Simplification for SSC GD

A simplification question gives you a line of numbers and signs and asks for the value. There is almost no theory. What the question tests is whether you do the operations in the right order, and whether you can calculate quickly without slipping.

That makes it a good place to collect marks early in the maths section. A well-practised candidate can clear most of these in 30 to 40 seconds each, leaving more time for word problems. The same skills also sit inside every other topic: a profit question or an average question ends with a small simplification.

The BODMAS order

Brackets inside brackets. Solve the innermost first. The usual order is small brackets ( ), then curly brackets { }, then square brackets [ ].

The "of" trap

"Of" means multiply, but it ranks above division. This single rule decides many questions.

• 24 ÷ 4 × 3: left to right, 6 × 3 = 18.
• 24 ÷ 4 of 3: "of" first, 4 of 3 = 12, then 24 ÷ 12 = 2.

Same numbers, very different answers. Both versions appear in options to catch you.

Powers, roots and fractions inside a line

Squares, cubes and square roots are done at the "O" stage, before division and multiplication. So √144 + 5² − 3 × 4 = 12 + 25 − 12 = 25.

For mixed numbers, you can add the whole parts and the fraction parts separately. Our fractions and decimals guide covers adding, dividing and comparing fractions in detail.

Two special question types

Missing number. The line has a "?" in it. Undo the operations: move everything else to the other side, reversing each sign (× becomes ÷, + becomes −).

Approximation. The question says "approximately" or uses "≈". Round each number to the nearest easy value, then calculate. The options are usually far enough apart that rounding gives the right one. Don't round when the options are close together.

Speed tricks worth learning

For the 11 trick, if the digit sum is 10 or more, carry the 1: 78 × 11 = 7, 15, 8 → 858.

Solved examples

Example 1. 18 + 36 ÷ 4 × 3 − 7 = ?

1. Division and multiplication, left to right: 36 ÷ 4 = 9, then 9 × 3 = 27.
2. Now 18 + 27 − 7.
3. Left to right: 45 − 7 = 38.

Example 2. 64 ÷ 4 of 2 + 5 = ?

1. "Of" first: 4 of 2 = 8.
2. Division: 64 ÷ 8 = 8.
3. Addition: 8 + 5 = 13. (Reading "of" as × would give 16 × 2 + 5 = 37, a trap option.)

Example 3. 120 − [48 ÷ {20 − (4 × 2)}] = ?

1. Innermost: 4 × 2 = 8.
2. Curly bracket: 20 − 8 = 12.
3. Square bracket: 48 ÷ 12 = 4.
4. Finally: 120 − 4 = 116.

Example 4. 2½ + 3⅓ − 1¼ = ?

1. Whole parts: 2 + 3 − 1 = 4.
2. Fraction parts, with denominator 12: 6/12 + 4/12 − 3/12 = 7/12.
3. Answer: 4 7/12. Check: 30/12 + 40/12 − 15/12 = 55/12 = 4 7/12.

Example 5. √196 + 4³ ÷ 8 − 3² = ?

1. Roots and powers: √196 = 14, 4³ = 64, 3² = 9.
2. Division: 64 ÷ 8 = 8.
3. Now 14 + 8 − 9 = 13.

Example 6. 45 × ? ÷ 9 = 75. Find ?.

1. 45 ÷ 9 = 5, so the line says 5 × ? = 75.
2. ? = 75 ÷ 5 = 15.
3. Check: 45 × 15 = 675, and 675 ÷ 9 = 75.

Example 7 (approximation). 299.8 ÷ 5.02 + 19.9 × 3.1 ≈ ?

1. Round: 300 ÷ 5 + 20 × 3.
2. 60 + 60 = 120 (approximately).
3. The exact value is about 121.4, so 120 is the closest sensible option.

Common mistakes

Practice set

1. 25 + 15 × 4 − 10
2. 72 ÷ 8 × 3
3. 72 ÷ 8 of 3
4. 90 − [30 − {12 − (9 − 5)}]
5. 1½ + 2¾ − 1⅛
6. √225 + 2⁴ − 6 × 3
7. 36 × ? ÷ 12 = 45
8. 24 × 25 (use the trick)

Answers:

1. 15 × 4 = 60; 25 + 60 − 10 = 75.
2. Left to right: 9 × 3 = 27.
3. 8 of 3 = 24; 72 ÷ 24 = 3.
4. 9 − 5 = 4; 12 − 4 = 8; 30 − 8 = 22; 90 − 22 = 68.
5. Wholes: 1 + 2 − 1 = 2. Fractions: 4/8 + 6/8 − 1/8 = 9/8 = 1⅛. Total 3⅛.
6. 15 + 16 − 18 = 13.
7. 36 ÷ 12 = 3, so 3 × ? = 45 and ? = 15.
8. 2,400 ÷ 4 = 600.

What to do next

• Do 20 BODMAS lines a day for one week, timing yourself.
• Write five "of" versus × pairs and solve both versions.
• Learn squares to 30 and cubes to 15 with our squares and square roots guide.
• Add one trick a day from our calculation tricks guide.