Solve (3/4*14/6+3/2)div(3/8+frac{7}{4})=

$$( \frac { 3 } { 4 } \times \frac { 14 } { 6 } + \frac { 3 } { 2 } ) \div ( \frac { 3 } { 8 } + \frac { 7 } { 4 } ) =$$

Evaluate

$$\frac{26}{17}\approx 1.529411765$$

Solution Steps

Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{4}\times \frac{7}{3}+\frac{3}{2}}{\frac{3}{8}+\frac{7}{4}}$$

Multiply \frac{3}{4} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 7}{4\times 3}+\frac{3}{2}}{\frac{3}{8}+\frac{7}{4}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{7}{4}+\frac{3}{2}}{\frac{3}{8}+\frac{7}{4}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{7}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{\frac{7}{4}+\frac{6}{4}}{\frac{3}{8}+\frac{7}{4}}$$

Since \frac{7}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7+6}{4}}{\frac{3}{8}+\frac{7}{4}}$$

Add 7 and 6 to get 13.

$$\frac{\frac{13}{4}}{\frac{3}{8}+\frac{7}{4}}$$

Least common multiple of 8 and 4 is 8. Convert \frac{3}{8} and \frac{7}{4} to fractions with denominator 8.

$$\frac{\frac{13}{4}}{\frac{3}{8}+\frac{14}{8}}$$

Since \frac{3}{8} and \frac{14}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{4}}{\frac{3+14}{8}}$$

Add 3 and 14 to get 17.

$$\frac{\frac{13}{4}}{\frac{17}{8}}$$

Divide \frac{13}{4} by \frac{17}{8} by multiplying \frac{13}{4} by the reciprocal of \frac{17}{8}.

$$\frac{13}{4}\times \frac{8}{17}$$

Multiply \frac{13}{4} times \frac{8}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 8}{4\times 17}$$

Do the multiplications in the fraction \frac{13\times 8}{4\times 17}.

$$\frac{104}{68}$$

Reduce the fraction \frac{104}{68} to lowest terms by extracting and canceling out 4.

$$\frac{26}{17}$$

Factor

$$\frac{2 \cdot 13}{17} = 1\frac{9}{17} = 1.5294117647058822$$