Solve 7/8div(3/4+2/3)

$$\frac { 7 } { 8 } \div ( \frac { 3 } { 4 } + \frac { 2 } { 3 } )$$

Evaluate

$$\frac{21}{34}\approx 0.617647059$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{\frac{7}{8}}{\frac{9}{12}+\frac{8}{12}}$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{8}}{\frac{9+8}{12}}$$

Add 9 and 8 to get 17.

$$\frac{\frac{7}{8}}{\frac{17}{12}}$$

Divide \frac{7}{8} by \frac{17}{12} by multiplying \frac{7}{8} by the reciprocal of \frac{17}{12}.

$$\frac{7}{8}\times \frac{12}{17}$$

Multiply \frac{7}{8} times \frac{12}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 12}{8\times 17}$$

Do the multiplications in the fraction \frac{7\times 12}{8\times 17}.

$$\frac{84}{136}$$

Reduce the fraction \frac{84}{136} to lowest terms by extracting and canceling out 4.

$$\frac{21}{34}$$

Factor

$$\frac{3 \cdot 7}{2 \cdot 17} = 0.6176470588235294$$