Solve 1/3*2/5div((5/8-5/4)+(frac{6}{7}+frac{7}{8}))=

$$\frac { 1 } { 3 } \times \frac { 2 } { 5 } \div ( ( \frac { 5 } { 8 } - \frac { 5 } { 4 } ) + ( \frac { 6 } { 7 } + \frac { 7 } { 8 } ) ) =$$

Evaluate

$$\frac{56}{465}\approx 0.120430108$$

Solution Steps

Multiply \frac{1}{3} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 2}{3\times 5}}{\frac{5}{8}-\frac{5}{4}+\frac{6}{7}+\frac{7}{8}}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 5}.

$$\frac{\frac{2}{15}}{\frac{5}{8}-\frac{5}{4}+\frac{6}{7}+\frac{7}{8}}$$

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

$$\frac{\frac{2}{15}}{\frac{5}{8}-\frac{10}{8}+\frac{6}{7}+\frac{7}{8}}$$

Since \frac{5}{8} and \frac{10}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2}{15}}{\frac{5-10}{8}+\frac{6}{7}+\frac{7}{8}}$$

Subtract 10 from 5 to get -5.

$$\frac{\frac{2}{15}}{-\frac{5}{8}+\frac{6}{7}+\frac{7}{8}}$$

Least common multiple of 8 and 7 is 56. Convert -\frac{5}{8} and \frac{6}{7} to fractions with denominator 56.

$$\frac{\frac{2}{15}}{-\frac{35}{56}+\frac{48}{56}+\frac{7}{8}}$$

Since -\frac{35}{56} and \frac{48}{56} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{15}}{\frac{-35+48}{56}+\frac{7}{8}}$$

Add -35 and 48 to get 13.

$$\frac{\frac{2}{15}}{\frac{13}{56}+\frac{7}{8}}$$

Least common multiple of 56 and 8 is 56. Convert \frac{13}{56} and \frac{7}{8} to fractions with denominator 56.

$$\frac{\frac{2}{15}}{\frac{13}{56}+\frac{49}{56}}$$

Since \frac{13}{56} and \frac{49}{56} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{15}}{\frac{13+49}{56}}$$

Add 13 and 49 to get 62.

$$\frac{\frac{2}{15}}{\frac{62}{56}}$$

Reduce the fraction \frac{62}{56} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{15}}{\frac{31}{28}}$$

Divide \frac{2}{15} by \frac{31}{28} by multiplying \frac{2}{15} by the reciprocal of \frac{31}{28}.

$$\frac{2}{15}\times \frac{28}{31}$$

Multiply \frac{2}{15} times \frac{28}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 28}{15\times 31}$$

Do the multiplications in the fraction \frac{2\times 28}{15\times 31}.

$$\frac{56}{465}$$

Factor

$$\frac{2 ^ {3} \cdot 7}{3 \cdot 5 \cdot 31} = 0.12043010752688173$$