Find each of the following products:

Solution:

(i) $\frac{3}{5} \times \frac{-7}{8}$

$=\frac{3 \times(-7)}{5 \times 8}$

$=-\frac{21}{40}$

(ii) $\frac{-9}{2} \times \frac{5}{4}$

$=\frac{(-9) \times 5}{2 \times 4}$

$=\frac{-45}{8}$

(iii) $\frac{-6}{11} \times \frac{-5}{3}$

$=\frac{(-6) \times(-5)}{11 \times 3}$

$=\frac{30}{33}$

Simplifying the above rational number, we get:

$\frac{30}{33}=\frac{30 \div 3}{33 \div 3}=\frac{10}{11}$

(iv) $\frac{-2}{3} \times \frac{6}{7}$

$=\frac{(-2) \times 6}{3 \times 7}$

$=\frac{-12}{21}$

Simplifying the above rational number, we get:

$\frac{-12}{21}=\frac{-12 \div 3}{21 \div 3}=\frac{-4}{7}$

(v) $\frac{-12}{5} \times \frac{10}{-3}$

$=\frac{(-12) \times 10}{5 \times(-3)}$

$=\frac{-120}{-15}$

$=\frac{120}{15}$

Simplifying the above rational number, we get:

$\frac{120}{15}=\frac{120 \div 3}{15 \div 3}=\frac{40}{5}=8$

(vi) $\frac{25}{-9} \times \frac{3}{-10}$

$=\frac{25 \times 3}{(-9) \times(-10)}$

$=\frac{75}{90}$

Simplifying the above rational number, we get:

$\frac{75}{90}=\frac{75 \div 15}{90 \div 15}=\frac{5}{6}$

(vii) $\frac{5}{-18} \times \frac{-9}{20}$

$=\frac{5 \times(-9)}{-18 \times 20}$

$=\frac{-45}{-360}$

$=\frac{45}{360}$

Simplifying the above rational number, we get:

$\frac{45}{360}=\frac{45 \div 45}{360 \div 45}=\frac{1}{8}$

(viii) $\frac{-13}{15} \times \frac{-25}{26}$

$=\frac{(-13) \times(-25)}{15 \times 26}$

$=\frac{325}{390}$

Simplifying the above rational number, we get:

$\frac{325}{390}=\frac{325 \div 5}{390 \div 5}=\frac{65}{78}=\frac{65 \div 13}{78 \div 13}=\frac{5}{6}$

(ix) $\frac{16}{-21} \times \frac{14}{5}$

$=\frac{16 \times 14}{(-21) \times 5}$

$=\frac{224}{-105}$

Simplifying the above rational number, we get:

$\frac{224}{-105}=\frac{224 \div 7}{(-105) \div 7}=\frac{32}{-15}=\frac{32 \times-1}{-15 \times-1}=\frac{-32}{15}$

(x) $\frac{-7}{6} \times 24$

$=\frac{(-7) \times 24}{6}$

$=\frac{-168}{6}$

Simplifying the above rational number, we get:

$\frac{-168}{6}=\frac{(-168) \div 2}{6 \div 2}=\frac{84}{3}=\frac{-84 \div 3}{3 \div 3}=-28$

(Xi) $\frac{7}{24} \times(-48)$

$=\frac{7 \times(-48)}{24}=-\frac{336}{24}$

Simplifying the above rational number, we get:

$\frac{-336}{24}=\frac{-336 \div 24}{24 \div 24}=-14$

(xii) $\frac{-13}{5} \times(-10)$

$=\frac{(-13) \times(-10)}{5}$

$=\frac{130}{5}$

Simplifying the above rational number, we get:

$\frac{130}{5}=\frac{130 \div 5}{5 \div 5}=26$