Solve (42/5-17/8)div3/10*1/2

$$( 4 \frac { 2 } { 5 } - 1 \frac { 7 } { 8 } ) \div \frac { 3 } { 10 } \times \frac { 1 } { 2 }$$

Evaluate

$$\frac{101}{24}\approx 4.208333333$$

Solution Steps

Multiply 4 and 5 to get 20.

$$\frac{\frac{20+2}{5}-\frac{1\times 8+7}{8}}{\frac{3}{10}}\times \frac{1}{2}$$

Add 20 and 2 to get 22.

$$\frac{\frac{22}{5}-\frac{1\times 8+7}{8}}{\frac{3}{10}}\times \frac{1}{2}$$

Multiply 1 and 8 to get 8.

$$\frac{\frac{22}{5}-\frac{8+7}{8}}{\frac{3}{10}}\times \frac{1}{2}$$

Add 8 and 7 to get 15.

$$\frac{\frac{22}{5}-\frac{15}{8}}{\frac{3}{10}}\times \frac{1}{2}$$

Least common multiple of 5 and 8 is 40. Convert \frac{22}{5} and \frac{15}{8} to fractions with denominator 40.

$$\frac{\frac{176}{40}-\frac{75}{40}}{\frac{3}{10}}\times \frac{1}{2}$$

Since \frac{176}{40} and \frac{75}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{176-75}{40}}{\frac{3}{10}}\times \frac{1}{2}$$

Subtract 75 from 176 to get 101.

$$\frac{\frac{101}{40}}{\frac{3}{10}}\times \frac{1}{2}$$

Divide \frac{101}{40} by \frac{3}{10} by multiplying \frac{101}{40} by the reciprocal of \frac{3}{10}.

$$\frac{101}{40}\times \frac{10}{3}\times \frac{1}{2}$$

Multiply \frac{101}{40} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{101\times 10}{40\times 3}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{101\times 10}{40\times 3}.

$$\frac{1010}{120}\times \frac{1}{2}$$

Reduce the fraction \frac{1010}{120} to lowest terms by extracting and canceling out 10.

$$\frac{101}{12}\times \frac{1}{2}$$

Multiply \frac{101}{12} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{101\times 1}{12\times 2}$$

Do the multiplications in the fraction \frac{101\times 1}{12\times 2}.

$$\frac{101}{24}$$

Factor

$$\frac{101}{2 ^ {3} \cdot 3} = 4\frac{5}{24} = 4.208333333333333$$