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

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

Evaluate

$$\frac{13}{12}\approx 1.083333333$$

Solution Steps

Multiply \frac{5}{6} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5 in both numerator and denominator.

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

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

Multiply \frac{2}{3} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 5}{3\times 8}.

$$\frac{2}{3}+\frac{10}{24}$$

Reduce the fraction \frac{10}{24} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}+\frac{5}{12}$$

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{5}{12} to fractions with denominator 12.

$$\frac{8}{12}+\frac{5}{12}$$

Since \frac{8}{12} and \frac{5}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+5}{12}$$

Add 8 and 5 to get 13.

$$\frac{13}{12}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 3} = 1\frac{1}{12} = 1.0833333333333333$$