Solve [21/2-13/7]-[33/4-21/2]

$$[ 2 \frac { 1 } { 2 } - 1 \frac { 3 } { 7 } ] - [ 3 \frac { 3 } { 4 } - 2 \frac { 1 } { 2 } ]$$

Evaluate

$$-\frac{5}{28}\approx -0.178571429$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{4+1}{2}-\frac{1\times 7+3}{7}-\left(\frac{3\times 4+3}{4}-\frac{2\times 2+1}{2}\right)$$

Add 4 and 1 to get 5.

$$\frac{5}{2}-\frac{1\times 7+3}{7}-\left(\frac{3\times 4+3}{4}-\frac{2\times 2+1}{2}\right)$$

Multiply 1 and 7 to get 7.

$$\frac{5}{2}-\frac{7+3}{7}-\left(\frac{3\times 4+3}{4}-\frac{2\times 2+1}{2}\right)$$

Add 7 and 3 to get 10.

$$\frac{5}{2}-\frac{10}{7}-\left(\frac{3\times 4+3}{4}-\frac{2\times 2+1}{2}\right)$$

Least common multiple of 2 and 7 is 14. Convert \frac{5}{2} and \frac{10}{7} to fractions with denominator 14.

$$\frac{35}{14}-\frac{20}{14}-\left(\frac{3\times 4+3}{4}-\frac{2\times 2+1}{2}\right)$$

Since \frac{35}{14} and \frac{20}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-20}{14}-\left(\frac{3\times 4+3}{4}-\frac{2\times 2+1}{2}\right)$$

Subtract 20 from 35 to get 15.

$$\frac{15}{14}-\left(\frac{3\times 4+3}{4}-\frac{2\times 2+1}{2}\right)$$

Multiply 3 and 4 to get 12.

$$\frac{15}{14}-\left(\frac{12+3}{4}-\frac{2\times 2+1}{2}\right)$$

Add 12 and 3 to get 15.

$$\frac{15}{14}-\left(\frac{15}{4}-\frac{2\times 2+1}{2}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{15}{14}-\left(\frac{15}{4}-\frac{4+1}{2}\right)$$

Add 4 and 1 to get 5.

$$\frac{15}{14}-\left(\frac{15}{4}-\frac{5}{2}\right)$$

Least common multiple of 4 and 2 is 4. Convert \frac{15}{4} and \frac{5}{2} to fractions with denominator 4.

$$\frac{15}{14}-\left(\frac{15}{4}-\frac{10}{4}\right)$$

Since \frac{15}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15}{14}-\frac{15-10}{4}$$

Subtract 10 from 15 to get 5.

$$\frac{15}{14}-\frac{5}{4}$$

Least common multiple of 14 and 4 is 28. Convert \frac{15}{14} and \frac{5}{4} to fractions with denominator 28.

$$\frac{30}{28}-\frac{35}{28}$$

Since \frac{30}{28} and \frac{35}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-35}{28}$$

Subtract 35 from 30 to get -5.

$$-\frac{5}{28}$$

Factor

$$-\frac{5}{28} = -0.17857142857142858$$