Fill in the blanks:
(i) $ -4 \times \frac{7}{9}=\frac{7}{9} \times -4 $
(ii) $ \frac{5}{11} \times \frac{-3}{8}=\frac{-3}{8} \times\frac{5}{11} $
(iii) $ \frac{1}{2} \times\left(\frac{3}{4}+\frac{-5}{12}\right)=\frac{1}{2} \times(\frac{3}{4})+\frac{1}{2} \times \frac{-5}{12}$
(iv) $\frac{-4}{5} \times(\frac{5}{7} \times \frac{-8}{9})=(\frac{-4}{5} \times$____ ) $\times\frac{-8}{9}$

To do:

We have to fill in the given blanks.

Solution:

We know that,

According to commutative property of multiplication,

$a \times b = b \times a$

Therefore,

(i) $-4 \times \frac{7}{9}=\frac{7}{9} \times(-4)$

(ii) $\frac{5}{11} \times \frac{-3}{8}=\frac{-3}{8} \times\frac{5}{11}$ .

(iii) We know that,

According to distributive property of multiplication,

$a(b+c) = a \times b + a \times c$

Therefore,

$\frac{1}{2} \times(\frac{3}{4}+\frac{-5}{12})=\frac{1}{2} \times \frac{3}{4}+\frac{1}{2}  \times \frac{-5}{12}$

(iv) We know that,

According to associative property of multiplication,

$a \times (b \times c) = (a \times b) \times c$

Therefore,

$\frac{-4}{5} \times(\frac{5}{7} \times \frac{-8}{9})=(\frac{-4}{5} \times \frac{5}{7})\times\frac{-8}{9}$