108 div ? of frac{1}{3} + frac{2}{5} times 3 | vedclass

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Question

(D) Let the missing number be $x$.The given equation is: $108 \div (x 	ext{ of } \frac{1}{3}) + \frac{2}{5} 	imes 3 \frac{3}{4} = 10 \frac{1}{2}$.Fi

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(D) Let the missing number be $x$.The given equation is: $108 \div (x 	ext{ of } \frac{1}{3}) + \frac{2}{5} 	imes 3 \frac{3}{4} = 10 \frac{1}{2}$.First,convert the mixed fractions to improper fractions: $3 \frac{3}{4} = \frac{15}{4}$ and $10 \frac{1}{2} = \frac{21}{2}$.The equation becomes: $108 \div (x 	imes \frac{1}{3}) + \frac{2}{5} 	imes \frac{15}{4} = \frac{21}{2}$.Simplify the multiplication term: $\frac{2}{5} 	imes \frac{15}{4} = \frac{1}{1} 	imes \frac{3}{2} = \frac{3}{2}$.Now the equation is: $108 \div \frac{x}{3} + \frac{3}{2} = \frac{21}{2}$.Convert division to multiplication by the reciprocal: $108 	imes \frac{3}{x} + \frac{3}{2} = \frac{21}{2}$.Subtract $\frac{3}{2}$ from both sides: $\frac{324}{x} = \frac{21}{2} - \frac{3}{2} = \frac{18}{2} = 9$.Solve for $x$: $9x = 324$,so $x = \frac{324}{9} = 36$.

$108 \div ?$ of $\frac{1}{3} + \frac{2}{5} \times 3 \frac{3}{4} = 10 \frac{1}{2}$

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