Solve 5/7div8/9+7/8+7/5-frac{5}{7}

$$\frac { 5 } { 7 } \div \frac { 8 } { 9 } + \frac { 7 } { 8 } + \frac { 7 } { 5 } - \frac { 5 } { 7 }$$

Evaluate

$$\frac{331}{140}\approx 2.364285714$$

Solution Steps

Divide \frac{5}{7} by \frac{8}{9} by multiplying \frac{5}{7} by the reciprocal of \frac{8}{9}.

$$\frac{5}{7}\times \frac{9}{8}+\frac{7}{8}+\frac{7}{5}-\frac{5}{7}$$

Multiply \frac{5}{7} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 9}{7\times 8}+\frac{7}{8}+\frac{7}{5}-\frac{5}{7}$$

Do the multiplications in the fraction \frac{5\times 9}{7\times 8}.

$$\frac{45}{56}+\frac{7}{8}+\frac{7}{5}-\frac{5}{7}$$

Least common multiple of 56 and 8 is 56. Convert \frac{45}{56} and \frac{7}{8} to fractions with denominator 56.

$$\frac{45}{56}+\frac{49}{56}+\frac{7}{5}-\frac{5}{7}$$

Since \frac{45}{56} and \frac{49}{56} have the same denominator, add them by adding their numerators.

$$\frac{45+49}{56}+\frac{7}{5}-\frac{5}{7}$$

Add 45 and 49 to get 94.

$$\frac{94}{56}+\frac{7}{5}-\frac{5}{7}$$

Reduce the fraction \frac{94}{56} to lowest terms by extracting and canceling out 2.

$$\frac{47}{28}+\frac{7}{5}-\frac{5}{7}$$

Least common multiple of 28 and 5 is 140. Convert \frac{47}{28} and \frac{7}{5} to fractions with denominator 140.

$$\frac{235}{140}+\frac{196}{140}-\frac{5}{7}$$

Since \frac{235}{140} and \frac{196}{140} have the same denominator, add them by adding their numerators.

$$\frac{235+196}{140}-\frac{5}{7}$$

Add 235 and 196 to get 431.

$$\frac{431}{140}-\frac{5}{7}$$

Least common multiple of 140 and 7 is 140. Convert \frac{431}{140} and \frac{5}{7} to fractions with denominator 140.

$$\frac{431}{140}-\frac{100}{140}$$

Since \frac{431}{140} and \frac{100}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{431-100}{140}$$

Subtract 100 from 431 to get 331.

$$\frac{331}{140}$$

Factor

$$\frac{331}{2 ^ {2} \cdot 5 \cdot 7} = 2\frac{51}{140} = 2.3642857142857143$$