Solve 7/8:3/5+7/5*8/3

$$\frac { 7 } { 8 } : \frac { 3 } { 5 } + \frac { 7 } { 5 } \cdot \frac { 8 } { 3 }$$

Evaluate

$$\frac{623}{120}\approx 5.191666667$$

Solution Steps

Divide \frac{7}{8} by \frac{3}{5} by multiplying \frac{7}{8} by the reciprocal of \frac{3}{5}.

$$\frac{7}{8}\times \frac{5}{3}+\frac{7}{5}\times \frac{8}{3}$$

Multiply \frac{7}{8} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 5}{8\times 3}+\frac{7}{5}\times \frac{8}{3}$$

Do the multiplications in the fraction \frac{7\times 5}{8\times 3}.

$$\frac{35}{24}+\frac{7}{5}\times \frac{8}{3}$$

Multiply \frac{7}{5} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{24}+\frac{7\times 8}{5\times 3}$$

Do the multiplications in the fraction \frac{7\times 8}{5\times 3}.

$$\frac{35}{24}+\frac{56}{15}$$

Least common multiple of 24 and 15 is 120. Convert \frac{35}{24} and \frac{56}{15} to fractions with denominator 120.

$$\frac{175}{120}+\frac{448}{120}$$

Since \frac{175}{120} and \frac{448}{120} have the same denominator, add them by adding their numerators.

$$\frac{175+448}{120}$$

Add 175 and 448 to get 623.

$$\frac{623}{120}$$

Factor

$$\frac{7 \cdot 89}{2 ^ {3} \cdot 3 \cdot 5} = 5\frac{23}{120} = 5.191666666666666$$