Question

Find each of the following products:
(i) $\frac{3}{5}\times \frac{-7}{8}$
(ii) $\frac{-9}{2}\times \frac{5}{4}$
(iii) $\frac{-6}{11}\times \frac{-5}{3}$
(iv) $\frac{-2}{3}\times \frac{6}{7}$
(v) $\frac{-12}{5}\times \frac{10}{-3}$
(vi) $\frac{25}{-9}\times \frac{3}{-10}$
(vii) $\frac{5}{-18}\times \frac{-9}{20}$
(viii) $\frac{-13}{15}\times \frac{-25}{26}$
(ix) $\frac{16}{-21}\times \frac{14}{5}$
(x) $\frac{-7}{6}\times 24$
(xi) $\frac{7}{24}\times \left(-48\right)$
(xii) $\frac{-13}{5}\times \left(-10\right)$

Answer 1

(i)

$$\begin{gathered} \frac{3}{5}\times \frac{-7}{8} \\ =\frac{3\times (-7)}{5\times 8} \\ =-\frac{21}{40} \end{gathered}$$

(ii)

$$\begin{gathered} \frac{-9}{2}\times \frac{5}{4} \\ =\frac{(-9)\times 5}{2\times 4} \\ =\frac{-45}{8} \end{gathered}$$

(iii)

$$\begin{gathered} \frac{-6}{11}\times \frac{-5}{3} \\ =\frac{(-6)\times (-5)}{11\times 3} \\ =\frac{30}{33} \end{gathered}$$

Simplifying the above rational number, we get:

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

(iv)

$$\begin{gathered} \frac{-2}{3}\times \frac{6}{7} \\ =\frac{(-2)\times 6}{3\times 7} \\ =\frac{-12}{21} \end{gathered}$$

Simplifying the above rational number, we get:

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

(v)

$$\begin{gathered} \frac{-12}{5}\times \frac{10}{-3} \\ =\frac{(-12)\times 10}{5\times (-3)} \\ =\frac{-120}{-15} \\ =\frac{120}{15} \end{gathered}$$

Simplifying the above rational number, we get:

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

(vi)

$$\begin{gathered} \frac{25}{-9}\times \frac{3}{-10} \\ =\frac{25\times 3}{(-9)\times (-10)} \\ =\frac{75}{90} \end{gathered}$$

Simplifying the above rational number, we get:

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

(vii)

$$\begin{gathered} \frac{5}{-18}\times \frac{-9}{20} \\ =\frac{5\times (-9)}{-18\times 20} \\ =\frac{-45}{-360} \\ =\frac{45}{360} \end{gathered}$$

Simplifying the above rational number, we get:

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

(viii)

$$\begin{gathered} \frac{-13}{15}\times \frac{-25}{26} \\ =\frac{(-13)\times (-25)}{15\times 26} \\ =\frac{325}{390} \end{gathered}$$

Simplifying the above rational number, we get:

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

(ix)

$$\begin{gathered} \frac{16}{-21}\times \frac{14}{5} \\ =\frac{16\times 14}{(-21)\times 5} \\ =\frac{224}{-105} \end{gathered}$$

Simplifying the above rational number, we get:

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

(x)

$$\begin{gathered} \frac{-7}{6}\times 24 \\ =\frac{(-7)\times 24}{6} \\ =\frac{-168}{6} \end{gathered}$$

Simplifying the above rational number, we get:

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

(xi)

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

Simplifying the above rational number, we get:

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

(xii)

$$\begin{gathered} \frac{-13}{5}\times (-10) \\ =\frac{(-13)\times (-10)}{5} \\ =\frac{130}{5} \end{gathered}$$

Simplifying the above rational number, we get:

$\frac{130}{5}=\frac{130÷5}{5÷5}=26$