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!

----> Brackets

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

D ----> Division

----> Multiplication

----> Addition

----> Subtraction

bodmas-rule.png

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.

Note :

Inside the brackets, if there are two or more operations, follow BODMAS Rule inside the brackets.

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 + 7----> 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) ÷ (3+ 5)] x 2 - 5 ----> Square Brackets

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

[42 ÷ (3+ 5)] x 2 - 5 ----> Brackets

[42 ÷ (3+ 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 :

bodmasrule1.png

Solution :

bodmasrule2.png

Problem 14 :

Evaluate :

bodmasrule3.png

Solution :

bodmasrule4.png

Problem 15 :

Evaluate :

bodmasrule5.png

Solution :

bodmasrule6.png

Problem 16 :

What is the value of

bodmasrule7.png

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

Solution :

bodmasrule8.png

Problem 17 :

What is the value of

bodmasrule9.png

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

Solution :

bodmasrule10.png

Problem 18 :

What is the value of

bodmasrule11.png

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

Solution :

bodmasrule12.png
bodmas-rule-1

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