Solve 1/3-1(2/3+1/5)*1/13

$$\frac { 1 } { 3 - 1 } ( \frac { 2 } { 3 } + \frac { 1 } { 5 } ) \times \frac { 1 } { 13 }$$

Evaluate

$$\frac{1}{30}\approx 0.033333333$$

Solution Steps

Subtract 1 from 3 to get 2.

$$\frac{1}{2}\left(\frac{2}{3}+\frac{1}{5}\right)\times \frac{1}{13}$$

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

$$\frac{1}{2}\left(\frac{10}{15}+\frac{3}{15}\right)\times \frac{1}{13}$$

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

$$\frac{1}{2}\times \frac{10+3}{15}\times \frac{1}{13}$$

Add 10 and 3 to get 13.

$$\frac{1}{2}\times \frac{13}{15}\times \frac{1}{13}$$

Multiply \frac{1}{2} times \frac{13}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 13}{2\times 15}\times \frac{1}{13}$$

Do the multiplications in the fraction \frac{1\times 13}{2\times 15}.

$$\frac{13}{30}\times \frac{1}{13}$$

Multiply \frac{13}{30} times \frac{1}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 1}{30\times 13}$$

Cancel out 13 in both numerator and denominator.

$$\frac{1}{30}$$

Factor

$$\frac{1}{2 \cdot 3 \cdot 5} = 0.03333333333333333$$