Solve (-83/7)+(-7.5)+(-214/7)+(+31/2)

$$( - 8 \frac { 3 } { 7 } ) + ( - 7.5 ) + ( - 21 \frac { 4 } { 7 } ) + ( + 3 \frac { 1 } { 2 } )$$

Evaluate

$$-34$$

Solution Steps

Multiply 8 and 7 to get 56.

$$-\frac{56+3}{7}-7.5-\frac{21\times 7+4}{7}+\frac{3\times 2+1}{2}$$

Add 56 and 3 to get 59.

$$-\frac{59}{7}-7.5-\frac{21\times 7+4}{7}+\frac{3\times 2+1}{2}$$

Convert decimal number 7.5 to fraction \frac{75}{10}. Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{59}{7}-\frac{15}{2}-\frac{21\times 7+4}{7}+\frac{3\times 2+1}{2}$$

Least common multiple of 7 and 2 is 14. Convert -\frac{59}{7} and \frac{15}{2} to fractions with denominator 14.

$$-\frac{118}{14}-\frac{105}{14}-\frac{21\times 7+4}{7}+\frac{3\times 2+1}{2}$$

Since -\frac{118}{14} and \frac{105}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-118-105}{14}-\frac{21\times 7+4}{7}+\frac{3\times 2+1}{2}$$

Subtract 105 from -118 to get -223.

$$-\frac{223}{14}-\frac{21\times 7+4}{7}+\frac{3\times 2+1}{2}$$

Multiply 21 and 7 to get 147.

$$-\frac{223}{14}-\frac{147+4}{7}+\frac{3\times 2+1}{2}$$

Add 147 and 4 to get 151.

$$-\frac{223}{14}-\frac{151}{7}+\frac{3\times 2+1}{2}$$

Least common multiple of 14 and 7 is 14. Convert -\frac{223}{14} and \frac{151}{7} to fractions with denominator 14.

$$-\frac{223}{14}-\frac{302}{14}+\frac{3\times 2+1}{2}$$

Since -\frac{223}{14} and \frac{302}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-223-302}{14}+\frac{3\times 2+1}{2}$$

Subtract 302 from -223 to get -525.

$$\frac{-525}{14}+\frac{3\times 2+1}{2}$$

Reduce the fraction \frac{-525}{14} to lowest terms by extracting and canceling out 7.

$$-\frac{75}{2}+\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$-\frac{75}{2}+\frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$-\frac{75}{2}+\frac{7}{2}$$

Since -\frac{75}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$\frac{-75+7}{2}$$

Add -75 and 7 to get -68.

$$\frac{-68}{2}$$

Divide -68 by 2 to get -34.

$$-34$$

Factor

$$-34$$