Order of Operations – BODMAS Rule

Example 14. Find the value of the expression 4 – 3.6 ÷ 4 + 0.2 × 0.5 – 0.1 of 3.2.

Solution. To find the value of the given expression, we will use BODMAS. Here, given expression is 4 – 3.6 ÷ 4 + 0.2 × 0.5 – 0.1 of 3.2.

	Evaluate	Final Expression
Step 1	0.1 of 3.2 = (0.1 × 3.2) = 0.32	= 4 – 3.6 ÷ 4 + 0.2 × 0.5 – 0.32
Step 2	3.6 ÷ 4  = 0.9	= 4 – 0.9 + 0.2 × 0.5 – 0.32
Step 3	0.2 × 0.5 = 0.1	= 4 – 0.9 + 0.1 – 0.32
Step 4	Rearrange	= 4 + 0.1 – 0.32 – 0.9
Step 5	4 + 0.1 = 4.1	= 4.1 – 0.32 – 0.9
Step 6	– 0.32 – 0.9 = – 1.22	= 4.1 – 1.22
Step 7	4.1 – 1.22 = 2.88	= 2.88

Therefore, required value of the expression is 2.88.

Example 15. Find the value of the expression (0.2 ÷ 0.5) ÷ 0.2 + [{(0.16 ÷ 0.8) × 0.2} – 0.2 × 0.3].

Solution. To find the value of the given expression, we will use BODMAS. Here, given expression is (0.2 ÷ 0.5) ÷ 0.2 + [{(0.16 ÷ 0.8) × 0.2} – 0.2 × 0.3].

Clearly, we need calculate (¯) bracket first. Then we will calculate ( ), { } and [ ] brackets.

	Evaluate	Final Expression
Step 1	0.16 ÷ 0.8 = 0.2	= (0.2 ÷ 0.5) ÷ 0.2 + [{0.2 × 0.2} – 0.2 × 0.3]
Step 2	0.2 ÷ 0.5 = 0.4	= 0.4 ÷ 0.2 + [{0.2 × 0.2} – 0.2 × 0.3]
Step 3	0.2 × 0.2 = 0.04	= 0.4 ÷ 0.2 + [0.04 – 0.2 × 0.3]
Step 4	0.04 – 0.2 × 0.3 = 0.04 – 0.06 = – 0.02	= 0.4 ÷ 0.2 + [– 0.02]
Step 5	[– 0.02] = – 0.02	= 0.4 ÷ 0.2 – 0.02
Step 6	0.4 ÷ 0.2  = 2	= 2 – 0.02
Step 7	2 – 0.02 = 1.98	= 1.98

Therefore, required value of the expression is 1.98.

Therefore, required value of the expression is 1.98.

Example 17. Simplify the expression [29 – (–2){6 – (7 – 3)}] ÷ [3 × {5 + (–3) × (–2)}].

Solution. To find the value of the given expression, we will use BODMAS. Here, given expression is (0.2 ÷ 0.5) ÷ 0.2 + [{(0.16 ÷ 0.8) × 0.2} – 0.2 × 0.3].

	Evaluate	Final Expression
Step 1	(7 – 3) = 4	= [29 – (–2){6 – 4}] ÷ [3 × {5 + (–3) × (–2)}]
Step 2	{6 – 4} = 2	= [29 – (–2)(2)] ÷ [3 × {5 + (–3) × (–2)}]
Step 3	{5 + (–3) × (–2)} = {5 + 6} = 11	= [29 – (–2)(2)] ÷ [3 × 11]
Step 4	[29 – (–2)(2)] = [29 + 4] = 33	= 33 ÷ [3 × 11]
Step 5	[3 × 11] = 33	= 33 ÷ 33
Step 6	33 ÷ 33 = 1	= 1

Therefore, required value of the expression is 1.

Exercise 1. Simplify the expression [{(8 × (2 ÷ 4} × 2] ÷ (4 – 2)

Exercise 2. Simplify the expression {18 + (6 ÷ 2) – 4} × {2 + (10 ÷ 2)}

Exercise 3. Simplify the expression {(7 – 2) × 3} + {(24 ÷ 6) + (3 ÷ 3)}

Exercise 4. Simplify the expression [{(24 ÷ 8) ÷ 3} + {(8 × 2) ÷ 4}] – 2

Exercise 5. Simplify the expression 36 – [18 – {14 – (15 – 4 ÷ 2× 2)}]

Exercise 6. Simplify the expression 45 – [38 – {60 ÷ 3 – (6 – 9 ÷ 3) ÷ 3}]

Exercise 7. Simplify the expression {3 + (12 ÷ 4) – 2} × {(8 ÷ 2) + 7 – (6 ÷ 3)}

Exercise 8. Simplify the expression

Exercise 9. Simplify the expression

Exercise 10. Simplify the expression [{(64 ÷ 4) + 9} – (5 of 5)] + {(8 ÷ 2) ÷ 8}

Exercise 11. Simplify the expression

Exercise 12. Simplify the expression [{(729 ÷ 9) ÷ 3} – {(15 × 3) ÷ 9}] – {(2 × 7) + (8 of 5)}]