Solve 1(2-9/4)-2(4-9/4)+3/2(2-9/4)

$$1 ( 2 - 9 / 4 ) - 2 ( 4 - 9 / 4 ) + 3 / 2 ( 2 - 9 / 4 )$$

Evaluate

$$-\frac{33}{8}=-4.125$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$1\left(\frac{8}{4}-\frac{9}{4}\right)-2\left(4-\frac{9}{4}\right)+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Since \frac{8}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$1\times \frac{8-9}{4}-2\left(4-\frac{9}{4}\right)+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Subtract 9 from 8 to get -1.

$$1\left(-\frac{1}{4}\right)-2\left(4-\frac{9}{4}\right)+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Multiply 1 and -\frac{1}{4} to get -\frac{1}{4}.

$$-\frac{1}{4}-2\left(4-\frac{9}{4}\right)+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Convert 4 to fraction \frac{16}{4}.

$$-\frac{1}{4}-2\left(\frac{16}{4}-\frac{9}{4}\right)+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Since \frac{16}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{4}-2\times \frac{16-9}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Subtract 9 from 16 to get 7.

$$-\frac{1}{4}-2\times \frac{7}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Express 2\times \frac{7}{4} as a single fraction.

$$-\frac{1}{4}-\frac{2\times 7}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Multiply 2 and 7 to get 14.

$$-\frac{1}{4}-\frac{14}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Since -\frac{1}{4} and \frac{14}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-14}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Subtract 14 from -1 to get -15.

$$-\frac{15}{4}+\frac{3}{2}\left(2-\frac{9}{4}\right)$$

Convert 2 to fraction \frac{8}{4}.

$$-\frac{15}{4}+\frac{3}{2}\left(\frac{8}{4}-\frac{9}{4}\right)$$

Since \frac{8}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{15}{4}+\frac{3}{2}\times \frac{8-9}{4}$$

Subtract 9 from 8 to get -1.

$$-\frac{15}{4}+\frac{3}{2}\left(-\frac{1}{4}\right)$$

Multiply \frac{3}{2} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{15}{4}+\frac{3\left(-1\right)}{2\times 4}$$

Do the multiplications in the fraction \frac{3\left(-1\right)}{2\times 4}.

$$-\frac{15}{4}+\frac{-3}{8}$$

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$-\frac{15}{4}-\frac{3}{8}$$

Least common multiple of 4 and 8 is 8. Convert -\frac{15}{4} and \frac{3}{8} to fractions with denominator 8.

$$-\frac{30}{8}-\frac{3}{8}$$

Since -\frac{30}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-30-3}{8}$$

Subtract 3 from -30 to get -33.

$$-\frac{33}{8}$$

Factor

$$-\frac{33}{8} = -4\frac{1}{8} = -4.125$$