Solve 9/4(1/2-4/1)-3/4(frac{1}{2}-frac{3}{8})=

$$\frac { 9 } { 4 } ( \frac { 1 } { 2 } - \frac { 4 } { 1 } ) - \frac { 3 } { 4 } ( \frac { 1 } { 2 } - \frac { 3 } { 8 } ) =$$

Evaluate

$$-\frac{255}{32}=-7.96875$$

Solution Steps

Anything divided by one gives itself.

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

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

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

Since \frac{1}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 8 from 1 to get -7.

$$\frac{9}{4}\left(-\frac{7}{2}\right)-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)$$

Multiply \frac{9}{4} times -\frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\left(-7\right)}{4\times 2}-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)$$

Do the multiplications in the fraction \frac{9\left(-7\right)}{4\times 2}.

$$\frac{-63}{8}-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)$$

Fraction \frac{-63}{8} can be rewritten as -\frac{63}{8} by extracting the negative sign.

$$-\frac{63}{8}-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{3}{8} to fractions with denominator 8.

$$-\frac{63}{8}-\frac{3}{4}\left(\frac{4}{8}-\frac{3}{8}\right)$$

Since \frac{4}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{63}{8}-\frac{3}{4}\times \frac{4-3}{8}$$

Subtract 3 from 4 to get 1.

$$-\frac{63}{8}-\frac{3}{4}\times \frac{1}{8}$$

Multiply \frac{3}{4} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{63}{8}-\frac{3\times 1}{4\times 8}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 8}.

$$-\frac{63}{8}-\frac{3}{32}$$

Least common multiple of 8 and 32 is 32. Convert -\frac{63}{8} and \frac{3}{32} to fractions with denominator 32.

$$-\frac{252}{32}-\frac{3}{32}$$

Since -\frac{252}{32} and \frac{3}{32} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-252-3}{32}$$

Subtract 3 from -252 to get -255.

$$-\frac{255}{32}$$

Factor

$$-\frac{255}{32} = -7\frac{31}{32} = -7.96875$$