Solve 21/2*5+41/5*8+61/8*11+81/11*13

$$2 \frac { 1 } { 2 \times 5 } + 4 \frac { 1 } { 5 \times 8 } + 6 \frac { 1 } { 8 \times 11 } + 8 \frac { 1 } { 11 \times 13 }$$

Evaluate

$$\frac{1213}{2860}\approx 0.424125874$$

Solution Steps

Multiply 2 and 5 to get 10.

$$2\times \frac{1}{10}+4\times \frac{1}{5\times 8}+6\times \frac{1}{8\times 11}+8\times \frac{1}{11\times 13}$$

Multiply 2 and \frac{1}{10} to get \frac{2}{10}.

$$\frac{2}{10}+4\times \frac{1}{5\times 8}+6\times \frac{1}{8\times 11}+8\times \frac{1}{11\times 13}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}+4\times \frac{1}{5\times 8}+6\times \frac{1}{8\times 11}+8\times \frac{1}{11\times 13}$$

Multiply 5 and 8 to get 40.

$$\frac{1}{5}+4\times \frac{1}{40}+6\times \frac{1}{8\times 11}+8\times \frac{1}{11\times 13}$$

Multiply 4 and \frac{1}{40} to get \frac{4}{40}.

$$\frac{1}{5}+\frac{4}{40}+6\times \frac{1}{8\times 11}+8\times \frac{1}{11\times 13}$$

Reduce the fraction \frac{4}{40} to lowest terms by extracting and canceling out 4.

$$\frac{1}{5}+\frac{1}{10}+6\times \frac{1}{8\times 11}+8\times \frac{1}{11\times 13}$$

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{2}{10}+\frac{1}{10}+6\times \frac{1}{8\times 11}+8\times \frac{1}{11\times 13}$$

Since \frac{2}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{10}+6\times \frac{1}{8\times 11}+8\times \frac{1}{11\times 13}$$

Add 2 and 1 to get 3.

$$\frac{3}{10}+6\times \frac{1}{8\times 11}+8\times \frac{1}{11\times 13}$$

Multiply 8 and 11 to get 88.

$$\frac{3}{10}+6\times \frac{1}{88}+8\times \frac{1}{11\times 13}$$

Multiply 6 and \frac{1}{88} to get \frac{6}{88}.

$$\frac{3}{10}+\frac{6}{88}+8\times \frac{1}{11\times 13}$$

Reduce the fraction \frac{6}{88} to lowest terms by extracting and canceling out 2.

$$\frac{3}{10}+\frac{3}{44}+8\times \frac{1}{11\times 13}$$

Least common multiple of 10 and 44 is 220. Convert \frac{3}{10} and \frac{3}{44} to fractions with denominator 220.

$$\frac{66}{220}+\frac{15}{220}+8\times \frac{1}{11\times 13}$$

Since \frac{66}{220} and \frac{15}{220} have the same denominator, add them by adding their numerators.

$$\frac{66+15}{220}+8\times \frac{1}{11\times 13}$$

Add 66 and 15 to get 81.

$$\frac{81}{220}+8\times \frac{1}{11\times 13}$$

Multiply 11 and 13 to get 143.

$$\frac{81}{220}+8\times \frac{1}{143}$$

Multiply 8 and \frac{1}{143} to get \frac{8}{143}.

$$\frac{81}{220}+\frac{8}{143}$$

Least common multiple of 220 and 143 is 2860. Convert \frac{81}{220} and \frac{8}{143} to fractions with denominator 2860.

$$\frac{1053}{2860}+\frac{160}{2860}$$

Since \frac{1053}{2860} and \frac{160}{2860} have the same denominator, add them by adding their numerators.

$$\frac{1053+160}{2860}$$

Add 1053 and 160 to get 1213.

$$\frac{1213}{2860}$$

Factor

$$\frac{1213}{2 ^ {2} \cdot 5 \cdot 11 \cdot 13} = 0.4241258741258741$$