Solve 3*(3/5+2/3)-(1/3-2/3)]divfrac{4}{5}=

$$3 \times ( \frac { 3 } { 5 } + \frac { 2 } { 3 } ) - ( \frac { 1 } { 3 } - \frac { 2 } { 3 } ) ] \div \frac { 4 } { 5 } =$$

Evaluate

$$\frac{62}{15}\approx 4.133333333$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{2}{3} to fractions with denominator 15.

$$3\left(\frac{9}{15}+\frac{10}{15}\right)-\left(\frac{1}{3}-\frac{2}{3}\right)$$

Since \frac{9}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$3\times \frac{9+10}{15}-\left(\frac{1}{3}-\frac{2}{3}\right)$$

Add 9 and 10 to get 19.

$$3\times \frac{19}{15}-\left(\frac{1}{3}-\frac{2}{3}\right)$$

Express 3\times \frac{19}{15} as a single fraction.

$$\frac{3\times 19}{15}-\left(\frac{1}{3}-\frac{2}{3}\right)$$

Multiply 3 and 19 to get 57.

$$\frac{57}{15}-\left(\frac{1}{3}-\frac{2}{3}\right)$$

Reduce the fraction \frac{57}{15} to lowest terms by extracting and canceling out 3.

$$\frac{19}{5}-\left(\frac{1}{3}-\frac{2}{3}\right)$$

Since \frac{1}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19}{5}-\frac{1-2}{3}$$

Subtract 2 from 1 to get -1.

$$\frac{19}{5}-\left(-\frac{1}{3}\right)$$

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$\frac{19}{5}+\frac{1}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{19}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{57}{15}+\frac{5}{15}$$

Since \frac{57}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{57+5}{15}$$

Add 57 and 5 to get 62.

$$\frac{62}{15}$$

Factor

$$\frac{2 \cdot 31}{3 \cdot 5} = 4\frac{2}{15} = 4.133333333333334$$