Solve 4/3div5/3/frac{4{2}--2/3}

$$\frac { \frac { 4 } { 3 } \div \frac { 5 } { 3 } } { \frac { 4 } { 2 } - \frac { - 2 } { 3 } }$$

Evaluate

$$\frac{3}{10}=0.3$$

Solution Steps

Divide \frac{4}{3} by \frac{5}{3} by multiplying \frac{4}{3} by the reciprocal of \frac{5}{3}.

$$\frac{\frac{4}{3}\times \frac{3}{5}}{\frac{4}{2}-\frac{-2}{3}}$$

Multiply \frac{4}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 3}{3\times 5}}{\frac{4}{2}-\frac{-2}{3}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{4}{5}}{\frac{4}{2}-\frac{-2}{3}}$$

Divide 4 by 2 to get 2.

$$\frac{\frac{4}{5}}{2-\frac{-2}{3}}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{\frac{4}{5}}{2-\left(-\frac{2}{3}\right)}$$

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

$$\frac{\frac{4}{5}}{2+\frac{2}{3}}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{\frac{4}{5}}{\frac{6}{3}+\frac{2}{3}}$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4}{5}}{\frac{6+2}{3}}$$

Add 6 and 2 to get 8.

$$\frac{\frac{4}{5}}{\frac{8}{3}}$$

Divide \frac{4}{5} by \frac{8}{3} by multiplying \frac{4}{5} by the reciprocal of \frac{8}{3}.

$$\frac{4}{5}\times \frac{3}{8}$$

Multiply \frac{4}{5} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 3}{5\times 8}$$

Do the multiplications in the fraction \frac{4\times 3}{5\times 8}.

$$\frac{12}{40}$$

Reduce the fraction \frac{12}{40} to lowest terms by extracting and canceling out 4.

$$\frac{3}{10}$$

Factor

$$\frac{3}{2 \cdot 5} = 0.3$$