Solve 7/25*(13/14-1:7/8)

$$\frac { 7 } { 25 } \cdot ( 1 \frac { 3 } { 14 } - 1 : \frac { 7 } { 8 } )$$

Evaluate

$$\frac{1}{50}=0.02$$

Solution Steps

Multiply 1 and 14 to get 14.

$$\frac{7}{25}\left(\frac{14+3}{14}-\frac{1}{\frac{7}{8}}\right)$$

Add 14 and 3 to get 17.

$$\frac{7}{25}\left(\frac{17}{14}-\frac{1}{\frac{7}{8}}\right)$$

Divide 1 by \frac{7}{8} by multiplying 1 by the reciprocal of \frac{7}{8}.

$$\frac{7}{25}\left(\frac{17}{14}-1\times \frac{8}{7}\right)$$

Multiply 1 and \frac{8}{7} to get \frac{8}{7}.

$$\frac{7}{25}\left(\frac{17}{14}-\frac{8}{7}\right)$$

Least common multiple of 14 and 7 is 14. Convert \frac{17}{14} and \frac{8}{7} to fractions with denominator 14.

$$\frac{7}{25}\left(\frac{17}{14}-\frac{16}{14}\right)$$

Since \frac{17}{14} and \frac{16}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{25}\times \frac{17-16}{14}$$

Subtract 16 from 17 to get 1.

$$\frac{7}{25}\times \frac{1}{14}$$

Multiply \frac{7}{25} times \frac{1}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 1}{25\times 14}$$

Do the multiplications in the fraction \frac{7\times 1}{25\times 14}.

$$\frac{7}{350}$$

Reduce the fraction \frac{7}{350} to lowest terms by extracting and canceling out 7.

$$\frac{1}{50}$$

Factor

$$\frac{1}{2 \cdot 5 ^ {2}} = 0.02$$