Solve (3/8div1/4+71/5div7)*8

$$( \frac { 3 } { 8 } \div \frac { 1 } { 4 } + \frac { 71 } { 5 } \div 7 ) \times 8$$

Evaluate

$$\frac{988}{35}\approx 28.228571429$$

Solution Steps

Divide \frac{3}{8} by \frac{1}{4} by multiplying \frac{3}{8} by the reciprocal of \frac{1}{4}.

$$\left(\frac{3}{8}\times 4+\frac{\frac{71}{5}}{7}\right)\times 8$$

Express \frac{3}{8}\times 4 as a single fraction.

$$\left(\frac{3\times 4}{8}+\frac{\frac{71}{5}}{7}\right)\times 8$$

Multiply 3 and 4 to get 12.

$$\left(\frac{12}{8}+\frac{\frac{71}{5}}{7}\right)\times 8$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

$$\left(\frac{3}{2}+\frac{\frac{71}{5}}{7}\right)\times 8$$

Express \frac{\frac{71}{5}}{7} as a single fraction.

$$\left(\frac{3}{2}+\frac{71}{5\times 7}\right)\times 8$$

Multiply 5 and 7 to get 35.

$$\left(\frac{3}{2}+\frac{71}{35}\right)\times 8$$

Least common multiple of 2 and 35 is 70. Convert \frac{3}{2} and \frac{71}{35} to fractions with denominator 70.

$$\left(\frac{105}{70}+\frac{142}{70}\right)\times 8$$

Since \frac{105}{70} and \frac{142}{70} have the same denominator, add them by adding their numerators.

$$\frac{105+142}{70}\times 8$$

Add 105 and 142 to get 247.

$$\frac{247}{70}\times 8$$

Express \frac{247}{70}\times 8 as a single fraction.

$$\frac{247\times 8}{70}$$

Multiply 247 and 8 to get 1976.

$$\frac{1976}{70}$$

Reduce the fraction \frac{1976}{70} to lowest terms by extracting and canceling out 2.

$$\frac{988}{35}$$

Factor

$$\frac{2 ^ {2} \cdot 13 \cdot 19}{5 \cdot 7} = 28\frac{8}{35} = 28.228571428571428$$