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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) \(\frac{-7}{6}\times24\)

(xi) \(\frac{7}{24}\times(-48)\)

(xii) \(\frac{-13}{5}(-10)\)

1 Answer

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(i)

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

\(=\frac{3\times-7}{5\times8}\)  

\(\frac{-21}{40}\)

(ii)

 \(\frac{-9}{2}\times\frac{5}{4}\)

\(\frac{-9\times5}{2\times4}\)

\(\frac{-45}{8}\)

(iii)

 \(\frac{-6}{11}\times\frac{-5}{3}\)

\(\frac{-6\times-5}{11\times3}\)

\(\frac{30}{33}\)

In lowest terms,

\(\frac{30}{33}= \frac{30 ÷3}{33 ÷3}=\frac{10}{11}\)

(iv)

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

\(\frac{-2\times6}{3\times7}\)

\(\frac{-12}{21}\)

In lowest terms,

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

(v)

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

\(\frac{-12\times10}{5\times-3}\) 

\(\frac{-120}{-15}=\frac{-120\times-1}{-15\times-1}=\frac{120}{15}\)

In lowest terms,

\(\frac{120}{15}=\frac{120 ÷3}{15 ÷3} =\frac{40}{5}\)

Further,

\(\frac{40}{5}= \frac{40 ÷5}{5 ÷5}=\frac{8}{1}=8\)

(vi)

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

\(\frac{25\times3}{-9\times-10}\)

\(\frac{75}{90}\)

In lowest terms,

\(\frac{75}{90}= \frac{75 ÷15}{90 ÷15}=\frac{5}{6}\)

(vii)

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

\(\frac{5\times-9}{-18\times20}\)

\(\frac{-45}{-360}= \frac{-45\times-1}{-360\times-1}\)\(\frac{45}{360}\)

in lowest terms,

\(\frac{45}{360}= \frac{45 ÷45}{360 ÷-45} =\frac{1}{8}\)

(viii)

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

\(\frac{-13\times-25}{15\times26}\)

\(\frac{325}{390}\)

In lowest terms,

\(\frac{325}{390}=\frac{325 ÷5}{390 ÷5}=\frac{65}{78}\)

Further,

\(\frac{65}{78}=\frac{65 ÷13}{78 ÷13}=\frac{5}{6}\)

(ix)

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

\(\frac{16\times14}{-21\times5}\)

\(\frac{224}{-105}=\frac{224\times-1}{-105\times-1}=\frac{-224}{105}\)

In lowest terms,

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

(x)

\(\frac{-7}{6}\times24\)

\(\frac{-7}{6}\times\frac{24}{1}\)

\(\frac{-7\times24}{6\times1}\)

\(\frac{-168}{6}\)

In lowest terms,

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

Further,

\(\frac{-84}{3}=\frac{-84 ÷3}{3 ÷3}=\frac{-28}{1}= -28\)

(xi)

\(\frac{7}{24}\times-48\)

\(\frac{7}{24}\times\frac{-48}{1}\)

\(\frac{7\times-48}{24\times1}\)

\(\frac{-336}{24}\) 

(xii)

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

\(\frac{-13}{5}\times\frac{-10}{1}\)

\(\frac{-13\times-10}{5\times1}\)

\(\frac{130}5{}\)

In lowest terms,

\(\frac{130}{5}=\frac{130 ÷5}{5 ÷5}=\frac{26}{1}=26\)

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