Question

Practice Set 9 1. Solve : (i) \( (-96) \div 16 \) (ii) \( 98 \div(-28) \) (iii) \( (-51) \div 68 \) (iv) \( 38 \div(-57) \) (v) \( (-85) \div 20 \) (vi) \( (-150) \div(-25) \) (vii) \( 100 \div 60 \) (viii) \( 9 \div(-54) \) (ix) \( 78 \div 65 \) (x) \( (-5) \div(-315) \) 2* Write three divisions of integers such that the fractional form of each will be \( \frac{24}{5} \). 3*. Write three divisions of integers such that the fractional form of each will be \( \frac{-5}{7} \). 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. \( (-13) \times(-15)=195 \) 2. \( (-24) \div 9=\frac{-24}{9}=\frac{-8}{3} \)

Answer 1

1. (i) (−96) ÷ 16 

\(=\frac{-96}{16}\)

\(= \frac{(-6) \times 16}{16}\)

\(= -6\)

(ii) 98 ÷ (−28)

\(= \frac{98}{-28}\)

\(=\frac{7 \times 14}{(-14) (2)}\)

\(= \frac{-7}2\)

(iii) (−51) ÷ 68

\(= \frac{-51}{68}\)

\(=\frac{(17)\times (-3)}{17 \times 4} \)

\(= \frac {-3}4\)

(iv) 38 ÷ (−57)

\(= \frac{38}{-57}\)

\(= \frac{19 \times 2}{(-19) \times 3}\)

\(= \frac{-2}3\)

(v) (−85) ÷ 20

\(= \frac{-85}{20}\)

\(= \frac{(-17) \times 5}{5 \times 4}\)

\(= \frac{-17}4\)

(vi) (−150) ÷ (−25)

\(= \frac{-150}{-25}\)

\(= \frac{(-25) \times 6}{-25}\)

\(= 6\)

(vii) 100 ÷ 60

\(= \frac{100}{60}\)

\(= \frac{20 \times 5}{20\times 3}\)

\(= \frac 53\)

(viii) 9 ÷ (−54)

\(= \frac 9{-54}\)

\(= \frac{9}{(-6) \times 6}\)

\(= \frac{-1}6\)

(ix) 78 ÷ 65

\(= \frac{78}{65}\)

\(= \frac{13 \times 6}{13 \times 5}\)

\(= \frac 65\)

(x) (−5) ÷ (−315)

\(=\frac{-5}{-315}\)

\(= \frac{(-5)}{(-5) \times (63)}\)

\(= \frac 1 {63}\)

2. The three divisions of integers are \(\frac{-24}{-5}, \frac{48}{10}\) and \(\frac{-48}{-10}\).

3. \(\frac{-5}{7} \times \frac 33 = \frac{-15}{21}\)

\(\frac{-5}{7} \times \frac 44 = \frac{-20}{28}\)

\(\frac{-5}{7} \times \frac 55 = \frac{-25}{35}\)

Hence, the three divisions of integers are \(\frac{-15}{21}, \frac{-20}{28}\) and \(\frac{-25}{35}\).

4. The four such multiplications are

(−13) × 9 = 117

(−15) × 12 = −180

(−8) × (−18) = 144

13 × 41 = 533

The four such division are

(−18) ÷ 9 = −2

(−24) ÷ 12 = −2

(−13) ÷ 13 = −1

(−27) ÷ 9 = −3