Solve (2/3+1/5)5/2+5/6

$$( \frac{ 2 }{ 3 } + \frac{ 1 }{ 5 } ) \frac{ 5 }{ 2 } + \frac{ 5 }{ 6 }$$

Evaluate

$$3$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{1}{5} to fractions with denominator 15.

$$\left(\frac{10}{15}+\frac{3}{15}\right)\times \frac{5}{2}+\frac{5}{6}$$

Since \frac{10}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{15}\times \frac{5}{2}+\frac{5}{6}$$

Add 10 and 3 to get 13.

$$\frac{13}{15}\times \frac{5}{2}+\frac{5}{6}$$

Multiply \frac{13}{15} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 5}{15\times 2}+\frac{5}{6}$$

Do the multiplications in the fraction \frac{13\times 5}{15\times 2}.

$$\frac{65}{30}+\frac{5}{6}$$

Reduce the fraction \frac{65}{30} to lowest terms by extracting and canceling out 5.

$$\frac{13}{6}+\frac{5}{6}$$

Since \frac{13}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{13+5}{6}$$

Add 13 and 5 to get 18.

$$\frac{18}{6}$$

Divide 18 by 6 to get 3.

$$3$$

Factor

$$3$$