Simplification Questions: Method and Worked Examples
Find the exact value of long expressions with BODMAS, shown step by step on six original questions.
A simplification question gives you a long expression and asks for its exact value. It mixes division, multiplication, fractions, decimals, squares and roots in one line. Sometimes one number is replaced by a question mark and you work backwards to find it.
These questions test order and care, not deep maths. If you apply BODMAS in the right order and know your squares and cubes, each one takes well under a minute.
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Types of Simplification Questions
- BODMAS expressions
- Brackets, Of, Division, Multiplication, Addition, Subtraction in one long line. You find the single exact answer.
- Fractions and "of"
- Expressions like 3/4 of 2/5 of a number, often added to a percentage of another number.
- Squares, cubes and roots
- √, ∛, squares and cubes of numbers up to about 30, mixed with ordinary operations.
- Decimals
- Products and quotients such as 6.4 × 2.5, where moving the decimal point carefully is the whole skill.
- Missing number
- The question mark sits inside the expression, for example ? × 12 + 150 = 23 × 18. You solve for the missing value.
The Method: Solve in This Order
- 1
1. Open the brackets first
Work out everything inside brackets before you touch anything outside them.
- 2
2. Do "of" next
"Of" means multiply, but it comes before ordinary division and multiplication. So 1/2 of 40 ÷ 4 is 20 ÷ 4 = 5.
- 3
3. Division and multiplication, left to right
These two have equal rank. Go from left to right. 48 ÷ 6 × 3 is 8 × 3 = 24, not 48 ÷ 18.
- 4
4. Addition and subtraction, left to right
Again equal rank, again left to right.
- 5
5. For a missing number, move everything else across
Work out the side with no question mark first. Then undo each operation on the other side, last one first.
Practice Questions With Full Solutions
Original questions written for this page. Try each one before reading the solution.
- 1
Practice question 1: 48 ÷ 6 × 3 + 15 − 4² = ?
Power first: 4² = 16. Then left to right: 48 ÷ 6 = 8, and 8 × 3 = 24. Now 24 + 15 = 39, and 39 − 16 = 23. Answer: 23.
- 2
Practice question 2: 3/4 of 2/5 of 960 + 25% of 180 = ?
2/5 of 960 = 384. 3/4 of 384 = 288. 25% of 180 = 45. Then 288 + 45 = 333. Answer: 333.
- 3
Practice question 3: √1764 + ∛2744 − 7 × 6 = ?
√1764 = 42, because 42 × 42 = 1764. ∛2744 = 14, because 14 × 14 × 14 = 2744. Multiply next: 7 × 6 = 42. So 42 + 14 − 42 = 14. Answer: 14.
- 4
Practice question 4: ? × 12 + 150 = 23 × 18
Right side: 23 × 18 = 414. Move 150 across: 414 − 150 = 264. Divide by 12: 264 ÷ 12 = 22. Check: 22 × 12 + 150 = 264 + 150 = 414. Answer: 22.
- 5
Practice question 5: 6.4 × 2.5 + 1.25 × 8 − 0.5 = ?
6.4 × 2.5 = 16 (64 × 25 = 1600, with two decimal places). 1.25 × 8 = 10. Then 16 + 10 − 0.5 = 25.5. Answer: 25.5.
- 6
Practice question 6: 18² ÷ 9 × 2 − 30% of 120 = ?
18² = 324. Left to right: 324 ÷ 9 = 36, then 36 × 2 = 72. 30% of 120 = 36. So 72 − 36 = 36. Answer: 36.
Common Traps
- check_circleDoing multiplication before division. They have equal rank, so the one on the left goes first.
- check_circleSplitting a root: √(16 + 9) is √25 = 5, not √16 + √9 = 7.
- check_circleLosing a minus sign when you move a term across the equals sign in missing-number questions.
- check_circleMiscounting decimal places. Count them in both numbers, then place the point in the answer.
- check_circleRounding numbers. Simplification wants the exact value. Rounding belongs to approximation questions, which are a different type.
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Learn These by Heart
Squares up to 30, cubes up to 20, and the fraction values of common percentages (12.5% = 1/8, 37.5% = 3/8, 62.5% = 5/8). Most of the time saved on these questions comes from not having to calculate them.
How Bank and SSC Papers Test This
In IBPS PO, simplification sits in the Quantitative Aptitude section of prelims (35 questions, 30 marks), inside a 60-minute paper shared with English and Reasoning. The mains section is Data Analysis & Interpretation, where the same calculation speed helps with data interpretation sets.
In SSC CGL, the Tier 1 Quantitative Aptitude section has 25 questions for 50 marks. Number system and simplification is one of its listed topics, and the same skills carry into the Tier 2 Mathematical Abilities section.
IBPS Clerk Simplification Questions
IBPS Clerk prelims calls the maths section Numerical Ability: 35 questions for 35 marks in a 60-minute paper. Simplification is one of the listed topics, next to approximation, number series and arithmetic. The mains section is Quantitative Aptitude, 35 questions for 50 marks.
Because the clerk prelims gives one mark per maths question, fast and correct simplification is a direct way to add marks. Practise the order of operations until you do not have to think about it.
IBPS RRB Clerk (Office Assistant) Simplification Questions
The RRB clerical post is called Office Assistant (Multipurpose). Its prelims is only 45 minutes long, with two sections: Reasoning and Numerical Ability, each 40 questions for 40 marks. Simplification and approximation are listed together in its maths topics. The mains Numerical Ability section has 40 questions for 50 marks.
With 80 questions in 45 minutes, the RRB prelims gives less time per question than the IBPS PO or Clerk prelims. Simplification is the type to finish quickly and correctly, so time is left for longer arithmetic questions.
FAQs
What is the BODMAS rule in simplification questions?expand_more
Brackets, Of, Division, Multiplication, Addition, Subtraction. Division and multiplication have equal rank and go left to right. So do addition and subtraction.
What is the difference between simplification and approximation?expand_more
Simplification asks for the exact value. Approximation gives numbers like 24.97 and asks for the nearest value, so you round first and then calculate.
Are simplification questions asked in IBPS Clerk and RRB exams?expand_more
Yes. Simplification is a listed topic in the IBPS Clerk Numerical Ability syllabus and in the IBPS RRB Numerical Ability syllabus, alongside approximation.
Next steps
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- IBPS Clerk exam guidearrow_forward
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