Solve (1/23+1/17)*23*172

$$( \frac { 1 } { 23 } + \frac { 1 } { 17 } ) \times 23 \times 172$$

Evaluate

$$\frac{6880}{17}\approx 404.705882353$$

Solution Steps

Least common multiple of 23 and 17 is 391. Convert \frac{1}{23} and \frac{1}{17} to fractions with denominator 391.

$$\left(\frac{17}{391}+\frac{23}{391}\right)\times 23\times 172$$

Since \frac{17}{391} and \frac{23}{391} have the same denominator, add them by adding their numerators.

$$\frac{17+23}{391}\times 23\times 172$$

Add 17 and 23 to get 40.

$$\frac{40}{391}\times 23\times 172$$

Express \frac{40}{391}\times 23 as a single fraction.

$$\frac{40\times 23}{391}\times 172$$

Multiply 40 and 23 to get 920.

$$\frac{920}{391}\times 172$$

Reduce the fraction \frac{920}{391} to lowest terms by extracting and canceling out 23.

$$\frac{40}{17}\times 172$$

Express \frac{40}{17}\times 172 as a single fraction.

$$\frac{40\times 172}{17}$$

Multiply 40 and 172 to get 6880.

$$\frac{6880}{17}$$

Factor

$$\frac{2 ^ {5} \cdot 5 \cdot 43}{17} = 404\frac{12}{17} = 404.70588235294116$$