Solve (1/13+1/17)*13*17

$$( \frac { 1 } { 13 } + \frac { 1 } { 17 } ) \times 13 \times 17$$

Evaluate

$$30$$

Solution Steps

Least common multiple of 13 and 17 is 221. Convert \frac{1}{13} and \frac{1}{17} to fractions with denominator 221.

$$\left(\frac{17}{221}+\frac{13}{221}\right)\times 13\times 17$$

Since \frac{17}{221} and \frac{13}{221} have the same denominator, add them by adding their numerators.

$$\frac{17+13}{221}\times 13\times 17$$

Add 17 and 13 to get 30.

$$\frac{30}{221}\times 13\times 17$$

Express \frac{30}{221}\times 13 as a single fraction.

$$\frac{30\times 13}{221}\times 17$$

Multiply 30 and 13 to get 390.

$$\frac{390}{221}\times 17$$

Reduce the fraction \frac{390}{221} to lowest terms by extracting and canceling out 13.

$$\frac{30}{17}\times 17$$

Cancel out 17 and 17.

$$30$$

Factor

$$2\times 3\times 5$$