Solve 12/3+(-56/13)+(-31/4)+(-27/13)+21frac{1}{3}+7frac{3}{4}

$$1 \frac{ 2 }{ 3 } +(-5 \frac{ 6 }{ 13 } )+(-3 \frac{ 1 }{ 4 } )+(-2 \frac{ 7 }{ 13 } )+21 \frac{ 1 }{ 3 } +7 \frac{ 3 }{ 4 }$$

Evaluate

$$\frac{39}{2}=19.5$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{3+2}{3}-\frac{5\times 13+6}{13}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Add 3 and 2 to get 5.

$$\frac{5}{3}-\frac{5\times 13+6}{13}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Multiply 5 and 13 to get 65.

$$\frac{5}{3}-\frac{65+6}{13}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Add 65 and 6 to get 71.

$$\frac{5}{3}-\frac{71}{13}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Least common multiple of 3 and 13 is 39. Convert \frac{5}{3} and \frac{71}{13} to fractions with denominator 39.

$$\frac{65}{39}-\frac{213}{39}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Since \frac{65}{39} and \frac{213}{39} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-213}{39}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Subtract 213 from 65 to get -148.

$$-\frac{148}{39}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Multiply 3 and 4 to get 12.

$$-\frac{148}{39}-\frac{12+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Add 12 and 1 to get 13.

$$-\frac{148}{39}-\frac{13}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Least common multiple of 39 and 4 is 156. Convert -\frac{148}{39} and \frac{13}{4} to fractions with denominator 156.

$$-\frac{592}{156}-\frac{507}{156}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Since -\frac{592}{156} and \frac{507}{156} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-592-507}{156}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Subtract 507 from -592 to get -1099.

$$-\frac{1099}{156}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Multiply 2 and 13 to get 26.

$$-\frac{1099}{156}-\frac{26+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Add 26 and 7 to get 33.

$$-\frac{1099}{156}-\frac{33}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Least common multiple of 156 and 13 is 156. Convert -\frac{1099}{156} and \frac{33}{13} to fractions with denominator 156.

$$-\frac{1099}{156}-\frac{396}{156}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Since -\frac{1099}{156} and \frac{396}{156} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1099-396}{156}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Subtract 396 from -1099 to get -1495.

$$\frac{-1495}{156}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Reduce the fraction \frac{-1495}{156} to lowest terms by extracting and canceling out 13.

$$-\frac{115}{12}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Multiply 21 and 3 to get 63.

$$-\frac{115}{12}+\frac{63+1}{3}+\frac{7\times 4+3}{4}$$

Add 63 and 1 to get 64.

$$-\frac{115}{12}+\frac{64}{3}+\frac{7\times 4+3}{4}$$

Least common multiple of 12 and 3 is 12. Convert -\frac{115}{12} and \frac{64}{3} to fractions with denominator 12.

$$-\frac{115}{12}+\frac{256}{12}+\frac{7\times 4+3}{4}$$

Since -\frac{115}{12} and \frac{256}{12} have the same denominator, add them by adding their numerators.

$$\frac{-115+256}{12}+\frac{7\times 4+3}{4}$$

Add -115 and 256 to get 141.

$$\frac{141}{12}+\frac{7\times 4+3}{4}$$

Reduce the fraction \frac{141}{12} to lowest terms by extracting and canceling out 3.

$$\frac{47}{4}+\frac{7\times 4+3}{4}$$

Multiply 7 and 4 to get 28.

$$\frac{47}{4}+\frac{28+3}{4}$$

Add 28 and 3 to get 31.

$$\frac{47}{4}+\frac{31}{4}$$

Since \frac{47}{4} and \frac{31}{4} have the same denominator, add them by adding their numerators.

$$\frac{47+31}{4}$$

Add 47 and 31 to get 78.

$$\frac{78}{4}$$

Reduce the fraction \frac{78}{4} to lowest terms by extracting and canceling out 2.

$$\frac{39}{2}$$

Factor

$$\frac{3 \cdot 13}{2} = 19\frac{1}{2} = 19.5$$