Solve 21/2-13/7-31/4-21/2

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

Evaluate

$$-\frac{131}{28}\approx -4.678571429$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{4+1}{2}-\frac{1\times 7+3}{7}-\frac{3\times 4+1}{4}-\frac{2\times 2+1}{2}$$

Add 4 and 1 to get 5.

$$\frac{5}{2}-\frac{1\times 7+3}{7}-\frac{3\times 4+1}{4}-\frac{2\times 2+1}{2}$$

Multiply 1 and 7 to get 7.

$$\frac{5}{2}-\frac{7+3}{7}-\frac{3\times 4+1}{4}-\frac{2\times 2+1}{2}$$

Add 7 and 3 to get 10.

$$\frac{5}{2}-\frac{10}{7}-\frac{3\times 4+1}{4}-\frac{2\times 2+1}{2}$$

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

$$\frac{35}{14}-\frac{20}{14}-\frac{3\times 4+1}{4}-\frac{2\times 2+1}{2}$$

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

$$\frac{35-20}{14}-\frac{3\times 4+1}{4}-\frac{2\times 2+1}{2}$$

Subtract 20 from 35 to get 15.

$$\frac{15}{14}-\frac{3\times 4+1}{4}-\frac{2\times 2+1}{2}$$

Multiply 3 and 4 to get 12.

$$\frac{15}{14}-\frac{12+1}{4}-\frac{2\times 2+1}{2}$$

Add 12 and 1 to get 13.

$$\frac{15}{14}-\frac{13}{4}-\frac{2\times 2+1}{2}$$

Least common multiple of 14 and 4 is 28. Convert \frac{15}{14} and \frac{13}{4} to fractions with denominator 28.

$$\frac{30}{28}-\frac{91}{28}-\frac{2\times 2+1}{2}$$

Since \frac{30}{28} and \frac{91}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-91}{28}-\frac{2\times 2+1}{2}$$

Subtract 91 from 30 to get -61.

$$-\frac{61}{28}-\frac{2\times 2+1}{2}$$

Multiply 2 and 2 to get 4.

$$-\frac{61}{28}-\frac{4+1}{2}$$

Add 4 and 1 to get 5.

$$-\frac{61}{28}-\frac{5}{2}$$

Least common multiple of 28 and 2 is 28. Convert -\frac{61}{28} and \frac{5}{2} to fractions with denominator 28.

$$-\frac{61}{28}-\frac{70}{28}$$

Since -\frac{61}{28} and \frac{70}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-61-70}{28}$$

Subtract 70 from -61 to get -131.

$$-\frac{131}{28}$$

Factor

$$-\frac{131}{28} = -4\frac{19}{28} = -4.678571428571429$$