Name the property of multiplication of rational numbers illustrated by the following statements : (i) -5/16 x 8/15 = 8/15 x -5/16

Question

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) \(\frac{7}{4}\times (\frac{-8}{3}+\frac{-13}{12})\) = \(\frac{7}{4}\times \frac{-8}{3}\)+\(\frac{7}{4}\times \frac{-13}{12}\)

(iv) \(\frac{-5}{9}\times (\frac{4}{15}+8)\) = \((\frac{-5}{9}\times \frac{4}{15})+\frac{-9}{8}\)

(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) \(\frac{-3}{2}\times \frac{5}{4}\)+\(\frac{-3}{2}\times \frac{-7}{6}\) = \(\frac{-3}{2}\times (\frac{5}{4}+\frac{-7}{6})\)

Answer 1

(i) In the above rational number the property of multiplication which is used is commutativity because: According to commutative law :

\(\frac{a}{b}\times \frac{c}{d} = \frac{c}{d}\times \frac{a}{b}\), which is mentioned above

(ii) In the above rational number the property of multiplication which is used is commutativity because :

According to commutative law :

\(\frac{a}{b}\times \frac{c}{d} = \frac{c}{d}\times \frac{a}{b}\), which is mentioned above

(iii) In the above rational number the property of multiplication which is used is distributivity of multiplication over addition because :

According to this law :

\(\frac{a}{b}(\frac{c}{d}+\frac{e}{f})\) = \((\frac{a}{b}\times \frac{c}{d})\)+\((\frac{a}{b}\times \frac{e}{f})\), which is mentioned above

(iv) In the above rational number the property of multiplication which is used is associativity of multiplication because :

According to associative law :

\(\frac{a}{b}\times (\frac{c}{d}\times \frac{e}{f})\) = \((\frac{a}{b}\times \frac{c}{d})\times \frac{e}{f}\), which is mentioned above

(v) In the above rational number the property of multiplication which is used is existence of identity for multiplication which is mentioned above

(vi) In the above rational number the property of multiplication which is used is existence of multiplication inverse which is mentioned above

(vii) In the above rational number the property of multiplication which is used is multiplication by zero because :

According to this law :

\(\frac{a}{b}\times 0 = 0\times \frac{a}{b}\), which is mentioned above

(viii) In the above rational number the property of multiplication which is used is distributive law because :

According to distributive law :

\(\frac{a}{b}\times \frac{c}{d}+\frac{a}{b}\times \frac{e}{f}\) = \(\frac{a}{b}\times (\frac{c}{d}+\frac{e}{f})\), which is mentioned above