Solve 1/7*(23/5-1/2)

$$\frac { 1 } { 7 } \times ( 2 \frac { 3 } { 5 } - \frac { 1 } { 2 } )$$

Evaluate

$$\frac{3}{10}=0.3$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{1}{7}\left(\frac{10+3}{5}-\frac{1}{2}\right)$$

Add 10 and 3 to get 13.

$$\frac{1}{7}\left(\frac{13}{5}-\frac{1}{2}\right)$$

Least common multiple of 5 and 2 is 10. Convert \frac{13}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{1}{7}\left(\frac{26}{10}-\frac{5}{10}\right)$$

Since \frac{26}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{7}\times \frac{26-5}{10}$$

Subtract 5 from 26 to get 21.

$$\frac{1}{7}\times \frac{21}{10}$$

Multiply \frac{1}{7} times \frac{21}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 21}{7\times 10}$$

Do the multiplications in the fraction \frac{1\times 21}{7\times 10}.

$$\frac{21}{70}$$

Reduce the fraction \frac{21}{70} to lowest terms by extracting and canceling out 7.

$$\frac{3}{10}$$

Factor

$$\frac{3}{2 \cdot 5} = 0.3$$