Solve 1/2+1/3(1/4+1/5)

$$\frac { 1 } { 2 } + \frac { 1 } { 3 } ( \frac { 1 } { 4 } + \frac { 1 } { 5 } )$$

Evaluate

$$\frac{13}{20}=0.65$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{1}{2}+\frac{1}{3}\left(\frac{5}{20}+\frac{4}{20}\right)$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}+\frac{1}{3}\times \frac{5+4}{20}$$

Add 5 and 4 to get 9.

$$\frac{1}{2}+\frac{1}{3}\times \frac{9}{20}$$

Multiply \frac{1}{3} times \frac{9}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{1\times 9}{3\times 20}$$

Do the multiplications in the fraction \frac{1\times 9}{3\times 20}.

$$\frac{1}{2}+\frac{9}{60}$$

Reduce the fraction \frac{9}{60} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}+\frac{3}{20}$$

Least common multiple of 2 and 20 is 20. Convert \frac{1}{2} and \frac{3}{20} to fractions with denominator 20.

$$\frac{10}{20}+\frac{3}{20}$$

Since \frac{10}{20} and \frac{3}{20} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{20}$$

Add 10 and 3 to get 13.

$$\frac{13}{20}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 5} = 0.65$$