# Name the property of multiplication of rational numbers illustrated by the following statements:

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

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

Solution:

(i) Commutative property
(ii) Commutative property
(iii) Distributivity of multiplication over addition
(iv) Associativity of multiplication
(v) Existence of identity for multiplication
(vi) Existence of multiplicative inverse
(vii) Multiplication by 0
(viii) Distributive property