Name the property of multiplication illustrated by each of the following statements: (i) -15/8 x -12/7 = -12/7 x -15/8

Question

Name the property of multiplication illustrated by each of the following statements:

(i) \(\frac{-15}{8}\times\frac{-12}{7}= \frac{-12}{7}\times\frac{-15}{8}\)

(ii) \((\frac{-2}{3}\times\frac{7}{9})\times\frac{-9}{5}= \frac{-2}{3}\times(\frac{7}{9}\times\frac{-9}{5})\)

(iii) \(\frac{-3}{4}\times(\frac{-5}{6}+\frac{7}{8})= (\frac{-3}{4}\times\frac{-5}{6})+(\frac{-3}{4}\times\frac{7}{8})\)

(iv) \(\frac{-16}{9}\times1=1\times\frac{-16}{9}=\frac{-16}{9}\)

(v) \(\frac{-11}{15}\times\frac{15}{-11}= \frac{15}{-11}\times\frac{-11}{15}=1\)

(vi) \(\frac{-7}{5}\times0= 0\)

Answer 1

(i) Commutative law i.e., a b = b a

(ii) Associative law i.e., a(bc) = (ab)c

(iii) Distributive law i.e., a(b + c) = ab + ac

(iv) Property of multiplicative identity i.e., a× 1=1× a

(v) Property of multiplicative inverse i.e., \(\frac{a}{b}\times\frac{b}{a}\) =1

(vi) Multiplicative property of 0 i.e., a× 0=0