Question

Find the product : $1\frac{1}{2}$$\times$$\frac{5}{6}$$\times$$\frac{8}{15}$$\times$$\frac{3}{4}$

Answer 1

Step 1. Convert the mixed fraction into an improper fraction.

$1\frac{1}{2}=\frac{\left(1\times 2\right)+1}{2}$

$=\frac{2+1}{2}$

$=\frac{3}{2}$

Step 2. Multiply the first fraction $\frac{3}{2}$ with the second fraction $\frac{5}{6}$.

$=\frac{3}{2}$$\times$$\frac{5}{6}$

$=\frac{3\times 5}{2\times 6}$

$=\frac{15}{12}$

And reduce the fraction$\frac{15}{12}$ into its lowest terms, dividing the numerator and denominator by the greatest common factor $3$.

$=\frac{15÷3}{12÷3}$

$=$$\frac{5}{4}$

Step 3. Multiply the third fraction $\frac{8}{15}$ with the third fraction $\frac{3}{4}$ .

$=\frac{8}{15}$$\times$$\frac{3}{4}$

$=\frac{8\times 3}{15\times 4}$

$=\frac{24}{60}$

And reduce the fraction $\frac{24}{60}$ into its lowest terms, dividing the numerator and denominator by the greatest common factor $12$

$=\frac{24÷12}{60÷12}$

$=\frac{2}{5}$

Step 4. Multiply both results to get the final answer.

$=\frac{5}{4}$$\times$$\frac{2}{5}$

$=$$\frac{5\times 2}{4\times 5}$

$=$$\frac{10}{20}$

And reduce the fraction $\frac{10}{20}$ into its lowest terms, dividing the numerator and denominator by the greatest common factor $10$.

$=\frac{10÷10}{20÷10}$

$=\frac{1}{2}$

Hence, the required answer is $\frac{1}{2}$.