Simplification for IBPS Clerk

A simplification question gives you an expression and asks for its value, or hides one number behind a "?" and asks you to find it. There is nothing to interpret and no trick in the wording. It is pure calculation, which is exactly why it matters: with sharp mental maths, each question takes 15–25 seconds, and the time you save pays for the harder questions later in the section.

This guide covers the order of operations, the shortcuts worth learning (and why they work, so you trust them under pressure), six worked examples and a practice set.

BODMAS, and where people slip

Work in this order:

1. Brackets
2. Orders and "of": powers, roots, and "of" as in "3/4 of 80"
3. Division and Multiplication, left to right
4. Addition and Subtraction, left to right

The word "left to right" is where most slips happen. Division and multiplication have equal priority, so 48 ÷ 4 × 3 means (48 ÷ 4) × 3 = 36, not 48 ÷ 12 = 4. The same goes for subtraction and addition: 50 − 20 + 5 = 35, not 25.

"Of" is multiplication done early. So 60 ÷ 1/4 of 8 means 60 ÷ (1/4 × 8) = 60 ÷ 2 = 30.

Shortcuts worth learning, and why they work

Two notes on the table:

• For × 11, if the middle sum is 10 or more, carry 1 to the left: 76 × 11 = 7 (13) 6, which becomes 836.
• For numbers near 100, 98 × 97: take 100 − 2 − 3 = 95, write it as 9,500, then add 2 × 3 = 6, giving 9,506. Above 100 it works the same way with additions: 103 × 106 = 10,900 + 18 = 10,918.

Fractions and percentages

Many "of" questions become one-step calculations once you swap a percentage for its fraction.

So 62.5% of 320 is 5/8 of 320 = 40 × 5 = 200, done in your head.

For mixed fractions, add the whole numbers and the fractions separately. 3¼ + 2⅚ − 1⅔: whole parts 3 + 2 − 1 = 4; fractions 3/12 + 10/12 − 8/12 = 5/12. Answer 4 5/12.

Worked examples

Example 1. 45% of 620 + 3/7 of 490 − 129 = ?

1. 45% of 620: 10% is 62, so 40% is 248; 5% is 31. Total 279.
2. 3/7 of 490: 490 ÷ 7 = 70, and 70 × 3 = 210.
3. 279 + 210 − 129 = 360.

Example 2. (21² − 16²) ÷ 37 × 4 = ?

1. 21² − 16² = (21 − 16)(21 + 16) = 5 × 37 = 185.
2. 185 ÷ 37 = 5. Then 5 × 4 = 20.
3. Note that the 37 was a hint. Spotting a² − b² saved squaring both numbers.

Example 3. √1,764 + ∛3,375 − 12² ÷ 16 = ?

1. √1,764 = 42 (42² = 1,764). ∛3,375 = 15 (15³ = 3,375).
2. 12² ÷ 16 = 144 ÷ 16 = 9. Orders first, then division.
3. 42 + 15 − 9 = 48.

Example 4 (missing percentage). ?% of 840 + 62.5% of 320 = 452

1. 62.5% of 320 = 5/8 of 320 = 200.
2. ?% of 840 = 452 − 200 = 252.
3. ? = 252 ÷ 840 × 100 = 30.

Example 5 (missing square). ?² + 24% of 450 = 17² + 44

1. 24% of 450 = 108. 17² + 44 = 289 + 44 = 333.
2. ?² = 333 − 108 = 225.
3. ? = 15.

Example 6. 2/3 of 3/4 of 480 = ?

1. 3/4 of 480 = 360.
2. 2/3 of 360 = 240. (Or multiply the fractions first: 2/3 × 3/4 = 1/2, and half of 480 is 240.)

What to memorise

• Tables to 30.
• Squares to 50 and cubes to 20.
• Square roots of perfect squares up to 2,500, and cube roots of perfect cubes up to 8,000.
• The fraction–percentage pairs in the table above.

These are not extras. They are the raw material of every simplification question. A candidate who knows 47² = 2,209 on sight answers √2,209 in two seconds; one who does not may spend thirty.

Speed habits

• Write only intermediate results, not every step.
• Look at the options before the last step. If only one option ends in the right digit, or is the right size, you may not need to finish.
• Unit-digit check: in 23 × 47, the answer must end in 1 (3 × 7 = 21). This kills wrong options fast.
• Keep one rough sheet in columns so you can find a number again.

Common mistakes

• Doing division before an earlier multiplication, or subtraction before an earlier addition, instead of going left to right.
• Treating "of" as ordinary multiplication after a division sign.
• Squaring both numbers when a² − b² would do it in one step.
• Guessing a square root from the first digits without checking the last digit.

Practice

Set a 4-minute timer for all eight.

1. 35% of 460 + 2/9 of 675
2. 24² − 18²
3. (156 ÷ 12) × 7 + 9²
4. √2,209 + ∛1,728
5. ? × 18 = 40% of 945 + 18
6. 85²
7. 4½ + 3⅔ − 2⅚
8. 103 × 106

Answers:

1. 311. 35% of 460 = 161 (46 × 3 = 138, plus 23); 675 ÷ 9 × 2 = 150.
2. 252. (24 − 18)(24 + 18) = 6 × 42.
3. 172. 13 × 7 = 91; 91 + 81.
4. 59. 47 + 12.
5. 22. 40% of 945 = 378; 378 + 18 = 396; 396 ÷ 18 = 22.
6. 7,225. 8 × 9 = 72, then 25.
7. 5⅓. Whole parts 4 + 3 − 2 = 5; fractions 3/6 + 4/6 − 5/6 = 2/6 = 1/3.
8. 10,918. 100 + 3 + 6 = 109, so 10,900; plus 3 × 6 = 18.

What to do next

• Write out squares to 50 and cubes to 20 once, then test yourself daily.
• Do ten simplification questions every day with a 4-minute timer, and log the time.
• Move on to approximation, which uses the same skills with rounding.
• See the numerical ability plan for where simplification fits in the six-week order.