Solve (5/7*7/10)-4/15*5/12

$$( \frac { 5 } { 7 } \times \frac { 7 } { 10 } ) - \frac { 4 } { 15 } \times \frac { 5 } { 12 }$$

Evaluate

$$\frac{7}{18}\approx 0.388888889$$

Solution Steps

Multiply \frac{5}{7} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 7}{7\times 10}-\frac{4}{15}\times \frac{5}{12}$$

Cancel out 7 in both numerator and denominator.

$$\frac{5}{10}-\frac{4}{15}\times \frac{5}{12}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}-\frac{4}{15}\times \frac{5}{12}$$

Multiply \frac{4}{15} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}-\frac{4\times 5}{15\times 12}$$

Do the multiplications in the fraction \frac{4\times 5}{15\times 12}.

$$\frac{1}{2}-\frac{20}{180}$$

Reduce the fraction \frac{20}{180} to lowest terms by extracting and canceling out 20.

$$\frac{1}{2}-\frac{1}{9}$$

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{1}{9} to fractions with denominator 18.

$$\frac{9}{18}-\frac{2}{18}$$

Since \frac{9}{18} and \frac{2}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-2}{18}$$

Subtract 2 from 9 to get 7.

$$\frac{7}{18}$$

Factor

$$\frac{7}{2 \cdot 3 ^ {2}} = 0.3888888888888889$$