Page 145 - ICSE Math 8

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Example 13: Simplify 60p ÷ (4p + p ) – of (6p + 18p ÷ 2p).
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Solution: 60p ÷ (4p + p ) – of (6p + 18p ÷ 2p)
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3  18p  4 3
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= 60p ÷ 5p – of 6p +   = 60p ÷ 5p – of (6p + 9p )
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 2p 
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= 60p ÷ 5p – of 15p = 60p ÷ 5p – × 15p (Removing small bracket and ‘of’)
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60p 6
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= – 3 × 3p = 12p – 9p = 3p 3
5p 3
EXERCISE 12.3
1. Multiply.
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(a) 5p by –3p 2 (b) 5 a b by 27 a b
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(c) 1 xyz by –9x y z (d) 3 pq by 4 pq 3
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(e) (3x + 4y) by (2x – 7y) (f) (x – 2xy) by (y + 5xy)
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(g) (5x – 2) by (7x + 7)
2. Simplify the following.
(a) (9x – 6y) × (2x + 5y) (b) (ax – by + cz) × (3a)
(c) (3x – 1) × (3x + 4) (d)  x + 1  x − 1  
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(e) (–3x + 2y) × (–10xy) (f) (2x – 3x + 3) × (3x – 4)
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(g) (x – 1) × (x + 2x + 2) (h) (ab + bc + ac) × (a + b + c)
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(i) (x – y)(x + y)(2x + 5y) (j) (2x + x + 2)(x + 3x + 4)
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(k) (x – 3)(x + 4)(x + 6) (l) (4x – 5x + 7)(3x – 2)
3. Divide.
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(a) 3a b by 6a b (b) 24x y z by –12x yz 5
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(c) 15x d by 50x (d) 9a b + 27ab – 18ab by –9a b
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1 3 5 3
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(e) l m n + 4l m + 8lmn by 16l m n (f) 1 pqr – p q r – p q r by 1 pqr
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4. Divide and verify the answer.
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(a) 9x – 1 by 3x – 1 (b) 24x – 38x + 10 by 6x – 2
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(c) x – x – 2x + 5x – 10 by x + x + 5 (d) 2x + 8x – x – 4 by 2x – 1
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(e) a + 2a b – a b – 2ab by a + 2b (f) x – y by x – y
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(g) x – 6x + 11x – 6 by x – 3
5. Simplify the following.
(a) –2x + [2y + {2x – (3y + x)}] (b) –[–{–(–x)}]–{x + (x – y – z)}
(c) 4ab + 2[ab – 2{–3ab – a(2b – 3a – 4b)}] (d) 3(3p – 5q) –5[p – (–q + 3p – q)]
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