Simplify the expression:

$$\left(\frac{9}{4} \div \frac{18}{7} ight) imes \left(\frac{8}{3} \div \frac{4}{9} ight)$$

Question

Simplify the expression:

$$\left(\frac{9}{4} \div \frac{18}{7}ight) 	imes \left(\frac{8}{3} \div \frac{4}{9}ight)$$

Accepted Answer

Solution:
Given expression:
$$ \left(\frac{9}{4} \div \frac{18}{7}ight) 	imes \left(\frac{8}{3} \div \frac{4}{9}ight) $$
Now change division into multiplication by taking the reciprocal:
$$ \left(\frac{9}{4} 	imes \frac{7}{18}ight) 	imes \left(\frac{8}{3} 	imes \frac{9}{4}ight) $$
Now solve the first bracket:
$$ \frac{9}{4} 	imes \frac{7}{18} $$
Cancel common terms:
$$ \frac{9}{18} = \frac{1}{2} $$
So,
$$ \frac{9}{4} 	imes \frac{7}{18} = \frac{7}{8} $$
Now solve the second bracket:
$$ \frac{8}{3} 	imes \frac{9}{4} $$
Cancel common terms:
$$ \frac{8}{4} = 2 $$
$$ \frac{9}{3} = 3 $$
So,
$$ \frac{8}{3} 	imes \frac{9}{4} = 2 	imes 3 = 6 $$
Now multiply both results:
$$ \frac{7}{8} 	imes 6 $$
$$ = \frac{42}{8} $$
Simplify:
$$ \frac{42}{8} = \frac{21}{4} $$
Therefore, the value of the expression is:
$$ \boxed{\frac{21}{4}} $$
Final Answer: **21/4**

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