Solve 2/3-7/10div(-7/15)

$$\frac { 2 } { 3 } - \frac { 7 } { 10 } \div ( - \frac { 7 } { 15 } )$$

Evaluate

$$\frac{13}{6}\approx 2.166666667$$

Solution Steps

Divide \frac{7}{10} by -\frac{7}{15} by multiplying \frac{7}{10} by the reciprocal of -\frac{7}{15}.

$$\frac{2}{3}-\frac{7}{10}\left(-\frac{15}{7}\right)$$

Multiply \frac{7}{10} times -\frac{15}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}-\frac{7\left(-15\right)}{10\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{2}{3}-\frac{-15}{10}$$

Reduce the fraction \frac{-15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{2}{3}-\left(-\frac{3}{2}\right)$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$\frac{2}{3}+\frac{3}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{4}{6}+\frac{9}{6}$$

Since \frac{4}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{4+9}{6}$$

Add 4 and 9 to get 13.

$$\frac{13}{6}$$

Factor

$$\frac{13}{2 \cdot 3} = 2\frac{1}{6} = 2.1666666666666665$$