SSC GD Simplification Notes 2026 – Complete Handwritten Notes, Formulas & Solved Questions

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SSC GD Simplification

Complete Handwritten Notes • Very Simple English • SSC GD 2026

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SSC GD Simplification Notes – Complete Chapter

Easy idea: Simplification means reducing a mathematical expression to its simplest value. In SSC GD questions, you may see brackets, fractions, decimals, percentages, powers, roots and mixed operations. The safest method is to follow the correct order and calculate one step at a time.

1. BODMAS Rule

BODMAS is the basic rule used to decide which operation should be done first.

\[B\rightarrow O\rightarrow D\rightarrow M\rightarrow A\rightarrow S\]

B — Brackets: solve brackets first.

O — Orders: solve powers and roots.

D — Division.

M — Multiplication.

A — Addition.

S — Subtraction.

Remember: Division and multiplication have equal priority, so work from left to right. Addition and subtraction also have equal priority and are solved from left to right.

Example: 18 + 24 ÷ 6 × 2
24 ÷ 6 = 4
4 × 2 = 8
18 + 8 = 26
Answer = 26

2. Brackets

When different brackets occur, start from the innermost bracket.

\[( )\rightarrow[ ]\rightarrow\{ \}\]

Example: 50 − [12 + (9 − 5)]
9 − 5 = 4
12 + 4 = 16
50 − 16 = 34
Answer = 34

Plus Sign Before a Bracket

A plus sign does not change the signs inside.

\[a+(b-c)=a+b-c\]\[a+(b+c)=a+b+c\]

Minus Sign Before a Bracket

A minus sign changes the sign of every term inside the bracket.

\[a-(b-c)=a-b+c\]\[a-(b+c)=a-b-c\]

3. Fractions

A fraction has a numerator above the line and a denominator below the line.

\[\frac{a}{b},\quad b\ne0\]

Addition of Fractions

\[\frac ab+\frac cd=\frac{ad+bc}{bd}\]

Example: \(\frac23+\frac16\)
LCM = 6
\(\frac23=\frac46\)
\(\frac46+\frac16=\frac56\)
Answer = \(\frac56\)

Subtraction of Fractions

\[\frac ab-\frac cd=\frac{ad-bc}{bd}\]

Example: \(\frac78-\frac14=\frac78-\frac28=\frac58\).

Multiplication of Fractions

\[\frac ab\times\frac cd=\frac{ac}{bd}\]

Division of Fractions

\[\frac ab\div\frac cd=\frac ab\times\frac dc\]

Shortcut: Cancel common factors before multiplying. This reduces the numbers and saves time.

4. Decimal Numbers

When adding or subtracting decimals, keep the decimal points aligned.

2.50 + 1.75 = 4.25
8.40 − 2.35 = 6.05

When multiplying by 10, 100 or 1000, the decimal moves to the right.

When dividing by 10, 100 or 1000, the decimal moves to the left.

\[3.45\times10=34.5\]\[3.45\times100=345\]\[3.45\div10=0.345\]

Decimal to Fraction

\[0.5=\frac12\]\[0.25=\frac14\]\[0.75=\frac34\]\[0.125=\frac18\]

5. Percentage in Simplification

Percent means per hundred.

\[x\%=\frac{x}{100}\]

Percentage	Fraction	Decimal
10%	1/10	0.10
12.5%	1/8	0.125
20%	1/5	0.20
25%	1/4	0.25
50%	1/2	0.50
75%	3/4	0.75

Example: Find 25% of 240.
25% = 1/4
240 ÷ 4 = 60
Answer = 60

6. Powers and Exponents

A power tells us how many times a base is multiplied by itself.

\[a^m\times a^n=a^{m+n}\]\[\frac{a^m}{a^n}=a^{m-n}\quad(a\ne0)\]\[(a^m)^n=a^{mn}\]\[(ab)^n=a^nb^n\]\[a^0=1\quad(a\ne0)\]\[a^{-n}=\frac1{a^n}\]

Example: \(2^3\times2^2=2^5=32\).

7. Squares and Square Roots

\[n^2=n\times n\]\[\sqrt{n^2}=n\quad\text{for }n\ge0\]

n	n²	n	n²
1	1	11	121
2	4	12	144
3	9	13	169
4	16	14	196
5	25	15	225
6	36	16	256
7	49	17	289
8	64	18	324
9	81	19	361
10	100	20	400

\(\sqrt{49}=7\) because \(7^2=49\).

8. Cubes and Cube Roots

\[n^3=n\times n\times n\]\[\sqrt[3]{27}=3\]

Useful cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.

9. Mixed Simplification

Example 1: 36 ÷ 6 + 4 × 5
6 + 20 = 26
Answer = 26

Example 2: 100 − 25 ÷ 5 × 2
25 ÷ 5 = 5
5 × 2 = 10
100 − 10 = 90
Answer = 90

Example 3: \(3^2+\sqrt{49}\)
9 + 7 = 16
Answer = 16

Example 4: \(\frac12+\frac34\times2\)
First multiplication: \(\frac34\times2=\frac32\)
Then \(\frac12+\frac32=2\)
Answer = 2

10. Fast Calculation Tricks

• Multiply by 5: multiply by 10 and divide by 2.
• Multiply by 25: multiply by 100 and divide by 4.
• Multiply by 50: multiply by 100 and divide by 2.
• 25% = 1/4.
• 50% = 1/2.
• 75% = 3/4.
• 125% = 5/4.

11. Simplification with Algebraic Identities

\[(a+b)^2=a^2+2ab+b^2\]\[(a-b)^2=a^2-2ab+b^2\]\[a^2-b^2=(a-b)(a+b)\]

Example: \(51^2-49^2\)
Use \(a^2-b^2=(a-b)(a+b)\)
\((51-49)(51+49)=2\times100=200\).
Answer = 200

12. SSC GD Solved Questions

Q1. Simplify: 48 ÷ 8 + 7 × 2

48 ÷ 8 = 6 and 7 × 2 = 14.
6 + 14 = 20.
Answer = 20

Q2. Simplify: 72 − [18 + (12 − 5)]

12 − 5 = 7, 18 + 7 = 25, 72 − 25 = 47.
Answer = 47

Q3. Simplify: \(\frac34+\frac58\)

\(\frac34=\frac68\), so \(\frac68+\frac58=\frac{11}{8}=1\frac38\).
Answer = \(1\frac38\)

Q4. Find 15% of 200.

10% = 20 and 5% = 10.
20 + 10 = 30.
Answer = 30

Q5. Simplify: \(2^4+\sqrt{36}\)

16 + 6 = 22.
Answer = 22

Q6. Simplify: 2.5 × 4 + 6

2.5 × 4 = 10.
10 + 6 = 16.
Answer = 16

Q7. Simplify: 120 ÷ 10 + 5 × 3

12 + 15 = 27.
Answer = 27

Q8. Simplify: \(\frac23\times\frac9{10}\)

Cancel 3 with 9: \(\frac{6}{10}=\frac35\).
Answer = \(\frac35\)

Q9. Simplify: 5² − 3²

25 − 9 = 16.
Answer = 16

Q10. Simplify: 25% of 160 + 10

25% of 160 = 40.
40 + 10 = 50.
Answer = 50

Q11. Simplify: 144 ÷ 12 + 18 − 5

12 + 18 − 5 = 25.
Answer = 25

Q12. Simplify: \(\frac56-\frac13+\frac12\)

\(\frac13=\frac26\), \(\frac12=\frac36\). So \(\frac56-\frac26+\frac36=\frac66=1\).
Answer = 1

Q13. Simplify: \((12+8)\div5+3^2\)

20 ÷ 5 = 4 and 3² = 9.
4 + 9 = 13.
Answer = 13

Q14. Simplify: 0.4 × 25

0.4 × 100 = 40, so half gives 20, or directly 0.4 × 25 = 10.
Answer = 10

Q15. Simplify: \(51^2-49^2\)

\((51-49)(51+49)=2×100=200\).
Answer = 200

13. Practice Set

1. 18 + 24 ÷ 6 × 2
2. 40 − [12 + (9 − 5)]
3. \(\frac25+\frac3{10}\)
4. \(\frac78-\frac14\)
5. 0.75 + 1.25
6. \(2^4+\sqrt{36}\)
7. 72 ÷ 8 + 5 × 3
8. 100 − 25 ÷ 5 × 2
9. \(\frac34\times\frac89\)
10. 5² − 3²
11. 35% of 200
12. \(3^3+\sqrt{64}\)
13. 2.5 × 8 − 5
14. \(\frac56-\frac13\)
15. 25% of 360
16. 96 ÷ 8 + 7 × 4
17. \(\frac34+\frac14\times2\)
18. 125% of 80
19. \((35+15)÷10+2^3\)
20. \(41^2-39^2\)

14. Answer Key

Answers

1. 26   2. 24   3. 7/10   4. 5/8   5. 2
6. 22   7. 24   8. 90   9. 2/3   10. 16
11. 70   12. 35   13. 15   14. 1/2   15. 90
16. 40   17. 5/4   18. 100   19. 13   20. 160

15. Common Mistakes

• Do not add before multiplication or division.
• Do not ignore brackets.
• For equal-priority operations, work from left to right.
• Do not forget to simplify the final fraction.
• Check decimal movement carefully.
• Do not confuse square with square root.
• Read the question again after calculation.

16. Quick Revision

\[B\rightarrow O\rightarrow D\rightarrow M\rightarrow A\rightarrow S\]\[\frac ab+\frac cd=\frac{ad+bc}{bd}\]\[\frac ab\times\frac cd=\frac{ac}{bd}\]\[x\%=\frac{x}{100}\]\[a^m\times a^n=a^{m+n}\]\[(a+b)^2=a^2+2ab+b^2\]\[a^2-b^2=(a-b)(a+b)\]

Golden rule: follow the order, write the steps, and then check the final answer.

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