Solve (3/4-11/16):(5/12+1/3)=

$$( \frac { 3 } { 4 } - \frac { 11 } { 16 } ) : ( \frac { 5 } { 12 } + \frac { 1 } { 3 } ) =$$

Evaluate

$$\frac{1}{12}\approx 0.083333333$$

Solution Steps

Least common multiple of 4 and 16 is 16. Convert \frac{3}{4} and \frac{11}{16} to fractions with denominator 16.

$$\frac{\frac{12}{16}-\frac{11}{16}}{\frac{5}{12}+\frac{1}{3}}$$

Since \frac{12}{16} and \frac{11}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{12-11}{16}}{\frac{5}{12}+\frac{1}{3}}$$

Subtract 11 from 12 to get 1.

$$\frac{\frac{1}{16}}{\frac{5}{12}+\frac{1}{3}}$$

Least common multiple of 12 and 3 is 12. Convert \frac{5}{12} and \frac{1}{3} to fractions with denominator 12.

$$\frac{\frac{1}{16}}{\frac{5}{12}+\frac{4}{12}}$$

Since \frac{5}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{16}}{\frac{5+4}{12}}$$

Add 5 and 4 to get 9.

$$\frac{\frac{1}{16}}{\frac{9}{12}}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{16}}{\frac{3}{4}}$$

Divide \frac{1}{16} by \frac{3}{4} by multiplying \frac{1}{16} by the reciprocal of \frac{3}{4}.

$$\frac{1}{16}\times \frac{4}{3}$$

Multiply \frac{1}{16} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{16\times 3}$$

Do the multiplications in the fraction \frac{1\times 4}{16\times 3}.

$$\frac{4}{48}$$

Reduce the fraction \frac{4}{48} to lowest terms by extracting and canceling out 4.

$$\frac{1}{12}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3} = 0.08333333333333333$$