Solve 1/8+3+2/7-3/5+2/9

$$\frac { 1 } { 8 } + 3 + \frac { 2 } { 7 } - \frac { 3 } { 5 } + \frac { 2 } { 9 }$$

Evaluate

$$\frac{7643}{2520}\approx 3.032936508$$

Solution Steps

Convert 3 to fraction \frac{24}{8}.

$$\frac{1}{8}+\frac{24}{8}+\frac{2}{7}-\frac{3}{5}+\frac{2}{9}$$

Since \frac{1}{8} and \frac{24}{8} have the same denominator, add them by adding their numerators.

$$\frac{1+24}{8}+\frac{2}{7}-\frac{3}{5}+\frac{2}{9}$$

Add 1 and 24 to get 25.

$$\frac{25}{8}+\frac{2}{7}-\frac{3}{5}+\frac{2}{9}$$

Least common multiple of 8 and 7 is 56. Convert \frac{25}{8} and \frac{2}{7} to fractions with denominator 56.

$$\frac{175}{56}+\frac{16}{56}-\frac{3}{5}+\frac{2}{9}$$

Since \frac{175}{56} and \frac{16}{56} have the same denominator, add them by adding their numerators.

$$\frac{175+16}{56}-\frac{3}{5}+\frac{2}{9}$$

Add 175 and 16 to get 191.

$$\frac{191}{56}-\frac{3}{5}+\frac{2}{9}$$

Least common multiple of 56 and 5 is 280. Convert \frac{191}{56} and \frac{3}{5} to fractions with denominator 280.

$$\frac{955}{280}-\frac{168}{280}+\frac{2}{9}$$

Since \frac{955}{280} and \frac{168}{280} have the same denominator, subtract them by subtracting their numerators.

$$\frac{955-168}{280}+\frac{2}{9}$$

Subtract 168 from 955 to get 787.

$$\frac{787}{280}+\frac{2}{9}$$

Least common multiple of 280 and 9 is 2520. Convert \frac{787}{280} and \frac{2}{9} to fractions with denominator 2520.

$$\frac{7083}{2520}+\frac{560}{2520}$$

Since \frac{7083}{2520} and \frac{560}{2520} have the same denominator, add them by adding their numerators.

$$\frac{7083+560}{2520}$$

Add 7083 and 560 to get 7643.

$$\frac{7643}{2520}$$

Factor

$$\frac{7643}{2 ^ {3} \cdot 3 ^ {2} \cdot 5 \cdot 7} = 3\frac{83}{2520} = 3.032936507936508$$