Solve {l}{53/4-21/4}{72/3+21/5}

$$\left. \begin{array} { l } { 5 \frac { 3 } { 4 } - 2 \frac { 1 } { 4 } } \\ { 7 \frac { 2 } { 3 } + 2 \frac { 1 } { 5 } } \end{array} \right.$$

Sort

$$\frac{7}{2},\ \frac{148}{15}$$

Solution Steps

Multiply 5 and 4 to get 20.

$$sort(\frac{20+3}{4}-\frac{2\times 4+1}{4},\frac{7\times 3+2}{3}+\frac{2\times 5+1}{5})$$

Add 20 and 3 to get 23.

$$sort(\frac{23}{4}-\frac{2\times 4+1}{4},\frac{7\times 3+2}{3}+\frac{2\times 5+1}{5})$$

Multiply 2 and 4 to get 8.

$$sort(\frac{23}{4}-\frac{8+1}{4},\frac{7\times 3+2}{3}+\frac{2\times 5+1}{5})$$

Add 8 and 1 to get 9.

$$sort(\frac{23}{4}-\frac{9}{4},\frac{7\times 3+2}{3}+\frac{2\times 5+1}{5})$$

Since \frac{23}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{23-9}{4},\frac{7\times 3+2}{3}+\frac{2\times 5+1}{5})$$

Subtract 9 from 23 to get 14.

$$sort(\frac{14}{4},\frac{7\times 3+2}{3}+\frac{2\times 5+1}{5})$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$sort(\frac{7}{2},\frac{7\times 3+2}{3}+\frac{2\times 5+1}{5})$$

Multiply 7 and 3 to get 21.

$$sort(\frac{7}{2},\frac{21+2}{3}+\frac{2\times 5+1}{5})$$

Add 21 and 2 to get 23.

$$sort(\frac{7}{2},\frac{23}{3}+\frac{2\times 5+1}{5})$$

Multiply 2 and 5 to get 10.

$$sort(\frac{7}{2},\frac{23}{3}+\frac{10+1}{5})$$

Add 10 and 1 to get 11.

$$sort(\frac{7}{2},\frac{23}{3}+\frac{11}{5})$$

Least common multiple of 3 and 5 is 15. Convert \frac{23}{3} and \frac{11}{5} to fractions with denominator 15.

$$sort(\frac{7}{2},\frac{115}{15}+\frac{33}{15})$$

Since \frac{115}{15} and \frac{33}{15} have the same denominator, add them by adding their numerators.

$$sort(\frac{7}{2},\frac{115+33}{15})$$

Add 115 and 33 to get 148.

$$sort(\frac{7}{2},\frac{148}{15})$$

Least common denominator of the numbers in the list \frac{7}{2},\frac{148}{15} is 30. Convert numbers in the list to fractions with denominator 30.

$$\frac{105}{30},\frac{296}{30}$$

Evaluate

$$\frac{7}{2},\ \frac{148}{15}$$