Simplification— Concepts, Formulas & Shortcuts
- BODMAS order: Brackets → Of → Division → Multiplication → Addition → Subtraction.
- Division and multiplication rank equally: work left to right. Same for addition and subtraction.
- Solve brackets inside out: ( ) first, then { }, then [ ].
- "Of" means multiplication but is resolved before ordinary division: ½ of 8 ÷ 2 = 4 ÷ 2 = 2.
- Convert fractions to a common denominator only after brackets are cleared.
- Approximation questions: round to convenient values first — the options are always far apart.
Simplification Practice Questions with Answers
Attempt each question first, then open the explanation. All 21 questions below are free to read and require no signup.
Q1.Simplify: 12 + 6 ÷ 3 × 2
Easy- A12
- B16
- C18
- D24
Simplification question 1 of 21+Show Answer & Explanation
Answer: B. 16
Explanation: 6 ÷ 3 = 2, then 2 × 2 = 4, so 12 + 4 = 16.
Q2.Simplify: (8 + 4) × 3 − 5
Easy- A19
- B25
- C31
- D36
Simplification question 2 of 21+Show Answer & Explanation
Answer: C. 31
Explanation: Brackets first: 12 × 3 = 36, then 36 − 5 = 31.
Q3.Simplify: 5 of 4 + 3 × 2
Moderate- A23
- B26
- C46
- D52
Simplification question 3 of 21+Show Answer & Explanation
Answer: B. 26
Explanation: "Of" first: 5 of 4 = 20; then 3 × 2 = 6, so 20 + 6 = 26.
Q4.Simplify: 36 ÷ 6 × 3 + 2
Easy- A4
- B8
- C20
- D38
Simplification question 4 of 21+Show Answer & Explanation
Answer: C. 20
Explanation: Left to right: 36 ÷ 6 = 6, 6 × 3 = 18, 18 + 2 = 20.
Q5.Simplify: 15 − [8 − (5 − 3)]
Moderate- A7
- B9
- C11
- D15
Simplification question 5 of 21+Show Answer & Explanation
Answer: B. 9
Explanation: Innermost bracket: 5 − 3 = 2 → 8 − 2 = 6 → 15 − 6 = 9.
Q6.Simplify: 2/3 of 45 + 1/5 of 25
Easy- A30
- B33
- C35
- D40
Simplification question 6 of 21+Show Answer & Explanation
Answer: C. 35
Explanation: 2/3 × 45 = 30 and 1/5 × 25 = 5, so the total is 35.
Q7.Simplify: √144 + √81
Easy- A15
- B18
- C21
- D25
Simplification question 7 of 21+Show Answer & Explanation
Answer: C. 21
Explanation: √144 = 12 and √81 = 9, so the sum is 12 + 9 = 21.
Q8.Simplify: 8 × 3 − 4 ÷ 2
Easy- A10
- B20
- C22
- D24
Simplification question 8 of 21+Show Answer & Explanation
Answer: C. 22
Explanation: 8 × 3 = 24 and 4 ÷ 2 = 2, so 24 − 2 = 22.
Q9.Simplify: 100 ÷ 5 ÷ 2
Moderate- A5
- B10
- C20
- D40
Simplification question 9 of 21+Show Answer & Explanation
Answer: B. 10
Explanation: Division works left to right: 100 ÷ 5 = 20, then 20 ÷ 2 = 10.
Q10.Simplify: 3 + 4 × 5 − 6
Easy- A11
- B17
- C23
- D29
Simplification question 10 of 21+Show Answer & Explanation
Answer: B. 17
Explanation: Multiplication first: 4 × 5 = 20, so 3 + 20 − 6 = 17.
Q11.Simplify: (18 ÷ 3) × (4 + 2)
Easy- A24
- B30
- C36
- D42
Simplification question 11 of 21+Show Answer & Explanation
Answer: C. 36
Explanation: Brackets first: 6 × 6 = 36.
Q12.Simplify: 1/2 of 60 + 1/3 of 30
Easy- A35
- B40
- C45
- D50
Simplification question 12 of 21+Show Answer & Explanation
Answer: B. 40
Explanation: “Of” means multiply: ½ × 60 = 30 and ⅓ × 30 = 10, giving 30 + 10 = 40.
Q13.Simplify: 50 − [20 − (10 − 5)]
Moderate- A25
- B30
- C35
- D45
Simplification question 13 of 21+Show Answer & Explanation
Answer: C. 35
Explanation: Innermost first: 10 − 5 = 5 → 20 − 5 = 15 → 50 − 15 = 35.
Q14.Simplify: √169 − √25
Easy- A6
- B8
- C10
- D12
Simplification question 14 of 21+Show Answer & Explanation
Answer: B. 8
Explanation: √169 = 13 and √25 = 5, so the difference is 13 − 5 = 8.
Q15.Simplify: 20 − 4 × 3
Easy- A8
- B12
- C48
- D56
Simplification question 15 of 21+Show Answer & Explanation
Answer: A. 8
Explanation: Multiplication first: 4 × 3 = 12, so 20 − 12 = 8.
Q16.Simplify: 6 + 12 ÷ 4
Easy- A4.5
- B9
- C12
- D18
Simplification question 16 of 21+Show Answer & Explanation
Answer: B. 9
Explanation: Division first: 12 ÷ 4 = 3, so 6 + 3 = 9.
Q17.Simplify: (25 − 5) ÷ 4
Easy- A4
- B5
- C6
- D20
Simplification question 17 of 21+Show Answer & Explanation
Answer: B. 5
Explanation: Brackets first: 20 ÷ 4 = 5.
Q18.Simplify: 3 × (8 − 5) + 7
Easy- A10
- B13
- C16
- D19
Simplification question 18 of 21+Show Answer & Explanation
Answer: C. 16
Explanation: 3 × 3 = 9, then 9 + 7 = 16.
Q19.Simplify: 40 ÷ 8 + 2 × 5
Moderate- A12
- B15
- C18
- D25
Simplification question 19 of 21+Show Answer & Explanation
Answer: B. 15
Explanation: 40 ÷ 8 = 5 and 2 × 5 = 10, so 5 + 10 = 15.
Q20.Simplify: 3/4 of 80 − 1/5 of 50
Moderate- A40
- B45
- C50
- D55
Simplification question 20 of 21+Show Answer & Explanation
Answer: C. 50
Explanation: “Of” means multiply: ¾ × 80 = 60 and ⅕ × 50 = 10, so 60 − 10 = 50.
Q21.Simplify: 100 − [40 − (15 − 5)]
Moderate- A50
- B60
- C70
- D75
Simplification question 21 of 21+Show Answer & Explanation
Answer: C. 70
Explanation: Innermost: 15 − 5 = 10 → 40 − 10 = 30 → 100 − 30 = 70.
Simplification — Frequently Asked Questions
What does BODMAS stand for?+
Brackets, Of, Division, Multiplication, Addition, Subtraction. Division and multiplication have equal priority and are evaluated left to right, as are addition and subtraction.
Where do candidates most often go wrong in simplification?+
Performing addition before division, and mishandling "of". In 12 + 6 ÷ 3 × 2, the division and multiplication must come first, giving 12 + 4 = 16, not 12.
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