Mathematical Operations Notes for SSC Exams

Mathematical operations is a Reasoning topic in which the usual meaning of signs such as +, −, × and ÷ is changed, or numbers and signs are interchanged, and you have to calculate the new value. For example, "if + means × and × means −, then what is 6 + 3 × 2?" These questions are asked in almost every SSC Reasoning paper. They do not need advanced mathematics, only a clear method and the BODMAS rule. These mathematical operations notes for SSC explain every type with tables, solved examples and practice questions.

Types of Mathematical Operation Questions

BODMAS Rule

Always solve an expression in the order shown by BODMAS.

• Division and multiplication have equal importance, so solve them from left to right.
• Addition and subtraction also have equal importance, so solve them from left to right.
• Example: 6 + 4 × 3 = 6 + 12 = 18, not 30.

Type 1: Symbol Replacement

Replace every symbol with its new meaning, and then solve the expression using BODMAS. Do not change the numbers.

Example 1. If + means ×, − means ÷, × means + and ÷ means −, find 12 + 3 − 2 × 5 ÷ 4.
Replace the signs: 12 × 3 ÷ 2 + 5 − 4.
12 × 3 = 36, 36 ÷ 2 = 18, 18 + 5 = 23, 23 − 4 = 19. Answer: 19.

Example 2. If + means − and − means +, find 15 + 5 − 3.
Replace the signs: 15 − 5 + 3 = 13. Answer: 13.

Type 2: Interchange of Signs and Numbers

• Interchange of signs means every + becomes × and every × becomes + if those two signs are swapped.
• Interchange of numbers means the two numbers swap their places everywhere in the expression.
• When both are given, change the numbers and the signs, then solve with BODMAS.

Example 3. If + and × are interchanged, find 4 + 3 × 5.
The expression becomes 4 × 3 + 5 = 12 + 5 = 17. Answer: 17.

Example 4. If 2 and 4 are interchanged and + and − are interchanged, find 2 + 4 − 3.
The expression becomes 4 − 2 + 3 = 2 + 3 = 5. Answer: 5.

Type 3: Fictitious (New) Operations

A new symbol is defined with a formula. Put the given numbers in the formula in the same order as written.

For a question like "find (2 ★ 3) ★ 4", first solve the bracket and then use its result for the next operation.

Type 4: Missing Signs

Try the signs one by one and check whether the statement becomes true. Start with the signs that give the nearest result.

Example 5. Find the correct signs: 12 ? 4 ? 2 = 6.
Try 12 ÷ 4 × 2: 12 ÷ 4 = 3, and 3 × 2 = 6. Answer: ÷ and ×.

Quick Tips

• Write the new meaning of every sign at the top before you start.
• Replace all signs first, and then calculate. Do not mix the two steps.
• Apply BODMAS carefully, especially division before addition.
• In fictitious operations, the order of numbers matters because a ★ b is not always equal to b ★ a.
• Check your final value once by substituting back into the statement.

Quick Revision Points

• BODMAS: Brackets, Of, Division, Multiplication, Addition, Subtraction.
• Division and multiplication, and addition and subtraction, are solved left to right.
• Replace signs first, then solve.
• In interchange questions, swap exactly what the question says and nothing else.
• In fictitious operations, substitute numbers in the same order as in the formula.

Practice Questions With Answers

1. If + means ×, × means −, − means ÷ and ÷ means +, find 8 + 6 − 3 × 4 ÷ 2.
   Answer: 14 (8 × 6 ÷ 3 − 4 + 2 = 16 − 4 + 2).
2. If + means − and − means +, find 15 + 5 − 3.
   Answer: 13.
3. If a ★ b = 2a + b, find 5 ★ 3.
   Answer: 13.
4. If + and × are interchanged, find 4 + 3 × 5.
   Answer: 17.
5. If 2 and 4 are interchanged and + and − are interchanged, find 2 + 4 − 3.
   Answer: 5.
6. Find the signs: 12 ? 4 ? 2 = 6.
   Answer: ÷ and ×.
7. If a @ b = a² − b², find 7 @ 5.
   Answer: 24.
8. If P # Q = P × Q + P, find 6 # 4.
   Answer: 30.
9. If ÷ means ×, × means −, − means + and + means ÷, find 18 ÷ 3 × 4 − 2 + 2.
   Answer: 51 (18 × 3 − 4 + 2 ÷ 2 = 54 − 4 + 1).
10. Simplify using BODMAS: 20 − 4 × (6 − 3) + 8 ÷ 2.
    Answer: 12 (20 − 12 + 4).

How to Practise This Chapter

Solve five questions daily from different types, and always write the new sign meanings at the top. Then practise timed sets from our practice papers and check the real exam level on the previous year papers page. If your calculation speed is slow, use the calculators and tools to check your answers. Read Ranking Order and Sequence before this chapter and Logical Venn Diagram after it.

Explore More SSC Subjects

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

• Quantitative Aptitude Notes
• English Notes
• General Awareness Notes
• Computer Knowledge Notes
• Stenography Notes
• All SSC subjects and notes

Frequently Asked Questions

What are mathematical operations in reasoning?

Mathematical operations is a reasoning topic in which the meaning of mathematical signs is changed, or numbers and signs are interchanged, and you have to find the value of an expression using the new meanings.

How many questions come from mathematical operations in SSC exams?

Usually one to three questions come from this topic in the Reasoning section of SSC CGL, CHSL, MTS and GD papers, but the number changes every year.

What is the BODMAS rule?

BODMAS is the order of solving an expression: Brackets, Of, Division, Multiplication, Addition and Subtraction. Division and multiplication, and addition and subtraction, are solved from left to right.

Should I replace the signs first or calculate first?

Always replace all the signs first and then calculate. Mixing the two steps is the most common reason for wrong answers.

How do I solve interchange questions?

Swap only the signs or numbers mentioned in the question, rewrite the expression and then solve it using BODMAS.

What is a fictitious operation?

A fictitious operation is a new symbol that is defined by a formula, such as a ★ b = 2a + b. You use the formula to calculate the answer for the given numbers.

Does the order of numbers matter in fictitious operations?

Yes. In a ★ b = 2a + b, 5 ★ 3 is 13, but 3 ★ 5 is 11. Always put the first number in place of a and the second number in place of b.

How do I find missing signs?

Try the most likely signs one by one in the expression and check whether the result matches. Using BODMAS in each trial prevents mistakes.

Are these questions difficult?

No. They need only basic arithmetic. Most students lose marks because of careless replacement of signs or because they ignore the order of operations.

How can I solve these questions faster?

Write the new meaning of every sign first, replace them in one pass, and calculate carefully. Practising multiplication tables up to 20 also helps.

What mistakes should I avoid?

Do not replace only some of the signs, do not forget that the numbers do not change in sign replacement questions, and do not solve addition before multiplication.

Can I use a calculator in the exam?

No calculator is allowed in the SSC exams. You must calculate on rough paper, so practise mental maths and simple calculations regularly.

Is this topic the same in Hindi medium papers?

Yes. The questions are the same in Hindi medium papers, with the symbols and numbers unchanged and only the instructions written in Hindi.