Solve (21/4+15/16):1/4

$$( 2 \frac { 1 } { 4 } + 1 \frac { 5 } { 16 } ) : \frac { 1 } { 4 }$$

Evaluate

$$\frac{57}{4}=14.25$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{\frac{8+1}{4}+\frac{1\times 16+5}{16}}{\frac{1}{4}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{9}{4}+\frac{1\times 16+5}{16}}{\frac{1}{4}}$$

Multiply 1 and 16 to get 16.

$$\frac{\frac{9}{4}+\frac{16+5}{16}}{\frac{1}{4}}$$

Add 16 and 5 to get 21.

$$\frac{\frac{9}{4}+\frac{21}{16}}{\frac{1}{4}}$$

Least common multiple of 4 and 16 is 16. Convert \frac{9}{4} and \frac{21}{16} to fractions with denominator 16.

$$\frac{\frac{36}{16}+\frac{21}{16}}{\frac{1}{4}}$$

Since \frac{36}{16} and \frac{21}{16} have the same denominator, add them by adding their numerators.

$$\frac{\frac{36+21}{16}}{\frac{1}{4}}$$

Add 36 and 21 to get 57.

$$\frac{\frac{57}{16}}{\frac{1}{4}}$$

Divide \frac{57}{16} by \frac{1}{4} by multiplying \frac{57}{16} by the reciprocal of \frac{1}{4}.

$$\frac{57}{16}\times 4$$

Express \frac{57}{16}\times 4 as a single fraction.

$$\frac{57\times 4}{16}$$

Multiply 57 and 4 to get 228.

$$\frac{228}{16}$$

Reduce the fraction \frac{228}{16} to lowest terms by extracting and canceling out 4.

$$\frac{57}{4}$$

Factor

$$\frac{3 \cdot 19}{2 ^ {2}} = 14\frac{1}{4} = 14.25$$