Page 40 - Math Skill - 5

38 Maths

Exercise 3.8

1. Simplify the following numerical expressions.

(a) 18 + 6 ÷ 3 (b) 173 × 15 ÷ 5 + 4 – 1 (c) 68 – 14 × 2
(d) 252 – 30 × 9 ÷ 3 + 11 (e) 18 + 36 ÷ 18 × 4 – 5 (f) 100 – 72 ÷ 9 + 4 × 2

Solving the Brackets

Brackets are useful in simplification of numerical expressions involving two or more operations.
Four kinds of brackets are used in numerical expressions.
™ Line bracket or Vinculum — ™ Curly Brackets or Braces { }

™ Round Brackets or Small Brackets ( ) ™ Square Brackets or Big Brackets [ ]
The order of simplifying these brackets is as below:

I. Vinculum II. Small brackets III. Curly brackets IV. Square brackets

To remember the rules easily, we use a mnemonic as VBODMAS.
V → Vinculum
B → Brackets [ { ( ) } ] Fact-o-meter
O → Of

D → Division Always multiply the two numbers
connected by ‘Of’.
M → Multiplication For example, 3 of 5 = 3 × 5 = 15,
A → Addition 6 of 15 = 6 × 15 = 90
S → Subtraction

Now, let’s learn through examples.

Let’s Attempt

Example 1: Simplify: 15 – [20 ÷ {6 – 2 × (7 – 4 – 2)}]

Solution: 15 – [20 ÷ {6 – 2 × (7 – 4 – 2)}]
= 15 – [20 ÷ {6 – 2 × 1}] [Removing small brackets]

= 15 – [20 ÷ {6 – 2}]
= 15 – [20 ÷ 4] [Removing curly brackets]
= 15 – 5 = 10 [Removing big brackets]

Example 2: Simplify: [28 ÷ {10 – (3 + 6 – 3)}]

Solution: [28 ÷ {10 – (3 + 6 – 3)}]
= [28 ÷ {10 – (3 + 3)}] (Removing vinculum)
= [28 ÷ {10 – 6}] (Removing small brackets)
= [28 ÷ 4] (Removing curly brackets)

= 7 (Removing square brackets)