Solve -35/11+13/8+25/16+(-46/11)

$$- 3 \frac { 5 } { 11 } + 1 \frac { 3 } { 8 } + 2 \frac { 5 } { 16 } + ( - 4 \frac { 6 } { 11 } )$$

Evaluate

$$-\frac{69}{16}=-4.3125$$

Solution Steps

Multiply 3 and 11 to get 33.

$$-\frac{33+5}{11}+\frac{1\times 8+3}{8}+\frac{2\times 16+5}{16}-\frac{4\times 11+6}{11}$$

Add 33 and 5 to get 38.

$$-\frac{38}{11}+\frac{1\times 8+3}{8}+\frac{2\times 16+5}{16}-\frac{4\times 11+6}{11}$$

Multiply 1 and 8 to get 8.

$$-\frac{38}{11}+\frac{8+3}{8}+\frac{2\times 16+5}{16}-\frac{4\times 11+6}{11}$$

Add 8 and 3 to get 11.

$$-\frac{38}{11}+\frac{11}{8}+\frac{2\times 16+5}{16}-\frac{4\times 11+6}{11}$$

Least common multiple of 11 and 8 is 88. Convert -\frac{38}{11} and \frac{11}{8} to fractions with denominator 88.

$$-\frac{304}{88}+\frac{121}{88}+\frac{2\times 16+5}{16}-\frac{4\times 11+6}{11}$$

Since -\frac{304}{88} and \frac{121}{88} have the same denominator, add them by adding their numerators.

$$\frac{-304+121}{88}+\frac{2\times 16+5}{16}-\frac{4\times 11+6}{11}$$

Add -304 and 121 to get -183.

$$-\frac{183}{88}+\frac{2\times 16+5}{16}-\frac{4\times 11+6}{11}$$

Multiply 2 and 16 to get 32.

$$-\frac{183}{88}+\frac{32+5}{16}-\frac{4\times 11+6}{11}$$

Add 32 and 5 to get 37.

$$-\frac{183}{88}+\frac{37}{16}-\frac{4\times 11+6}{11}$$

Least common multiple of 88 and 16 is 176. Convert -\frac{183}{88} and \frac{37}{16} to fractions with denominator 176.

$$-\frac{366}{176}+\frac{407}{176}-\frac{4\times 11+6}{11}$$

Since -\frac{366}{176} and \frac{407}{176} have the same denominator, add them by adding their numerators.

$$\frac{-366+407}{176}-\frac{4\times 11+6}{11}$$

Add -366 and 407 to get 41.

$$\frac{41}{176}-\frac{4\times 11+6}{11}$$

Multiply 4 and 11 to get 44.

$$\frac{41}{176}-\frac{44+6}{11}$$

Add 44 and 6 to get 50.

$$\frac{41}{176}-\frac{50}{11}$$

Least common multiple of 176 and 11 is 176. Convert \frac{41}{176} and \frac{50}{11} to fractions with denominator 176.

$$\frac{41}{176}-\frac{800}{176}$$

Since \frac{41}{176} and \frac{800}{176} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41-800}{176}$$

Subtract 800 from 41 to get -759.

$$\frac{-759}{176}$$

Reduce the fraction \frac{-759}{176} to lowest terms by extracting and canceling out 11.

$$-\frac{69}{16}$$

Factor

$$-\frac{69}{16} = -4\frac{5}{16} = -4.3125$$