Solve 3/5:14/15*7/9-1/7

$$\frac { 3 } { 5 } : \frac { 14 } { 15 } \cdot \frac { 7 } { 9 } - \frac { 1 } { 7 }$$

Evaluate

$$\frac{5}{14}\approx 0.357142857$$

Solution Steps

Divide \frac{3}{5} by \frac{14}{15} by multiplying \frac{3}{5} by the reciprocal of \frac{14}{15}.

$$\frac{3}{5}\times \frac{15}{14}\times \frac{7}{9}-\frac{1}{7}$$

Multiply \frac{3}{5} times \frac{15}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 15}{5\times 14}\times \frac{7}{9}-\frac{1}{7}$$

Do the multiplications in the fraction \frac{3\times 15}{5\times 14}.

$$\frac{45}{70}\times \frac{7}{9}-\frac{1}{7}$$

Reduce the fraction \frac{45}{70} to lowest terms by extracting and canceling out 5.

$$\frac{9}{14}\times \frac{7}{9}-\frac{1}{7}$$

Multiply \frac{9}{14} times \frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 7}{14\times 9}-\frac{1}{7}$$

Cancel out 9 in both numerator and denominator.

$$\frac{7}{14}-\frac{1}{7}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{1}{2}-\frac{1}{7}$$

Least common multiple of 2 and 7 is 14. Convert \frac{1}{2} and \frac{1}{7} to fractions with denominator 14.

$$\frac{7}{14}-\frac{2}{14}$$

Since \frac{7}{14} and \frac{2}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-2}{14}$$

Subtract 2 from 7 to get 5.

$$\frac{5}{14}$$

Factor

$$\frac{5}{2 \cdot 7} = 0.35714285714285715$$