Solve 4/5+5/8+3/4+7/9+frac{2}{7}+frac{6}{2}=

$$\frac { 4 } { 5 } + \frac { 5 } { 8 } + \frac { 3 } { 4 } + \frac { 7 } { 9 } + \frac { 2 } { 7 } + \frac { 6 } { 2 } =$$

Evaluate

$$\frac{15721}{2520}\approx 6.238492063$$

Solution Steps

Least common multiple of 5 and 8 is 40. Convert \frac{4}{5} and \frac{5}{8} to fractions with denominator 40.

$$\frac{32}{40}+\frac{25}{40}+\frac{3}{4}+\frac{7}{9}+\frac{2}{7}+\frac{6}{2}$$

Since \frac{32}{40} and \frac{25}{40} have the same denominator, add them by adding their numerators.

$$\frac{32+25}{40}+\frac{3}{4}+\frac{7}{9}+\frac{2}{7}+\frac{6}{2}$$

Add 32 and 25 to get 57.

$$\frac{57}{40}+\frac{3}{4}+\frac{7}{9}+\frac{2}{7}+\frac{6}{2}$$

Least common multiple of 40 and 4 is 40. Convert \frac{57}{40} and \frac{3}{4} to fractions with denominator 40.

$$\frac{57}{40}+\frac{30}{40}+\frac{7}{9}+\frac{2}{7}+\frac{6}{2}$$

Since \frac{57}{40} and \frac{30}{40} have the same denominator, add them by adding their numerators.

$$\frac{57+30}{40}+\frac{7}{9}+\frac{2}{7}+\frac{6}{2}$$

Add 57 and 30 to get 87.

$$\frac{87}{40}+\frac{7}{9}+\frac{2}{7}+\frac{6}{2}$$

Least common multiple of 40 and 9 is 360. Convert \frac{87}{40} and \frac{7}{9} to fractions with denominator 360.

$$\frac{783}{360}+\frac{280}{360}+\frac{2}{7}+\frac{6}{2}$$

Since \frac{783}{360} and \frac{280}{360} have the same denominator, add them by adding their numerators.

$$\frac{783+280}{360}+\frac{2}{7}+\frac{6}{2}$$

Add 783 and 280 to get 1063.

$$\frac{1063}{360}+\frac{2}{7}+\frac{6}{2}$$

Least common multiple of 360 and 7 is 2520. Convert \frac{1063}{360} and \frac{2}{7} to fractions with denominator 2520.

$$\frac{7441}{2520}+\frac{720}{2520}+\frac{6}{2}$$

Since \frac{7441}{2520} and \frac{720}{2520} have the same denominator, add them by adding their numerators.

$$\frac{7441+720}{2520}+\frac{6}{2}$$

Add 7441 and 720 to get 8161.

$$\frac{8161}{2520}+\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$\frac{8161}{2520}+3$$

Convert 3 to fraction \frac{7560}{2520}.

$$\frac{8161}{2520}+\frac{7560}{2520}$$

Since \frac{8161}{2520} and \frac{7560}{2520} have the same denominator, add them by adding their numerators.

$$\frac{8161+7560}{2520}$$

Add 8161 and 7560 to get 15721.

$$\frac{15721}{2520}$$

Factor

$$\frac{79 \cdot 199}{2 ^ {3} \cdot 3 ^ {2} \cdot 5 \cdot 7} = 6\frac{601}{2520} = 6.238492063492063$$