Solve 51/3div(-31/3)div2/7

$$5 \frac { 1 } { 3 } \div ( - 3 \frac { 1 } { 3 } ) \div \frac { 2 } { 7 }$$

Evaluate

$$-\frac{28}{5}=-5.6$$

Solution Steps

Divide \frac{\frac{5\times 3+1}{3}}{-\frac{3\times 3+1}{3}} by \frac{2}{7} by multiplying \frac{\frac{5\times 3+1}{3}}{-\frac{3\times 3+1}{3}} by the reciprocal of \frac{2}{7}.

$$\frac{\frac{5\times 3+1}{3}\times 7}{\left(-\frac{3\times 3+1}{3}\right)\times 2}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{15+1}{3}\times 7}{\left(-\frac{3\times 3+1}{3}\right)\times 2}$$

Add 15 and 1 to get 16.

$$\frac{\frac{16}{3}\times 7}{\left(-\frac{3\times 3+1}{3}\right)\times 2}$$

Express \frac{16}{3}\times 7 as a single fraction.

$$\frac{\frac{16\times 7}{3}}{\left(-\frac{3\times 3+1}{3}\right)\times 2}$$

Multiply 16 and 7 to get 112.

$$\frac{\frac{112}{3}}{\left(-\frac{3\times 3+1}{3}\right)\times 2}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{112}{3}}{\left(-\frac{9+1}{3}\right)\times 2}$$

Add 9 and 1 to get 10.

$$\frac{\frac{112}{3}}{-\frac{10}{3}\times 2}$$

Express -\frac{10}{3}\times 2 as a single fraction.

$$\frac{\frac{112}{3}}{\frac{-10\times 2}{3}}$$

Multiply -10 and 2 to get -20.

$$\frac{\frac{112}{3}}{\frac{-20}{3}}$$

Fraction \frac{-20}{3} can be rewritten as -\frac{20}{3} by extracting the negative sign.

$$\frac{\frac{112}{3}}{-\frac{20}{3}}$$

Divide \frac{112}{3} by -\frac{20}{3} by multiplying \frac{112}{3} by the reciprocal of -\frac{20}{3}.

$$\frac{112}{3}\left(-\frac{3}{20}\right)$$

Multiply \frac{112}{3} times -\frac{3}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{112\left(-3\right)}{3\times 20}$$

Do the multiplications in the fraction \frac{112\left(-3\right)}{3\times 20}.

$$\frac{-336}{60}$$

Reduce the fraction \frac{-336}{60} to lowest terms by extracting and canceling out 12.

$$-\frac{28}{5}$$

Factor

$$-\frac{28}{5} = -5\frac{3}{5} = -5.6$$