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Name the property of multiplication of rational numbers illustrated by the following statements:
(i) $ \frac{-5}{16} \times \frac{8}{15}=\frac{8}{15} \times \frac{-5}{16} $
(ii) $ \frac{-17}{5} \times 9=9 \times \frac{-17}{5} $
(iii) $ \frac{7}{4} \times\left(\frac{-8}{3}+\frac{-13}{12}\right)=\frac{7}{4} \times \frac{-8}{3}+\frac{7}{4} \times \frac{-13}{12} $
(iv) $ \frac{-5}{9} \times\left(\frac{4}{15} \times \frac{-9}{8}\right)=\left(\frac{-5}{9} \times \frac{4}{15}\right) \times \frac{-9}{8} $
(v) $ \frac{13}{-17} \times 1=\frac{13}{-17}=1 \times \frac{13}{-17} $
(vi) $ \frac{-11}{16} \times \frac{16}{-11}=1 $
(vii) $ \frac{2}{13} \times 0=0=0 \times \frac{2}{13} $
(viii) $ \frac{-3}{2} \times \frac{5}{4}+\frac{-3}{2} \times \frac{-7}{6}=\frac{-3}{2} \times (\frac{5}{4}+\frac{-7}{6}) $
To do:
We have to name the property of multiplication of rational numbers given.
Solution:
(i) \( \frac{-5}{16} \times \frac{8}{15}=\frac{8}{15} \times \frac{-5}{16} \) is commutative property.
(ii) \( \frac{-17}{5} \times 9=9 \times \frac{-17}{5} \) is commutative property.
(iii) \( \frac{7}{4} \times\left(\frac{-8}{3}+\frac{-13}{12}\right)=\frac{7}{4} \times \frac{-8}{3}+\frac{7}{4} \times \frac{-13}{12} \) is distributive property.
(iv) \( \frac{-5}{9} \times\left(\frac{4}{15} \times \frac{-9}{8}\right)=\left(\frac{-5}{9} \times \frac{4}{15}\right) \times \frac{-9}{8} \) is associative property.
(v) \( \frac{13}{-17} \times 1=\frac{13}{-17}=1 \times \frac{13}{-17} \) is multiplicative identity property.
(vi) \( \frac{-11}{16} \times \frac{16}{-11}=1 \) is multiplicative inverse property.
(vii) \( \frac{2}{13} \times 0=0=0 \times \frac{2}{13} \) is zero property of multiplication.
(viii) \( \frac{-3}{2} \times \frac{5}{4}+\frac{-3}{2} \times \frac{-7}{6}=\frac{-3}{2} \times \) \( \left(\frac{5}{4}+\frac{-7}{6}\right) \) is distributive law of multiplication over addition.
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