Simplification and BODMAS Notes for SSC Exams

Simplification and BODMAS is the base of speed in SSC Quantitative Aptitude. Four to six questions of simplification and approximation come in each Tier 1 paper, and every other chapter needs the same calculation skills. These simplification and BODMAS notes for SSC explain the rule, the shortcuts and the approximation methods with solved examples.

The BODMAS Rule

BODMAS tells us the order in which we must perform the operations in an expression.

Division and multiplication have equal priority, so solve them from left to right. The same applies to addition and subtraction.

Important Identities and Values

• (a + b) squared = a squared + 2ab + b squared.
• (a - b) squared = a squared - 2ab + b squared.
• a squared - b squared = (a + b)(a - b).
• a cubed + b cubed = (a + b)(a squared - ab + b squared).
• Squares up to 30 and cubes up to 15 should be memorised.

Fractions and Decimals

• "Of" means multiplication: 2/3 of 450 = 2/3 x 450 = 300.
• To add or subtract fractions, make the denominators equal.
• To divide by a fraction, multiply by its reciprocal.
• When multiplying decimals, multiply as whole numbers and put the decimal point by counting the total decimal places.
• To divide by a decimal, make the divisor a whole number by multiplying both numbers by 10, 100 and so on.

Approximation Tricks

In approximation questions, you are not asked for the exact value but the nearest value from the options. Round each number to the nearest convenient number, calculate and choose the closest option. For example, 49.8 x 20.1 is nearly 50 x 20 = 1000. Also use the fact that the square root of a number near a perfect square is close to that square (for example, the square root of 146 is nearly 12).

Where Simplification Appears in the Exam

Simplification questions appear as direct expressions in Tier 1 and as longer expressions with fractions, decimals and powers in Tier 2. Approximation questions use "approximately" in the question and ask for the nearest value. Practising with a timer is important, because accuracy alone is not enough; the aim is to solve each simplification question in about 30 seconds.

Solved Examples

Example 1: Simplify: 8 + 12 / 4 x 3 - 5
Solution: Division and multiplication first, left to right: 12 / 4 = 3, then 3 x 3 = 9. So 8 + 9 - 5 = 12.

Example 2: Simplify: 15 - [3 + {2 x (6 - 4)}]
Solution: Inner bracket: 6 - 4 = 2. Then 2 x 2 = 4. Then 3 + 4 = 7. So 15 - 7 = 8.

Example 3: Simplify: 0.4 x 0.5 + 1.2 / 0.4
Solution: 0.4 x 0.5 = 0.2 and 1.2 / 0.4 = 3. Sum = 3.2.

Example 4: Find the value of 25 squared - 15 squared.
Solution: Use a squared - b squared = (a + b)(a - b) = 40 x 10 = 400.

Example 5: Find the value of 2/3 of 450 + 1/5 of 250.
Solution: 2/3 of 450 = 300 and 1/5 of 250 = 50. Sum = 350.

Example 6: Find the value of (5 + 3) squared - 4 x 5 x 3.
Solution: (8) squared = 64 and 4 x 5 x 3 = 60. So 64 - 60 = 4.

Quick Tips to Solve Faster

• Always solve the innermost bracket first and work outwards.
• Use the identities for squares to avoid long multiplication.
• Learn squares up to 30 and cubes up to 15 for faster simplification.
• Convert decimals into fractions when the denominators are simple (0.25 = 1/4).
• In approximation questions, round numbers to make the multiplication easy, but keep the same direction.

Common Mistakes to Avoid

• Doing multiplication before division when division comes first from the left.
• Ignoring the order of brackets.
• Making sign errors while removing a minus sign in front of a bracket.
• Putting the decimal point in the wrong place after multiplication.
• Over-rounding in approximation, which gives a wrong option.

Quick Revision Points

• BODMAS: brackets, orders, division, multiplication, addition, subtraction.
• "Of" means multiplication.
• a squared - b squared = (a + b)(a - b).
• Divide by a fraction = multiply by its reciprocal.
• Approximation needs the nearest value, not the exact value.

Practice Questions With Answers

1. Simplify: 6 + 18 / 3 x 2
   Answer: 18 (18 / 3 = 6, 6 x 2 = 12, 6 + 12).
2. Simplify: 5 + [6 - (4 - 2)]
   Answer: 9 (Inner bracket first: 6 - 2 = 4).
3. Find 3/4 of 160 - 2/5 of 100.
   Answer: 80 (120 - 40).
4. Simplify: (0.5) squared + (0.3) squared
   Answer: 0.34 (0.25 + 0.09).
5. Simplify: 144 / 12 x 3 - 7
   Answer: 29 (12 x 3 = 36, 36 - 7).
6. Simplify: 2.5 x 0.4 / 0.05
   Answer: 20 (1 / 0.05).
7. Find 12 squared - 8 squared.
   Answer: 80 (20 x 4).
8. Simplify: 1/2 + 1/3 + 1/6
   Answer: 1 (3/6 + 2/6 + 1/6).
9. Estimate: 49.8 x 20.1
   Answer: About 1,000 (50 x 20).
10. Find the value of the square root of 144 + the cube root of 27.
    Answer: 15 (12 + 3).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC simplification practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Fractions and Decimals Notes
• Number System Notes
• HCF and LCM Notes
• Percentage Notes
• SSC Simplification Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is BODMAS?

BODMAS is the rule for the order of operations: Brackets, Orders, Division, Multiplication, Addition and Subtraction.

How many questions come from simplification in SSC exams?

Four to six questions come from simplification and approximation in SSC CGL and CHSL Tier 1.

What does "of" mean in simplification?

"Of" means multiplication, for example 1/2 of 100 = 1/2 x 100 = 50.

What is the difference between simplification and approximation?

Simplification gives the exact value, while approximation gives the nearest value from the options.

Which identities help in simplification?

(a + b) squared, (a - b) squared and a squared - b squared are used the most.

How can I improve calculation speed?

Memorise squares up to 30 and cubes up to 15, learn fraction-decimal values and practise daily.

Do division and multiplication have equal priority?

Yes. Solve them in the order they appear from left to right.

How should I practise simplification?

Solve timed sets daily and attempt the simplification practice paper.