Solve 9/4div(3/4+1/16)

$$\frac { 9 } { 4 } \div ( \frac { 3 } { 4 } + \frac { 1 } { 16 } )$$

Evaluate

$$\frac{36}{13}\approx 2.769230769$$

Solution Steps

Least common multiple of 4 and 16 is 16. Convert \frac{3}{4} and \frac{1}{16} to fractions with denominator 16.

$$\frac{\frac{9}{4}}{\frac{12}{16}+\frac{1}{16}}$$

Since \frac{12}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9}{4}}{\frac{12+1}{16}}$$

Add 12 and 1 to get 13.

$$\frac{\frac{9}{4}}{\frac{13}{16}}$$

Divide \frac{9}{4} by \frac{13}{16} by multiplying \frac{9}{4} by the reciprocal of \frac{13}{16}.

$$\frac{9}{4}\times \frac{16}{13}$$

Multiply \frac{9}{4} times \frac{16}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 16}{4\times 13}$$

Do the multiplications in the fraction \frac{9\times 16}{4\times 13}.

$$\frac{144}{52}$$

Reduce the fraction \frac{144}{52} to lowest terms by extracting and canceling out 4.

$$\frac{36}{13}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {2}}{13} = 2\frac{10}{13} = 2.769230769230769$$