Solve 2/3*5+3/5*8+5/8*13+7/13*20

$$\frac { 2 } { 3 \cdot 5 } + \frac { 3 } { 5 \cdot 8 } + \frac { 5 } { 8 \cdot 13 } + \frac { 7 } { 13 \cdot 20 }$$

Evaluate

$$\frac{17}{60}\approx 0.283333333$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\frac{2}{15}+\frac{3}{5\times 8}+\frac{5}{8\times 13}+\frac{7}{13\times 20}$$

Multiply 5 and 8 to get 40.

$$\frac{2}{15}+\frac{3}{40}+\frac{5}{8\times 13}+\frac{7}{13\times 20}$$

Least common multiple of 15 and 40 is 120. Convert \frac{2}{15} and \frac{3}{40} to fractions with denominator 120.

$$\frac{16}{120}+\frac{9}{120}+\frac{5}{8\times 13}+\frac{7}{13\times 20}$$

Since \frac{16}{120} and \frac{9}{120} have the same denominator, add them by adding their numerators.

$$\frac{16+9}{120}+\frac{5}{8\times 13}+\frac{7}{13\times 20}$$

Add 16 and 9 to get 25.

$$\frac{25}{120}+\frac{5}{8\times 13}+\frac{7}{13\times 20}$$

Reduce the fraction \frac{25}{120} to lowest terms by extracting and canceling out 5.

$$\frac{5}{24}+\frac{5}{8\times 13}+\frac{7}{13\times 20}$$

Multiply 8 and 13 to get 104.

$$\frac{5}{24}+\frac{5}{104}+\frac{7}{13\times 20}$$

Least common multiple of 24 and 104 is 312. Convert \frac{5}{24} and \frac{5}{104} to fractions with denominator 312.

$$\frac{65}{312}+\frac{15}{312}+\frac{7}{13\times 20}$$

Since \frac{65}{312} and \frac{15}{312} have the same denominator, add them by adding their numerators.

$$\frac{65+15}{312}+\frac{7}{13\times 20}$$

Add 65 and 15 to get 80.

$$\frac{80}{312}+\frac{7}{13\times 20}$$

Reduce the fraction \frac{80}{312} to lowest terms by extracting and canceling out 8.

$$\frac{10}{39}+\frac{7}{13\times 20}$$

Multiply 13 and 20 to get 260.

$$\frac{10}{39}+\frac{7}{260}$$

Least common multiple of 39 and 260 is 780. Convert \frac{10}{39} and \frac{7}{260} to fractions with denominator 780.

$$\frac{200}{780}+\frac{21}{780}$$

Since \frac{200}{780} and \frac{21}{780} have the same denominator, add them by adding their numerators.

$$\frac{200+21}{780}$$

Add 200 and 21 to get 221.

$$\frac{221}{780}$$

Reduce the fraction \frac{221}{780} to lowest terms by extracting and canceling out 13.

$$\frac{17}{60}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3 \cdot 5} = 0.2833333333333333$$