?
1/5 × (8000) + 30 = 1600 + 30 = 1630
Rule 2:
To solve problems with large numbers involved in multiplication, we can consider the approximate value of the large numbers by increasing or decreasing the round off values making the computation easy. for example, 239 × 111 is approximated to 240 × 110.
Example 2: 192 × 397 + 560 × 5/7 + 729.80 =?
192 × 397 + 560 × 5/7 + 730 =?
190 × 400 + 400 + 730 = 76000 + 1130 = 77130
Rule 3:
To solve problems with large numbers involved in the division, we can consider the approximate value of the large numbers by increasing or decreasing the round off values making the computation easy. for example, 6198.36/38.69 is approximated as 6200/40.
Example 3: 862.5/18.64 =?
860/20 = 43
Example 1:
Practice Problem: Simplify the expression 15/5 + 3(4 − 2)
Solution:
We can simplify by first evaluating the expression inside the parentheses:
15/5 + 3(4 − 2) = 15/5 + 3(2)
Then, we can calculate each part:
15/5 = 3
and
3(2) = 6
Now, we add the two results together:
3 + 6 = 9
Therefore, the expression 15/5 + 3(4 − 2) simplifies to 9.
Example 2:
Practice Problem: Approximate the value of 1.28÷0.41.28 \div 0.41.28÷0.4 using rounding to two decimal places.
Solution:
- Round 1.28 to two decimal places.
- Round 0.4 to two decimal places.
- Perform the division with the rounded values.
Related Reads:
Practice Quiz on Simplification and Approximation.
Summary
Simplification reduces complex expressions to their simplest form for easier calculation, while approximation estimates values, often through rounding, to speed up computations. Mastering both skills enhances problem-solving efficiency, making them crucial for success in quantitative aptitude tests.
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