Solve 31/2-64/6+113/4-21/3

$$3 \frac { 1 } { 2 } - 6 \frac { 4 } { 6 } + 11 \frac { 3 } { 4 } - 2 \frac { 1 } { 3 }$$

Evaluate

$$\frac{25}{4}=6.25$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{6+1}{2}-\frac{6\times 6+4}{6}+\frac{11\times 4+3}{4}-\frac{2\times 3+1}{3}$$

Add 6 and 1 to get 7.

$$\frac{7}{2}-\frac{6\times 6+4}{6}+\frac{11\times 4+3}{4}-\frac{2\times 3+1}{3}$$

Multiply 6 and 6 to get 36.

$$\frac{7}{2}-\frac{36+4}{6}+\frac{11\times 4+3}{4}-\frac{2\times 3+1}{3}$$

Add 36 and 4 to get 40.

$$\frac{7}{2}-\frac{40}{6}+\frac{11\times 4+3}{4}-\frac{2\times 3+1}{3}$$

Reduce the fraction \frac{40}{6} to lowest terms by extracting and canceling out 2.

$$\frac{7}{2}-\frac{20}{3}+\frac{11\times 4+3}{4}-\frac{2\times 3+1}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{7}{2} and \frac{20}{3} to fractions with denominator 6.

$$\frac{21}{6}-\frac{40}{6}+\frac{11\times 4+3}{4}-\frac{2\times 3+1}{3}$$

Since \frac{21}{6} and \frac{40}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-40}{6}+\frac{11\times 4+3}{4}-\frac{2\times 3+1}{3}$$

Subtract 40 from 21 to get -19.

$$-\frac{19}{6}+\frac{11\times 4+3}{4}-\frac{2\times 3+1}{3}$$

Multiply 11 and 4 to get 44.

$$-\frac{19}{6}+\frac{44+3}{4}-\frac{2\times 3+1}{3}$$

Add 44 and 3 to get 47.

$$-\frac{19}{6}+\frac{47}{4}-\frac{2\times 3+1}{3}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{19}{6} and \frac{47}{4} to fractions with denominator 12.

$$-\frac{38}{12}+\frac{141}{12}-\frac{2\times 3+1}{3}$$

Since -\frac{38}{12} and \frac{141}{12} have the same denominator, add them by adding their numerators.

$$\frac{-38+141}{12}-\frac{2\times 3+1}{3}$$

Add -38 and 141 to get 103.

$$\frac{103}{12}-\frac{2\times 3+1}{3}$$

Multiply 2 and 3 to get 6.

$$\frac{103}{12}-\frac{6+1}{3}$$

Add 6 and 1 to get 7.

$$\frac{103}{12}-\frac{7}{3}$$

Least common multiple of 12 and 3 is 12. Convert \frac{103}{12} and \frac{7}{3} to fractions with denominator 12.

$$\frac{103}{12}-\frac{28}{12}$$

Since \frac{103}{12} and \frac{28}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{103-28}{12}$$

Subtract 28 from 103 to get 75.

$$\frac{75}{12}$$

Reduce the fraction \frac{75}{12} to lowest terms by extracting and canceling out 3.

$$\frac{25}{4}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {2}} = 6\frac{1}{4} = 6.25$$