Solve 10/3+(3/10-8/15)div(-7/20)

$$\frac { 10 } { 3 } + ( \frac { 3 } { 10 } - \frac { 8 } { 15 } ) \div ( - \frac { 7 } { 20 } )$$

Evaluate

$$4$$

Solution Steps

Least common multiple of 10 and 15 is 30. Convert \frac{3}{10} and \frac{8}{15} to fractions with denominator 30.

$$\frac{10}{3}+\frac{\frac{9}{30}-\frac{16}{30}}{-\frac{7}{20}}$$

Since \frac{9}{30} and \frac{16}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}+\frac{\frac{9-16}{30}}{-\frac{7}{20}}$$

Subtract 16 from 9 to get -7.

$$\frac{10}{3}+\frac{-\frac{7}{30}}{-\frac{7}{20}}$$

Divide -\frac{7}{30} by -\frac{7}{20} by multiplying -\frac{7}{30} by the reciprocal of -\frac{7}{20}.

$$\frac{10}{3}-\frac{7}{30}\left(-\frac{20}{7}\right)$$

Multiply -\frac{7}{30} times -\frac{20}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10}{3}+\frac{-7\left(-20\right)}{30\times 7}$$

Do the multiplications in the fraction \frac{-7\left(-20\right)}{30\times 7}.

$$\frac{10}{3}+\frac{140}{210}$$

Reduce the fraction \frac{140}{210} to lowest terms by extracting and canceling out 70.

$$\frac{10}{3}+\frac{2}{3}$$

Since \frac{10}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{10+2}{3}$$

Add 10 and 2 to get 12.

$$\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$4$$

Factor

$$2^{2}$$