Solve (4/15-3/5)div(3/4-5/8)+5frac{2}{3}

$$( \frac { 4 } { 15 } - \frac { 3 } { 5 } ) \div ( \frac { 3 } { 4 } - \frac { 5 } { 8 } ) + 5 \frac { 2 } { 3 }$$

Evaluate

$$3$$

Solution Steps

Least common multiple of 15 and 5 is 15. Convert \frac{4}{15} and \frac{3}{5} to fractions with denominator 15.

$$\frac{\frac{4}{15}-\frac{9}{15}}{\frac{3}{4}-\frac{5}{8}}+\frac{5\times 3+2}{3}$$

Since \frac{4}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-9}{15}}{\frac{3}{4}-\frac{5}{8}}+\frac{5\times 3+2}{3}$$

Subtract 9 from 4 to get -5.

$$\frac{\frac{-5}{15}}{\frac{3}{4}-\frac{5}{8}}+\frac{5\times 3+2}{3}$$

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

$$\frac{-\frac{1}{3}}{\frac{3}{4}-\frac{5}{8}}+\frac{5\times 3+2}{3}$$

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{5}{8} to fractions with denominator 8.

$$\frac{-\frac{1}{3}}{\frac{6}{8}-\frac{5}{8}}+\frac{5\times 3+2}{3}$$

Since \frac{6}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{3}}{\frac{6-5}{8}}+\frac{5\times 3+2}{3}$$

Subtract 5 from 6 to get 1.

$$\frac{-\frac{1}{3}}{\frac{1}{8}}+\frac{5\times 3+2}{3}$$

Divide -\frac{1}{3} by \frac{1}{8} by multiplying -\frac{1}{3} by the reciprocal of \frac{1}{8}.

$$-\frac{1}{3}\times 8+\frac{5\times 3+2}{3}$$

Express -\frac{1}{3}\times 8 as a single fraction.

$$\frac{-8}{3}+\frac{5\times 3+2}{3}$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$-\frac{8}{3}+\frac{5\times 3+2}{3}$$

Multiply 5 and 3 to get 15.

$$-\frac{8}{3}+\frac{15+2}{3}$$

Add 15 and 2 to get 17.

$$-\frac{8}{3}+\frac{17}{3}$$

Since -\frac{8}{3} and \frac{17}{3} have the same denominator, add them by adding their numerators.

$$\frac{-8+17}{3}$$

Add -8 and 17 to get 9.

$$\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$3$$

Factor

$$3$$