Chapter 2 – Multiplication and Division of Integers
Practice Set 8
Multiply.
(i) (– 5) × (– 7)
Solution:
(– 5) × (– 7) = 35
(ii) (– 9) × (6)
Solution:
(– 9) × (6) = – 54
(iii) (9) × (– 4)
Solution:
(9) × (– 4) = – 36
(iv) (8) × (– 7)
Solution:
(8) × (– 7) = – 56
(v) (– 124) × (– 1)
Solution:
(– 124) × (– 1) = 124
(vi) (– 12) × (– 7)
Solution:
(– 12) × (– 7) = 84
(vii) (– 63) × (– 7)
Solution:
(– 63) × (– 7) = 441
(viii) (– 7) × (15)
Solution:
(– 7) × (15) = – 105
Practice set 9
1. Solve :
(i) (– 96) ÷ 16
Solution:
(– 96) ÷ 16 = (–1)×9616
∴ (– 96) ÷ 16 = (–1)×16×616
∴ (– 96) ÷ 16 = (– 1) × 6
∴ (– 96) ÷ 16 = – 6
(ii) 98 ÷ (– 28)
Solution:
98 ÷ (– 28) = 98(–1)×28
∴ 98 ÷ (– 28) = 14×7(–1)×14×2
∴ 98 ÷ (– 28) = 7(–1)×2
∴ 98 ÷ (– 28) = 7–2
∴ 98 ÷ (– 28) = –72
(iii) (– 51) ÷ 68
Solution:
(– 51) ÷ 68 = (–1)×5168
∴ (– 51) ÷ 68 = (–1)×17×317×4
∴ (– 51) ÷ 68 = (–1)×34
∴ (– 51) ÷ 68 = –34
(iv) 38 ÷ (– 57)
Solution:
38 ÷ (– 57) = 38(–1)×57
∴ 38 ÷ (– 57) = 19×2(–1)×19×3
∴ 38 ÷ (– 57) = 2(–1)×3
∴ 38 ÷ (– 57) = 2–3
∴ 38 ÷ (– 57) = –23
(v) (– 85) ÷ 20
Solution:
(– 85) ÷ 20 = (–1)×8520
∴ (– 85) ÷ 20 = (–1)×17×54×5
∴ (– 85) ÷ 20 = (–1)×174
∴ (– 85) ÷ 20 = –174
(vi) (– 150) ÷ (– 25)
Solution:
(– 150) ÷ (– 25) = (–1)×150(–1)×25
∴ (– 150) ÷ (– 25) = 25×625
∴ (– 150) ÷ (– 25) = 6
(vii) 100 ÷ 60
Solution:
100 ÷ 60 = 10060
∴ 100 ÷ 60 = 20×520×3
∴ 100 ÷ 60 = 53
(viii) 9 ÷ (– 54)
Solution:
9 ÷ (– 54) = 99(–1)×54
∴ 9 ÷ (– 54) = 9(–1)×9×6
∴ 9 ÷ (– 54) = 1(–1)×6
∴ 9 ÷ (– 54) = 1–6
∴ 9 ÷ (– 54) = –16
(ix) 78 ÷ 65
Solution:
78 ÷ 65 = 7865
∴ 78 ÷ 65 = 13×613×5
∴ 78 ÷ 65 = 65
(ix) 78 ÷ 65
Solution:
78 ÷ 65 = 7865
∴ 78 ÷ 65 = 13×613×5
∴ 78 ÷ 65 = 65
(x) (– 5) ÷ (– 315)
Solution:
(– 5) ÷ (– 315) = (–1)×5(–1)×315
∴ (– 5) ÷ (– 315) = 55×63
∴ (– 5) ÷ (– 315) = 163
2 . Write three divisions of integers such that the fractional form of each will be 245.
Solution:
(i) 245 = (–1)×24(–1)×5
∴ 245 = –24–5
(ii) 245 = 2×242×5
∴ 245 = 4810
(iii) 245 = 10×2410×5
∴ 245 = 24050
3. Write three divisions of integers such that the fractional form of each will be –57.
Solution:
(i) \–57 = 2×–52×7
∴ –57\) = –1014
(ii) –57 = 5×–55×7
∴ –57 = –2535
(iii) –57 = 3×–53×7
∴ –57 = –1521
4. The fish in the pond below, carry some numbers. Choose any 4 pairs and carry out four multiplications with those numbers. Now, choose four other pairs and carry out divisions with these numbers.
For example,
1. (– 13) × (– 15) = 195
2. (– 24) ÷ 9 = –249 = –83
Solution:
Multiplication Pairs
(i) (– 13) × 9 = – 117
(ii) 12 × 13 = 156
(iii) 9 × (– 37) = – 333
(iv) (– 15) × (– 8) = 120
Division Pairs
(i) – 28 ÷ 12 = –2812 = –1×2812 = –73
(ii) 12 ÷ 9 = 129 = 43
(iii) 9 ÷ (– 24) = 9–24 = 9–1×24 = 3–1×8 = –38
(iv) – 18 ÷ (– 27) = –18–27 = –1×18–1×27 = 23