Solve {l}{21/2-3/4}{51/8-12/3}

$$\left. \begin{array} { l } { 2 \frac { 1 } { 2 } - \frac { 3 } { 4 } } \\ { 5 \frac { 1 } { 8 } - 1 \frac { 2 } { 3 } } \end{array} \right.$$

Sort

$$\frac{7}{4},\ \frac{83}{24}$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{3}{4} to fractions with denominator 4.

$$sort(\frac{10}{4}-\frac{3}{4},\frac{5\times 8+1}{8}-\frac{1\times 3+2}{3})$$

Since \frac{10}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{10-3}{4},\frac{5\times 8+1}{8}-\frac{1\times 3+2}{3})$$

Subtract 3 from 10 to get 7.

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

Multiply 5 and 8 to get 40.

$$sort(\frac{7}{4},\frac{40+1}{8}-\frac{1\times 3+2}{3})$$

Add 40 and 1 to get 41.

$$sort(\frac{7}{4},\frac{41}{8}-\frac{1\times 3+2}{3})$$

Multiply 1 and 3 to get 3.

$$sort(\frac{7}{4},\frac{41}{8}-\frac{3+2}{3})$$

Add 3 and 2 to get 5.

$$sort(\frac{7}{4},\frac{41}{8}-\frac{5}{3})$$

Least common multiple of 8 and 3 is 24. Convert \frac{41}{8} and \frac{5}{3} to fractions with denominator 24.

$$sort(\frac{7}{4},\frac{123}{24}-\frac{40}{24})$$

Since \frac{123}{24} and \frac{40}{24} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{7}{4},\frac{123-40}{24})$$

Subtract 40 from 123 to get 83.

$$sort(\frac{7}{4},\frac{83}{24})$$

Least common denominator of the numbers in the list \frac{7}{4},\frac{83}{24} is 24. Convert numbers in the list to fractions with denominator 24.

$$\frac{42}{24},\frac{83}{24}$$

Evaluate

$$\frac{7}{4},\ \frac{83}{24}$$