Page 23 - Start Up Mathematics_7

Example 29: Simplify 36 – [5 + {27 – (16 – 9)}]

Solution: Using BODMAS rule and order of brackets,

36 – [5 + {27 – (16 – 9)}] = 36 – [5 + {27 – 7}] (Removing parenthesis)

= 36 – [5 + 20] (Removing curly brackets)
= 36 – 25 = 11 (Removing square brackets)

Example 30: Simplify 49 ÷ [49 + {49 – (49 + 49 – 49)}]

Solution: Using BODMAS rule and order of brackets,

49 ÷ [49 + {49 – (49 + 49 – 49)}] = 49 ÷ [49 + {49 – (49 + 0)}]
(Removing vinculum)

= 49 ÷ [49 + {49 – 49}] (Removing parenthesis)

= 49 ÷ [49 + 0] (Removing curly brackets)
= 49 ÷ 49 = 1 (Removing square brackets)

EXERCISE 1.5

1. Simplify each of the following:

(a) –25 + 12 ÷ (9 – 3) (b) 29 – [38 – {40 ÷ 2 – (6 – 9 ÷ 3) ÷ 3}]
1 1
(c) 14 – {13 + 2 – (7 + 5 – 2 + 3 )} (d) 14 + [{–10 × (25 – 13 – 3)} ÷ (–5)]
2 5
1
(e) 27 – {–5 – (–48) ÷ (–16)}
4

2. Using appropriate brackets, write a mathematical expression for each of the following:
(a) Sixty-three divided by one more than the sum of three and five

(b) Three multiplied by two less than the difference of sixteen and four
(c) Eighteen subtracted from one third the sum of sixty and thirty
(d) Eighty divided by four times the sum of two and three

(e) Nine multiplied by the sum of three, four and five

At a Glance

1. The whole numbers along with their negatives, i.e., …, –4, –3, –2, –1, 0, 1 , 2 , 3, … constitute
integers.

2. Absolute value of an integer is always positive. It is the distance of any integer from 0.
3. Addition: For any integers a and b, we define, –a + (–b) = –(a + b)
Properties
(a) Closure: a + b is again an integer. (b) Commutative: a + b = b + a

(c) Associative: (a + b) + c = a + (b + c)

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