Solve (-15/24)+[(-23/7)+(21/14)]

$$( - \frac { 15 } { 24 } ) + [ ( - 2 \frac { 3 } { 7 } ) + ( 2 \frac { 1 } { 14 } ) ]$$

Evaluate

$$-\frac{55}{56}\approx -0.982142857$$

Solution Steps

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$-\frac{5}{8}-\frac{2\times 7+3}{7}+\frac{2\times 14+1}{14}$$

Multiply 2 and 7 to get 14.

$$-\frac{5}{8}-\frac{14+3}{7}+\frac{2\times 14+1}{14}$$

Add 14 and 3 to get 17.

$$-\frac{5}{8}-\frac{17}{7}+\frac{2\times 14+1}{14}$$

Least common multiple of 8 and 7 is 56. Convert -\frac{5}{8} and \frac{17}{7} to fractions with denominator 56.

$$-\frac{35}{56}-\frac{136}{56}+\frac{2\times 14+1}{14}$$

Since -\frac{35}{56} and \frac{136}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-35-136}{56}+\frac{2\times 14+1}{14}$$

Subtract 136 from -35 to get -171.

$$-\frac{171}{56}+\frac{2\times 14+1}{14}$$

Multiply 2 and 14 to get 28.

$$-\frac{171}{56}+\frac{28+1}{14}$$

Add 28 and 1 to get 29.

$$-\frac{171}{56}+\frac{29}{14}$$

Least common multiple of 56 and 14 is 56. Convert -\frac{171}{56} and \frac{29}{14} to fractions with denominator 56.

$$-\frac{171}{56}+\frac{116}{56}$$

Since -\frac{171}{56} and \frac{116}{56} have the same denominator, add them by adding their numerators.

$$\frac{-171+116}{56}$$

Add -171 and 116 to get -55.

$$-\frac{55}{56}$$

Factor

$$-\frac{55}{56} = -0.9821428571428571$$