Solve (-24)*(3/8-5/12+1/4)-(-0.25+9/4)

$$( - 24 ) \times ( \frac { 3 } { 8 } - \frac { 5 } { 12 } + \frac { 1 } { 4 } ) - ( - 0.25 + \frac { 9 } { 4 } )$$

Evaluate

$$-7$$

Solution Steps

Least common multiple of 8 and 12 is 24. Convert \frac{3}{8} and \frac{5}{12} to fractions with denominator 24.

$$-24\left(\frac{9}{24}-\frac{10}{24}+\frac{1}{4}\right)-\left(-0.25+\frac{9}{4}\right)$$

Since \frac{9}{24} and \frac{10}{24} have the same denominator, subtract them by subtracting their numerators.

$$-24\left(\frac{9-10}{24}+\frac{1}{4}\right)-\left(-0.25+\frac{9}{4}\right)$$

Subtract 10 from 9 to get -1.

$$-24\left(-\frac{1}{24}+\frac{1}{4}\right)-\left(-0.25+\frac{9}{4}\right)$$

Least common multiple of 24 and 4 is 24. Convert -\frac{1}{24} and \frac{1}{4} to fractions with denominator 24.

$$-24\left(-\frac{1}{24}+\frac{6}{24}\right)-\left(-0.25+\frac{9}{4}\right)$$

Since -\frac{1}{24} and \frac{6}{24} have the same denominator, add them by adding their numerators.

$$-24\times \frac{-1+6}{24}-\left(-0.25+\frac{9}{4}\right)$$

Add -1 and 6 to get 5.

$$-24\times \frac{5}{24}-\left(-0.25+\frac{9}{4}\right)$$

Multiply -24 times \frac{5}{24}.

$$-5-\left(-0.25+\frac{9}{4}\right)$$

Convert decimal number -0.25 to fraction -\frac{25}{100}. Reduce the fraction -\frac{25}{100} to lowest terms by extracting and canceling out 25.

$$-5-\left(-\frac{1}{4}+\frac{9}{4}\right)$$

Since -\frac{1}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$-5-\frac{-1+9}{4}$$

Add -1 and 9 to get 8.

$$-5-\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$-5-2$$

Subtract 2 from -5 to get -7.

$$-7$$

Factor

$$-7$$