Solve {l}{1/4+4/7+9/28}{17/8+frac{23}{90}+frac{11}{60}}

$$\left. \begin{array} { l } { \frac { 1 } { 4 } + \frac { 4 } { 7 } + \frac { 9 } { 28 } } \\ { \frac { 17 } { 8 } + \frac { 23 } { 90 } + \frac { 11 } { 60 } } \end{array} \right.$$

Sort

$$\frac{8}{7},\ \frac{923}{360}$$

Solution Steps

Least common multiple of 4 and 7 is 28. Convert \frac{1}{4} and \frac{4}{7} to fractions with denominator 28.

$$sort(\frac{7}{28}+\frac{16}{28}+\frac{9}{28},\frac{17}{8}+\frac{23}{90}+\frac{11}{60})$$

Since \frac{7}{28} and \frac{16}{28} have the same denominator, add them by adding their numerators.

$$sort(\frac{7+16}{28}+\frac{9}{28},\frac{17}{8}+\frac{23}{90}+\frac{11}{60})$$

Add 7 and 16 to get 23.

$$sort(\frac{23}{28}+\frac{9}{28},\frac{17}{8}+\frac{23}{90}+\frac{11}{60})$$

Since \frac{23}{28} and \frac{9}{28} have the same denominator, add them by adding their numerators.

$$sort(\frac{23+9}{28},\frac{17}{8}+\frac{23}{90}+\frac{11}{60})$$

Add 23 and 9 to get 32.

$$sort(\frac{32}{28},\frac{17}{8}+\frac{23}{90}+\frac{11}{60})$$

Reduce the fraction \frac{32}{28} to lowest terms by extracting and canceling out 4.

$$sort(\frac{8}{7},\frac{17}{8}+\frac{23}{90}+\frac{11}{60})$$

Least common multiple of 8 and 90 is 360. Convert \frac{17}{8} and \frac{23}{90} to fractions with denominator 360.

$$sort(\frac{8}{7},\frac{765}{360}+\frac{92}{360}+\frac{11}{60})$$

Since \frac{765}{360} and \frac{92}{360} have the same denominator, add them by adding their numerators.

$$sort(\frac{8}{7},\frac{765+92}{360}+\frac{11}{60})$$

Add 765 and 92 to get 857.

$$sort(\frac{8}{7},\frac{857}{360}+\frac{11}{60})$$

Least common multiple of 360 and 60 is 360. Convert \frac{857}{360} and \frac{11}{60} to fractions with denominator 360.

$$sort(\frac{8}{7},\frac{857}{360}+\frac{66}{360})$$

Since \frac{857}{360} and \frac{66}{360} have the same denominator, add them by adding their numerators.

$$sort(\frac{8}{7},\frac{857+66}{360})$$

Add 857 and 66 to get 923.

$$sort(\frac{8}{7},\frac{923}{360})$$

Least common denominator of the numbers in the list \frac{8}{7},\frac{923}{360} is 2520. Convert numbers in the list to fractions with denominator 2520.

$$\frac{2880}{2520},\frac{6461}{2520}$$

Evaluate

$$\frac{8}{7},\ \frac{923}{360}$$