Solve (4/6+3/5)*(11/8div3/8)

$$( \frac{ 4 }{ 6 } + \frac{ 3 }{ 5 } ) \times ( \frac{ 11 }{ 8 } \div \frac{ 3 }{ 8 } )$$

Evaluate

$$\frac{209}{45}\approx 4.644444444$$

Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\left(\frac{2}{3}+\frac{3}{5}\right)\times \frac{\frac{11}{8}}{\frac{3}{8}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{3}{5} to fractions with denominator 15.

$$\left(\frac{10}{15}+\frac{9}{15}\right)\times \frac{\frac{11}{8}}{\frac{3}{8}}$$

Since \frac{10}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+9}{15}\times \frac{\frac{11}{8}}{\frac{3}{8}}$$

Add 10 and 9 to get 19.

$$\frac{19}{15}\times \frac{\frac{11}{8}}{\frac{3}{8}}$$

Divide \frac{11}{8} by \frac{3}{8} by multiplying \frac{11}{8} by the reciprocal of \frac{3}{8}.

$$\frac{19}{15}\times \frac{11}{8}\times \frac{8}{3}$$

Multiply \frac{11}{8} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19}{15}\times \frac{11\times 8}{8\times 3}$$

Cancel out 8 in both numerator and denominator.

$$\frac{19}{15}\times \frac{11}{3}$$

Multiply \frac{19}{15} times \frac{11}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 11}{15\times 3}$$

Do the multiplications in the fraction \frac{19\times 11}{15\times 3}.

$$\frac{209}{45}$$

Factor

$$\frac{11 \cdot 19}{3 ^ {2} \cdot 5} = 4\frac{29}{45} = 4.644444444444445$$