Solve 5/6*(7/4-3/8)+5/2=

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

Evaluate

$$\frac{175}{48}\approx 3.645833333$$

Solution Steps

Least common multiple of 4 and 8 is 8. Convert \frac{7}{4} and \frac{3}{8} to fractions with denominator 8.

$$\frac{5}{6}\left(\frac{14}{8}-\frac{3}{8}\right)+\frac{5}{2}$$

Since \frac{14}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}\times \frac{14-3}{8}+\frac{5}{2}$$

Subtract 3 from 14 to get 11.

$$\frac{5}{6}\times \frac{11}{8}+\frac{5}{2}$$

Multiply \frac{5}{6} times \frac{11}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 11}{6\times 8}+\frac{5}{2}$$

Do the multiplications in the fraction \frac{5\times 11}{6\times 8}.

$$\frac{55}{48}+\frac{5}{2}$$

Least common multiple of 48 and 2 is 48. Convert \frac{55}{48} and \frac{5}{2} to fractions with denominator 48.

$$\frac{55}{48}+\frac{120}{48}$$

Since \frac{55}{48} and \frac{120}{48} have the same denominator, add them by adding their numerators.

$$\frac{55+120}{48}$$

Add 55 and 120 to get 175.

$$\frac{175}{48}$$

Factor

$$\frac{5 ^ {2} \cdot 7}{2 ^ {4} \cdot 3} = 3\frac{31}{48} = 3.6458333333333335$$