Simplification

Simplification

Table of Contents

Formula and Concept of Simplification

BODMAS Rule

BODMAS is an acronym that stands for:

  • Brackets
  • Orders (i.e., powers and square roots, etc.)
  • Division and Multiplication (from left to right)
  • Addition and Subtraction (from left to right)

Example:

8+3×(52)2


Using BODMAS:

=8+3×32

 

=8+3×9

 

=8+27

 

=35

 

Simplification Rules

a. Removing Brackets:

Example:

3×(4+5)

 

=3×9

 

=27

 

b. Simplifying Fractions:

Example:

69

 

=23

 

c. Combining Like Terms:

Example:

=

d. Expanding Expressions:

Example:

 

=a2+2ab+b2

 

Concept of Simplification

a. Factorization:
Breaking down an expression into its factors.

Example:

 

=

b. Combining Similar Terms:
Combine terms with the same variable and exponent.

Example:

=

c. Removing Common Factors:
Dividing the terms by their highest common factor.

Example:

 

=

Formula for Simplification

a. LCM (Least Common Multiple)

LCM of a and b=a×bHCF of a and b

 

b. HCF (Highest Common Factor)

HCF of a and b=a×bLCM of a and b

 

Key Concepts in Simplification

a. Distributive Property:

 

b. Associative Property:

c. Commutative Property:

d. Identity Element:

 

Problems of Simplification


Question: 5 + (8 x 2) – 3
Steps: Perform multiplication first: 8 x 2 = 16.

Then follow with addition and subtraction: 5 + 16 – 3 = 18.

Answer: 18

 

Question: (12 ÷ 3) x 5 + 1
Steps: Perform division first: 12 ÷ 3 = 4.

Then multiply by 5 and add 1: 4 x 5 + 1 = 21.

Answer: 21

 

Question: 20 – [3 x (4 – 1)]
Steps: Solve the expression in the bracket first: 4 – 1 = 3. 

Then multiply inside the bracket: 3 x 3 = 9. 

Finally, subtract 9 from 20: 20 – 9 = 11. 

Answer: 11

 

Question: 7 ^ 2 + (5 x 2) – 1
Steps: Perform the exponent first: 7 ^ 2 = 49. 

Then multiply 5 x 2 = 10. 

Finally, add and subtract: 49 + 10 – 1 = 58. 

Answer: 58

 

Question: (8 + 2) ÷ 2 x 3
Steps: Solve the expression in the bracket first: 8 + 2 = 10. 

Then divide by 2: 10 ÷ 2 = 5. 

Finally, multiply by 3: 5 x 3 = 15. 

Answer: 15

 

Question: 100 – {25 – [3 + (2 x 1)]}
Steps: Solve the innermost bracket first: 2 x 1 = 2. 

Then add inside the next bracket: 3 + 2 = 5. 

Then subtract 5 from 25: 25 – 5 = 20. 

Finally, subtract 20 from 100: 100 – 20 = 80. 

Answer: 80

 

Question: 4 x (6 – 2) + 7
Steps: Solve the expression in the bracket first: 6 – 2 = 4. 

Then multiply 4 x 4 = 16. 

Finally, add 7: 16 + 7 = 23. 

Answer: 23

 

Question: (3 ^ 3 – 1) / 2 + 4
Steps: Perform the exponent first: 3 ^ 3 = 27. 

Then subtract 1 from 27: 27 – 1 = 26. Then divide by 2: 26 / 2 = 13. 

Finally, add 4: 13 + 4 = 17. 

Answer: 17

 

Question: 5 + {2 x [3 + (1 – 0.5)]}
Steps: Solve the expression in the innermost bracket first: 1 – 0.5 = 0.5. Then add inside the next bracket: 3 + 0.5 = 3.5. 

Then multiply by 2: 3.5 x 2 = 7. 

Finally, add 5 + 7 = 12. 

Answer: 12

 

Question: (15 ÷ 3) x (2 + 1) – 2
Steps: Solve the expression in both brackets first: 15 ÷ 3 = 5 and 2 + 1 = 3. 

Then multiply 5 x 3 = 15. 

Finally, subtract 2: 15 – 2 = 13. 

Answer: 13

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MCQ’s


1. Which rule is used to simplify the expression 4+3×(52)2?
A) Associative Property
B) BODMAS Rule
C) Distributive Property
D) Commutative Property
Answer: B) BODMAS Rule


2. What is the value of 2×(3+4)5?
A) 11
B) 9
C) 13
D) 7
Answer: B) 9


3. Simplify: 1218
A) 23
B) 32
C) 46
D) 12
Answer: A) 23


4. What is ?
A) 15x
B) 8x
C) 2x
D) 10x
Answer: B) 8x


5. Expand: (.
A) a2+ab+b2
B) a2ab+b2
C) a2+2ab+b2
D) a22ab+b2
Answer: C) a2+2ab+b2


6. What is

?

A) 
B)

C)
D)

Answer: A)


7. Simplify: 7a2b14ab
A) 12a

B) 7
C) 114ab

D) 12b

Answer: A) 12


8. What is ?
A)
B)


C)

D)

Answer: B)


9. Simplify: a2b2ab
A)
B)

C) a2+b2
D) a22ab+b2
Answer: A)


10. What is 2x2+3x5x2+2
A) 3x2+3x+2
B) 3x22x+2
C) 3x2+x+4
D) 3x2+5x+2
Answer: A) 3x2+3x+2


11. Simplify: 5×(4+3).
A) 35
B) 40
C) 25
D) 30
Answer: A) 35

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