BODMAS RULE

The rule or order that we use to simplify numerical expressions in math is called BODMAS rule.

Very simply way to remember BODMAS rule!

B ----> Brackets

O ----> Of (orders :Powers and radicals)

D ----> Division

M ----> Multiplication

A ----> Addition

S ----> Subtraction

Important Notes :

1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right.

2. Division does not always come before multiplication. We have to do one by one in the order from left to right.

3. In a particular simplification, if you have both addition and subtraction, do the operations one by one in the order from left to right.

Examples :

12 ÷ 3 x 5 = 4 x 5 = 20

13 - 5 + 9 = 8 + 9 = 17

In the above simplification, we have both division and multiplication. From left to right, we have division first and multiplication next. So we do division first and multiplication next.

Problem 1 :

Evaluate :

5 + 3 x 12

Solution :

= 5 + 3 x 12 ----> Multiplication

= 5 + 36 ----> Addition

= 41 ----> Answer

Problem 2 :

Evaluate :

24 ÷ 6 + 7²

Solution :

= 24 ÷ 6 + 7² ----> Exponent

= 24 ÷ 6 + 49 ----> Division

= 4 + 49 ----> Addition

= 53 ----> Answer

Problem 3 :

Evaluate :

3 x (27 - 16)

Solution :

= 3 x (27 - 16) ----> Brackets

= 3 x 11 ----> Multiplication

= 33 ----> Answer

Problem 4 :

Evaluate :

25 - 4 x (7 + 5) ÷ 4 + 3

Solution :

= 25 - 4 x (7 + 5) ÷ 4 + 3 ----> Brackets

= 25 - 4 x 12 ÷ 4 + 3 ----> Multiplication

= 25 - 48 ÷ 4 + 3 ----> Division

= 25 - 12 + 3 ----> Subtraction

= 13 + 3 ----> Addition

= 16 ----> Answer

Problem 5 :

Evaluate :

64 - 3(13 + 2 x 12 ÷ 8 - 3 x 3) + 11

Solution :

= 64 - 3(13 + 2 x 12 ÷ 8 - 3 x 3) + 11 ----> Brackets

= 64 - 3(13 + 2 x 12 ÷ 8 - 3 x 3) + 11 ----> Multiplication

= 64 - 3(13 + 24 ÷ 8 - 3 x 3) + 11 ----> Division

= 64 - 3(13 + 3 - 3 x 3) + 11 ----> Multiplication

= 64 - 3(13 +  3 - 9) + 11 ----> Addition

= 64 - 3(16 - 9) + 11 ----> Brackets

= 64 - 3(7) + 11 ----> Multiplication

= 64 - 21 + 10 ----> Subtraction

= 43 + 10 ----> Addition

= 53 ----> Answer

Problem 6 :

Evaluate :

[(45 - 3) ÷ (3² + 5)] x 2 - 5

Solution :

= [(45 - 3) ÷ (3² + 5)] x 2 - 5 ----> Square Brackets

= [(45 - 3) ÷ (3² + 5)] x 2 - 5 ----> Brackets

= [42 ÷ (3² + 5)] x 2 - 5 ----> Brackets

= [42 ÷ (3² + 5)] x 2 - 5 ----> Exponent

= [42 ÷ (9 + 5)] x 2 - 5 ----> Brackets

= [42 ÷ 14] x 2 - 5 ----> Square Brackets

= 3 x 2 - 5 ----> Multiplication

= 6 - 5 ----> Subtraction 

= 1 ----> Answer

Problem 7 :

Evaluate :

(2 x 3³ ÷ 9) - 2 x (6 + 8) ÷ 7

Solution :

= (2 x 3³ ÷ 9) - 2 x (6 + 8) ÷ 7 ----> Brackets

= (2 x 3³ ÷ 9) - 2 x (6 + 8) ÷ 7 ----> Exponent

= (2 x 27 ÷ 9) - 2 x (6 + 8) ÷ 7 ----> Multiplication

= (54 ÷ 9) - 2 x (6 + 8) ÷ 7 ----> Brackets

= 6 - 2 x (6 + 8) ÷ 7 ----> Brackets

= 6 - 2 x 14 ÷ 7 ----> Multiplication

= 6 - 28 ÷ 7 ----> Multiplication

= 6 - 4 ----> Multiplication

= 2 ----> Answer

Problem 8 :

Evaluate :

(120 - 12) ÷ (36 ÷ 3) - 22 + 7

Solution :

= (120 - 12) ÷ (36 ÷ 3) - 22 + 7 ----> Brackets

= 108 ÷ (36 ÷ 3) - 22 + 7 ----> Brackets

= 108 ÷ 12 - 22 + 7 ----> Division

= 9 - 22 + 7 ----> Subtraction

= -13 + 7 ----> Subtraction

= -6 ----> Answer

Problem 9 :

Evaluate :

5 x 12 ÷ 10 - (6 x 4) ÷ 12

Solution :

= 5 x 12 ÷ 10 - (6 x 4) ÷ 12 ----> Brackets

= 5 x 12 ÷ 10 - 24 ÷ 12 ----> Multiplication

= 60 ÷ 10 - 24 ÷ 12 ----> Division

= 6 - 24 ÷ 12 ----> Division

= 6 - 2 ----> Subtraction

= 4 ----> Answer

Problem 10 :

Evaluate :

(29 - 13) x 3 ÷ (15 - 7) + 8

Solution :

= (29 - 13) x 3 ÷ (15 - 7) + 8 ----> Brackets

= 16 x 3 ÷ (15 - 7) + 8 ----> Brackets

= 16 x 3 ÷ 8 + 8 ----> Multiplication

= 48 ÷ 8 + 8 ----> Division

= 6 + 8 ----> Addition

= 14 ----> Answer

Problem 11 :

Evaluate :

[96 ÷ (6² - 12) ÷ 4 - 3] x 2 + 13

Solution :

= [96 ÷ (6² - 12) ÷ 4 - 3] x 2 + 13 ----> Square Brackets

= [96 ÷ (6² - 12) ÷ 4 - 3] x 2 + 13 ----> Brackets

= [96 ÷ (6² - 12) ÷ 4 - 3] x 2 + 13 ----> Exponent

= [96 ÷ (36 - 12) ÷ 4 - 3] x 2 + 13 ----> Brackets

= [96 ÷ 24 ÷ 4 - 3] x 2 + 13 ----> Division

= [4 ÷ 4 - 3] x 2 + 13 ----> Division

= [1 - 3] x 2 + 13 ----> Square Brackets

= -2 x 2 + 13 ----> Multiplication

= -4 + 13 ----> Subtraction

= 9 ----> Answer

Problem 12 :

Evaluate :

(a² + bc) + c³ ÷ (a² + b) - c

if a = 3, b = -5 and c = 4.

Solution :

(a² + bc) + c³ ÷ (a² + b) - c

Substitute a = 3, b = -5 and c = 4.

[3² + (-5)4] + 4³ ÷ [3² + (-5)] - 4

 Evaluation :

= [3² + (-5)4] + 4³ ÷ [3² + (-5)] - 4 ----> Square Brackets

= [3² + (-5)4] + 4³ ÷ [3² + (-5)] - 4 ----> Exponent

= [9 + (-5)4] + 4³ ÷ [3² + (-5)] - 4 ----> Multiplication

= [9 - 20] + 4³ ÷ [3² + (-5)] - 4 ----> Square Brackets

= -11 + 4³ ÷ [3² + (-5)] - 4 ----> Square Brackets

= -11 + 4³ ÷ [3² + (-5)] - 4 ----> Exponent

= -11 + 4³ ÷ [9 + (-5)] - 4 ----> Multiplication

= -11 + 4³ ÷ [9 - 5] - 4 ----> Square Brackets

= -11 + 4³ ÷ 4 - 4 ----> Exponent

= -11 + 64 ÷ 4 - 4 ----> Division

= -11 + 16 - 4 ----> Subtraction

= 5 - 4 ----> Subtraction

= 1 ----> Answer

Problem 13 :

Evaluate :

Solution :

Problem 14 :

Evaluate :

Solution :

Problem 15 :

Evaluate :

Solution :

Problem 16 :

What is the value of

if a = -2, b = 3 and c = 5.

Solution :

Problem 17 :

What is the value of

if a = 4, b = -3 and c = 7.

Solution :

Problem 18 :

What is the value of

if a = 3, b = -1 and c = -2.

Solution :

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