Solve 1/21+3/13-1/49+2/65=

$$\frac { 1 } { 21 } + \frac { 3 } { 13 } - \frac { 1 } { 49 } + \frac { 2 } { 65 } =$$

Evaluate

$$\frac{2759}{9555}\approx 0.288749346$$

Solution Steps

Least common multiple of 21 and 13 is 273. Convert \frac{1}{21} and \frac{3}{13} to fractions with denominator 273.

$$\frac{13}{273}+\frac{63}{273}-\frac{1}{49}+\frac{2}{65}$$

Since \frac{13}{273} and \frac{63}{273} have the same denominator, add them by adding their numerators.

$$\frac{13+63}{273}-\frac{1}{49}+\frac{2}{65}$$

Add 13 and 63 to get 76.

$$\frac{76}{273}-\frac{1}{49}+\frac{2}{65}$$

Least common multiple of 273 and 49 is 1911. Convert \frac{76}{273} and \frac{1}{49} to fractions with denominator 1911.

$$\frac{532}{1911}-\frac{39}{1911}+\frac{2}{65}$$

Since \frac{532}{1911} and \frac{39}{1911} have the same denominator, subtract them by subtracting their numerators.

$$\frac{532-39}{1911}+\frac{2}{65}$$

Subtract 39 from 532 to get 493.

$$\frac{493}{1911}+\frac{2}{65}$$

Least common multiple of 1911 and 65 is 9555. Convert \frac{493}{1911} and \frac{2}{65} to fractions with denominator 9555.

$$\frac{2465}{9555}+\frac{294}{9555}$$

Since \frac{2465}{9555} and \frac{294}{9555} have the same denominator, add them by adding their numerators.

$$\frac{2465+294}{9555}$$

Add 2465 and 294 to get 2759.

$$\frac{2759}{9555}$$

Factor

$$\frac{31 \cdot 89}{3 \cdot 5 \cdot 7 ^ {2} \cdot 13} = 0.288749345892203$$