Solve (37/11+48/13+515/17)div(22/11+2frac{10}{13}+3frac{9}{17})

$$( 3 \frac { 7 } { 11 } + 4 \frac { 8 } { 13 } + 5 \frac { 15 } { 17 } ) \div ( 2 \frac { 2 } { 11 } + 2 \frac { 10 } { 13 } + 3 \frac { 9 } { 17 } )$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Multiply 3 and 11 to get 33.

$$\frac{\frac{33+7}{11}+\frac{4\times 13+8}{13}+\frac{5\times 17+15}{17}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Add 33 and 7 to get 40.

$$\frac{\frac{40}{11}+\frac{4\times 13+8}{13}+\frac{5\times 17+15}{17}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Multiply 4 and 13 to get 52.

$$\frac{\frac{40}{11}+\frac{52+8}{13}+\frac{5\times 17+15}{17}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Add 52 and 8 to get 60.

$$\frac{\frac{40}{11}+\frac{60}{13}+\frac{5\times 17+15}{17}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Least common multiple of 11 and 13 is 143. Convert \frac{40}{11} and \frac{60}{13} to fractions with denominator 143.

$$\frac{\frac{520}{143}+\frac{660}{143}+\frac{5\times 17+15}{17}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Since \frac{520}{143} and \frac{660}{143} have the same denominator, add them by adding their numerators.

$$\frac{\frac{520+660}{143}+\frac{5\times 17+15}{17}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Add 520 and 660 to get 1180.

$$\frac{\frac{1180}{143}+\frac{5\times 17+15}{17}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Multiply 5 and 17 to get 85.

$$\frac{\frac{1180}{143}+\frac{85+15}{17}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Add 85 and 15 to get 100.

$$\frac{\frac{1180}{143}+\frac{100}{17}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Least common multiple of 143 and 17 is 2431. Convert \frac{1180}{143} and \frac{100}{17} to fractions with denominator 2431.

$$\frac{\frac{20060}{2431}+\frac{14300}{2431}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Since \frac{20060}{2431} and \frac{14300}{2431} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20060+14300}{2431}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Add 20060 and 14300 to get 34360.

$$\frac{\frac{34360}{2431}}{\frac{2\times 11+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Multiply 2 and 11 to get 22.

$$\frac{\frac{34360}{2431}}{\frac{22+2}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Add 22 and 2 to get 24.

$$\frac{\frac{34360}{2431}}{\frac{24}{11}+\frac{2\times 13+10}{13}+\frac{3\times 17+9}{17}}$$

Multiply 2 and 13 to get 26.

$$\frac{\frac{34360}{2431}}{\frac{24}{11}+\frac{26+10}{13}+\frac{3\times 17+9}{17}}$$

Add 26 and 10 to get 36.

$$\frac{\frac{34360}{2431}}{\frac{24}{11}+\frac{36}{13}+\frac{3\times 17+9}{17}}$$

Least common multiple of 11 and 13 is 143. Convert \frac{24}{11} and \frac{36}{13} to fractions with denominator 143.

$$\frac{\frac{34360}{2431}}{\frac{312}{143}+\frac{396}{143}+\frac{3\times 17+9}{17}}$$

Since \frac{312}{143} and \frac{396}{143} have the same denominator, add them by adding their numerators.

$$\frac{\frac{34360}{2431}}{\frac{312+396}{143}+\frac{3\times 17+9}{17}}$$

Add 312 and 396 to get 708.

$$\frac{\frac{34360}{2431}}{\frac{708}{143}+\frac{3\times 17+9}{17}}$$

Multiply 3 and 17 to get 51.

$$\frac{\frac{34360}{2431}}{\frac{708}{143}+\frac{51+9}{17}}$$

Add 51 and 9 to get 60.

$$\frac{\frac{34360}{2431}}{\frac{708}{143}+\frac{60}{17}}$$

Least common multiple of 143 and 17 is 2431. Convert \frac{708}{143} and \frac{60}{17} to fractions with denominator 2431.

$$\frac{\frac{34360}{2431}}{\frac{12036}{2431}+\frac{8580}{2431}}$$

Since \frac{12036}{2431} and \frac{8580}{2431} have the same denominator, add them by adding their numerators.

$$\frac{\frac{34360}{2431}}{\frac{12036+8580}{2431}}$$

Add 12036 and 8580 to get 20616.

$$\frac{\frac{34360}{2431}}{\frac{20616}{2431}}$$

Divide \frac{34360}{2431} by \frac{20616}{2431} by multiplying \frac{34360}{2431} by the reciprocal of \frac{20616}{2431}.

$$\frac{34360}{2431}\times \frac{2431}{20616}$$

Multiply \frac{34360}{2431} times \frac{2431}{20616} by multiplying numerator times numerator and denominator times denominator.

$$\frac{34360\times 2431}{2431\times 20616}$$

Cancel out 2431 in both numerator and denominator.

$$\frac{34360}{20616}$$

Reduce the fraction \frac{34360}{20616} to lowest terms by extracting and canceling out 6872.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$