Solve (2-15/32):21/24+3/4:4

$$( 2 - \frac { 15 } { 32 } ) : \frac { 21 } { 24 } + \frac { 3 } { 4 } : 4$$

Evaluate

$$\frac{31}{16}=1.9375$$

Solution Steps

Convert 2 to fraction \frac{64}{32}.

$$\frac{\frac{64}{32}-\frac{15}{32}}{\frac{21}{24}}+\frac{\frac{3}{4}}{4}$$

Since \frac{64}{32} and \frac{15}{32} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{64-15}{32}}{\frac{21}{24}}+\frac{\frac{3}{4}}{4}$$

Subtract 15 from 64 to get 49.

$$\frac{\frac{49}{32}}{\frac{21}{24}}+\frac{\frac{3}{4}}{4}$$

Reduce the fraction \frac{21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{49}{32}}{\frac{7}{8}}+\frac{\frac{3}{4}}{4}$$

Divide \frac{49}{32} by \frac{7}{8} by multiplying \frac{49}{32} by the reciprocal of \frac{7}{8}.

$$\frac{49}{32}\times \frac{8}{7}+\frac{\frac{3}{4}}{4}$$

Multiply \frac{49}{32} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 8}{32\times 7}+\frac{\frac{3}{4}}{4}$$

Do the multiplications in the fraction \frac{49\times 8}{32\times 7}.

$$\frac{392}{224}+\frac{\frac{3}{4}}{4}$$

Reduce the fraction \frac{392}{224} to lowest terms by extracting and canceling out 56.

$$\frac{7}{4}+\frac{\frac{3}{4}}{4}$$

Express \frac{\frac{3}{4}}{4} as a single fraction.

$$\frac{7}{4}+\frac{3}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$\frac{7}{4}+\frac{3}{16}$$

Least common multiple of 4 and 16 is 16. Convert \frac{7}{4} and \frac{3}{16} to fractions with denominator 16.

$$\frac{28}{16}+\frac{3}{16}$$

Since \frac{28}{16} and \frac{3}{16} have the same denominator, add them by adding their numerators.

$$\frac{28+3}{16}$$

Add 28 and 3 to get 31.

$$\frac{31}{16}$$

Factor

$$\frac{31}{2 ^ {4}} = 1\frac{15}{16} = 1.9375$$