Solve (+13/4)+(-5/6)+(-11/4)+(31/3)

$$( + 1 \frac { 3 } { 4 } ) + ( - \frac { 5 } { 6 } ) + ( - 1 \frac { 1 } { 4 } ) + ( 3 \frac { 1 } { 3 } )$$

Evaluate

$$3$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{4+3}{4}-\frac{5}{6}-\frac{1\times 4+1}{4}+\frac{3\times 3+1}{3}$$

Add 4 and 3 to get 7.

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

Least common multiple of 4 and 6 is 12. Convert \frac{7}{4} and \frac{5}{6} to fractions with denominator 12.

$$\frac{21}{12}-\frac{10}{12}-\frac{1\times 4+1}{4}+\frac{3\times 3+1}{3}$$

Since \frac{21}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-10}{12}-\frac{1\times 4+1}{4}+\frac{3\times 3+1}{3}$$

Subtract 10 from 21 to get 11.

$$\frac{11}{12}-\frac{1\times 4+1}{4}+\frac{3\times 3+1}{3}$$

Multiply 1 and 4 to get 4.

$$\frac{11}{12}-\frac{4+1}{4}+\frac{3\times 3+1}{3}$$

Add 4 and 1 to get 5.

$$\frac{11}{12}-\frac{5}{4}+\frac{3\times 3+1}{3}$$

Least common multiple of 12 and 4 is 12. Convert \frac{11}{12} and \frac{5}{4} to fractions with denominator 12.

$$\frac{11}{12}-\frac{15}{12}+\frac{3\times 3+1}{3}$$

Since \frac{11}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-15}{12}+\frac{3\times 3+1}{3}$$

Subtract 15 from 11 to get -4.

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

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{3}+\frac{3\times 3+1}{3}$$

Multiply 3 and 3 to get 9.

$$-\frac{1}{3}+\frac{9+1}{3}$$

Add 9 and 1 to get 10.

$$-\frac{1}{3}+\frac{10}{3}$$

Since -\frac{1}{3} and \frac{10}{3} have the same denominator, add them by adding their numerators.

$$\frac{-1+10}{3}$$

Add -1 and 10 to get 9.

$$\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$3$$

Factor

$$3$$