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Mathematical Operations Tricks & Examples
In such type of questions some relationships are shown with the help of certain symbols/notations and/ or mathematical signs. Each symbol or sign is defined clearly in the question statement itself. In other words, each symbol or sign is accorded two values –one real value and another assigned value of each symbol or sign and then solve the questions accordingly.
For example, Suppose the triangle (∆) means addition.
Math Trick
We know that triangle is a plane figure but here it has been assigned the value of addition (+).
Thus, 3 ∆ 5 ⇒ 3 + 5 = 8
In this way, two work out such questions substitute the assigned/ implied meanings of the symbol or sign and proceed accordingly.
How to Solve the questions
To solve this type of questions, substitute the real signs in the given expression and then solve the expression according to the BODMAS rule.
Order of Operations – BODMAS
- 1st. B – Brackets, do all the maths contained in brackets first
- 2nd. O – Orders, square roots, powers and anything else not listed
- 3rd. D – Division, do your divisions now
- 4th. M – Multiplication
- 5th. A – Addition
- 6th. S – Subtraction
Example: If + means ÷, × means –, ÷ means × and – means +, then, 8 + 6 × 4 ÷ 3 – 4 = ?
(a) – 12
(b) – 20/3
(c) 12
(d) 20/3
Ans: (c)
Using the given symbols, we have:
Given expression: = 8 ÷ 6 – 4 × 3 + 4 = 4/3 – 4 × 3 + 4
= 4/3 – 12 + 4 = -20/3.
Type 1: Value of the Given Expression
Example 1: If ‘÷’ means ‘+’, ‘–’ means ‘÷’, ‘×’ means ‘–’ and ‘+’ means ‘×’ then, 62 ÷ 8 – 4 × 12 + 4 = ?
(a) 16
(b) 26
(c) 1/16
(d) 6
Ans: (a)
Given expression, 62 ÷ 8 – 4 × 12 + 4 = ?
According to question, after replacement of mathematical sign
62 + 8 ÷ 4 – 12 × 4 = ?
= 64 – 48 = 16
Hence, ? ⇒ 16
Type 2: Identification of Correct Equation
Example 2: If ‘–’ means ‘+’, ‘+’ means ‘–’, ‘×’ means ‘÷’ and ‘÷’ means ‘×’; then which of the given equations is correct?
(a) 30 + 5 – 4 ÷ 10 × 5 = 58
(b) 30 + 5 ÷ 4 – 10 × 5 = 22
(c) 30 – 5 + 4 ÷ 10 × 5 = 62
(d) 30 × 5 – 4 ÷ 10 + 5 = 41
Ans: (d)
From option 4:
30 × 5 – 4 ÷ 10 + 5 = 41
According to question, after replacement of mathematical sign
30 ÷ 5 + 4 × 10 – 5 = 41 = 6 + 40 – 5 = 41 = 46 – 5 = 41
Hence option (4) is correct.
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FAQs on Tips and Tricks: Mathematical Operations - General Intelligence and Reasoning for SSC CGL
| 1. What are some tricks for performing mathematical operations quickly and accurately? |  |
| 2. Can you provide an example of using the distributive property for multiplication? | |
Ans. Yes, for example, if you have to multiply 23 by 8, you can break it down as (20 + 3) × 8. Using the distributive property, this becomes (20 × 8) + (3 × 8) = 160 + 24 = 184.
| 3. How can mental math techniques like rounding and estimation help in mathematical operations? | |
Ans. Mental math techniques like rounding and estimation can help in mathematical operations by providing quick approximations. For example, if you need to multiply 37 by 4, you can round 37 to 40 and multiply it by 4 to get 160, which is a close approximation to the actual answer of 148.
| 4. Are there any shortcuts for addition and subtraction that can save time? | |
Ans. Yes, there are several shortcuts for addition and subtraction. One such shortcut is the "complement method" for subtraction, where you subtract the complement of a number instead of the number itself. Another shortcut is the "left-to-right addition" method, where you add the digits from left to right, rather than right to left.
| 5. How can breaking down complex operations into simpler ones help in mathematical calculations? | |
Ans. Breaking down complex operations into simpler ones can make calculations easier and reduce the chances of errors. For example, if you have to calculate 25 × 16, you can break it down as (20 × 10) + (20 × 6) + (5 × 10) + (5 × 6) = 200 + 120 + 50 + 30 = 400. By breaking it down, you can perform each operation separately and then add the results together.
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