Solve 3/8quadtext{(6)}7/8*4/5+1/5divfrac{1}{4}

$$\frac { 3 } { 8 } \quad \text { (6) } \frac { 7 } { 8 } \times \frac { 4 } { 5 } + \frac { 1 } { 5 } \div \frac { 1 } { 4 }$$

Evaluate

$$\frac{19}{8}=2.375$$

Solution Steps

Express \frac{3}{8}\times 6 as a single fraction.

$$\frac{3\times 6}{8}\times \frac{7}{8}\times \frac{4}{5}+\frac{\frac{1}{5}}{\frac{1}{4}}$$

Multiply 3 and 6 to get 18.

$$\frac{18}{8}\times \frac{7}{8}\times \frac{4}{5}+\frac{\frac{1}{5}}{\frac{1}{4}}$$

Reduce the fraction \frac{18}{8} to lowest terms by extracting and canceling out 2.

$$\frac{9}{4}\times \frac{7}{8}\times \frac{4}{5}+\frac{\frac{1}{5}}{\frac{1}{4}}$$

Multiply \frac{9}{4} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 7}{4\times 8}\times \frac{4}{5}+\frac{\frac{1}{5}}{\frac{1}{4}}$$

Do the multiplications in the fraction \frac{9\times 7}{4\times 8}.

$$\frac{63}{32}\times \frac{4}{5}+\frac{\frac{1}{5}}{\frac{1}{4}}$$

Multiply \frac{63}{32} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{63\times 4}{32\times 5}+\frac{\frac{1}{5}}{\frac{1}{4}}$$

Do the multiplications in the fraction \frac{63\times 4}{32\times 5}.

$$\frac{252}{160}+\frac{\frac{1}{5}}{\frac{1}{4}}$$

Reduce the fraction \frac{252}{160} to lowest terms by extracting and canceling out 4.

$$\frac{63}{40}+\frac{\frac{1}{5}}{\frac{1}{4}}$$

Divide \frac{1}{5} by \frac{1}{4} by multiplying \frac{1}{5} by the reciprocal of \frac{1}{4}.

$$\frac{63}{40}+\frac{1}{5}\times 4$$

Multiply \frac{1}{5} and 4 to get \frac{4}{5}.

$$\frac{63}{40}+\frac{4}{5}$$

Least common multiple of 40 and 5 is 40. Convert \frac{63}{40} and \frac{4}{5} to fractions with denominator 40.

$$\frac{63}{40}+\frac{32}{40}$$

Since \frac{63}{40} and \frac{32}{40} have the same denominator, add them by adding their numerators.

$$\frac{63+32}{40}$$

Add 63 and 32 to get 95.

$$\frac{95}{40}$$

Reduce the fraction \frac{95}{40} to lowest terms by extracting and canceling out 5.

$$\frac{19}{8}$$

Factor

$$\frac{19}{2 ^ {3}} = 2\frac{3}{8} = 2.375$$