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 = \(\large \frac {(–\,1)\,×\,96}{16}\)
∴ (– 96) ÷ 16 = \(\large \frac {(–\,1)\,×\,16\,×\,6}{16}\)
∴ (– 96) ÷ 16 = (– 1) × 6
∴ (– 96) ÷ 16 = – 6
(ii) 98 ÷ (– 28)
Solution:
98 ÷ (– 28) = \(\large \frac {98}{(–\,1)\,×\,28}\)
∴ 98 ÷ (– 28) = \(\large \frac {14\,×\,7}{(–\,1)\,×\,14\,×\,2}\)
∴ 98 ÷ (– 28) = \(\large \frac {7}{(–\,1)\,×\,2}\)
∴ 98 ÷ (– 28) = \(\large \frac {7}{–\,2}\)
∴ 98 ÷ (– 28) = \(\large \frac {–\,7}{2}\)
(iii) (– 51) ÷ 68
Solution:
(– 51) ÷ 68 = \(\large \frac {(–\,1)\,×\,51}{68}\)
∴ (– 51) ÷ 68 = \(\large \frac {(–\,1)\,×\,17\,×\,3}{17\,×\,4}\)
∴ (– 51) ÷ 68 = \(\large \frac {(–\,1)\,×\,3}{4}\)
∴ (– 51) ÷ 68 = \(\large \frac {–\,3}{4}\)
(iv) 38 ÷ (– 57)
Solution:
38 ÷ (– 57) = \(\large \frac {38}{(–\,1)\,×\,57}\)
∴ 38 ÷ (– 57) = \(\large \frac {19\,×\,2}{(–\,1)\,×\,19\,×\,3}\)
∴ 38 ÷ (– 57) = \(\large \frac {2}{(–\,1)\,×\,3}\)
∴ 38 ÷ (– 57) = \(\large \frac {2}{–\,3}\)
∴ 38 ÷ (– 57) = \(\large \frac {–\,2}{3}\)
(v) (– 85) ÷ 20
Solution:
(– 85) ÷ 20 = \(\large \frac {(–\,1)\,×\,85}{20}\)
∴ (– 85) ÷ 20 = \(\large \frac {(–\,1)\,×\,17\,×\,5}{4\,×\,5}\)
∴ (– 85) ÷ 20 = \(\large \frac {(–\,1)\,×\,17}{4}\)
∴ (– 85) ÷ 20 = \(\large \frac {–\,17}{4}\)
(vi) (– 150) ÷ (– 25)
Solution:
(– 150) ÷ (– 25) = \(\large \frac {(–\,1)\,×\,150}{(–\,1)\,×\,25}\)
∴ (– 150) ÷ (– 25) = \(\large \frac {25\,×\,6}{25}\)
∴ (– 150) ÷ (– 25) = 6
(vii) 100 ÷ 60
Solution:
100 ÷ 60 = \(\large \frac {100}{60}\)
∴ 100 ÷ 60 = \(\large \frac {20\,×\,5}{20\,×\,3}\)
∴ 100 ÷ 60 = \(\large \frac {5}{3}\)
(viii) 9 ÷ (– 54)
Solution:
9 ÷ (– 54) = \(\large \frac {99}{(–\,1)\,×\,54}\)
∴ 9 ÷ (– 54) = \(\large \frac {9}{(–\,1)\,×\,9\,×\,6}\)
∴ 9 ÷ (– 54) = \(\large \frac {1}{(–\,1)\,×\,6}\)
∴ 9 ÷ (– 54) = \(\large \frac {1}{–\,6}\)
∴ 9 ÷ (– 54) = \(\large \frac {–\,1}{6}\)
(ix) 78 ÷ 65
Solution:
78 ÷ 65 = \(\large \frac {78}{65}\)
∴ 78 ÷ 65 = \(\large \frac {13\,×\,6}{13\,×\,5}\)
∴ 78 ÷ 65 = \(\large \frac {6}{5}\)
(ix) 78 ÷ 65
Solution:
78 ÷ 65 = \(\large \frac {78}{65}\)
∴ 78 ÷ 65 = \(\large \frac {13\,×\,6}{13\,×\,5}\)
∴ 78 ÷ 65 = \(\large \frac {6}{5}\)
(x) (– 5) ÷ (– 315)
Solution:
(– 5) ÷ (– 315) = \(\large \frac {(–\,1)\,×\,5}{(–\,1)\,×\,315}\)
∴ (– 5) ÷ (– 315) = \(\large \frac {5}{5\,×\,63}\)
∴ (– 5) ÷ (– 315) = \(\large \frac {1}{63}\)
2 . Write three divisions of integers such that the fractional form of each will be \(\large \frac {24}{5}\).
Solution:
(i) \(\large \frac {24}{5}\) = \(\large \frac {(–\,1)\,×\,24}{(–\,1)\,×\,5}\)
∴ \(\large \frac {24}{5}\) = \(\large \frac {–\,24}{–\,5}\)
(ii) \(\large \frac {24}{5}\) = \(\large \frac {2\,×\,24}{2\,×\,5}\)
∴ \(\large \frac {24}{5}\) = \(\large \frac {48}{10}\)
(iii) \(\large \frac {24}{5}\) = \(\large \frac {10\,×\,24}{10\,×\,5}\)
∴ \(\large \frac {24}{5}\) = \(\large \frac {240}{50}\)
3. Write three divisions of integers such that the fractional form of each will be \(\large \frac {–\,5}{7}\).
Solution:
(i) \\(\large \frac {–\,5}{7}\) = \(\large \frac {2\,×\,–\,5}{2\,×\,7}\)
∴ \(\large \frac {–\,5}{7}\)\) = \(\large \frac {–\,10}{14}\)
(ii) \(\large \frac {–\,5}{7}\) = \(\large \frac {5\,×\,–\,5}{5\,×\,7}\)
∴ \(\large \frac {–\,5}{7}\) = \(\large \frac {–\,25}{35}\)
(iii) \(\large \frac {–\,5}{7}\) = \(\large \frac {3\,×\,–\,5}{3\,×\,7}\)
∴ \(\large \frac {–\,5}{7}\) = \(\large \frac {–\,15}{21}\)
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 = \(\large \frac {–\,24}{9}\) = \(\large \frac {–\,8}{3}\)
Solution:
Multiplication Pairs
(i) (– 13) × 9 = – 117
(ii) 12 × 13 = 156
(iii) 9 × (– 37) = – 333
(iv) (– 15) × (– 8) = 120
Division Pairs
(i) – 28 ÷ 12 = \(\large \frac {–\,28}{12}\) = \(\large \frac {–\,1\,×\,28}{12}\) = \(\large \frac {–\,7}{3}\)
(ii) 12 ÷ 9 = \(\large \frac {12}{9}\) = \(\large \frac {4}{3}\)
(iii) 9 ÷ (– 24) = \(\large \frac {9}{–\,24}\) = \(\large \frac {9}{–\,1\,×\,24}\) = \(\large \frac {3}{–\,1\,×\,8}\) = \(\large \frac {–\,3}{8}\)
(iv) – 18 ÷ (– 27) = \(\large \frac {–\,18}{–\,27}\) = \(\large \frac {–\,1\,×\,18}{–\,1\,×\,27}\) = \(\large \frac {2}{3}\)