Solve 2(49/58+49/85)

$$2 ( \frac { 49 } { 58 } + \frac { 49 } { 85 } )$$

Evaluate

$$\frac{7007}{2465}\approx 2.842596349$$

Solution Steps

Least common multiple of 58 and 85 is 4930. Convert \frac{49}{58} and \frac{49}{85} to fractions with denominator 4930.

$$2\left(\frac{4165}{4930}+\frac{2842}{4930}\right)$$

Since \frac{4165}{4930} and \frac{2842}{4930} have the same denominator, add them by adding their numerators.

$$2\times \frac{4165+2842}{4930}$$

Add 4165 and 2842 to get 7007.

$$2\times \frac{7007}{4930}$$

Express 2\times \frac{7007}{4930} as a single fraction.

$$\frac{2\times 7007}{4930}$$

Multiply 2 and 7007 to get 14014.

$$\frac{14014}{4930}$$

Reduce the fraction \frac{14014}{4930} to lowest terms by extracting and canceling out 2.

$$\frac{7007}{2465}$$

Factor

$$\frac{7 ^ {2} \cdot 11 \cdot 13}{5 \cdot 17 \cdot 29} = 2\frac{2077}{2465} = 2.8425963488843813$$