Solve (3/4m+1)(2/3m-1/2)=

$$( \frac { 3 } { 4 } m + 1 ) ( \frac { 2 } { 3 } m - \frac { 1 } { 2 } ) =$$

Evaluate

$$\frac{m^{2}}{2}+\frac{7m}{24}-\frac{1}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{3}{4}m+1 by each term of \frac{2}{3}m-\frac{1}{2}.

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

Multiply m and m to get m^{2}.

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

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

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

Cancel out 3 in both numerator and denominator.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

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

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

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

$$\frac{1}{2}m^{2}+\frac{-3}{8}m+\frac{2}{3}m-\frac{1}{2}$$

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

$$\frac{1}{2}m^{2}-\frac{3}{8}m+\frac{2}{3}m-\frac{1}{2}$$

Combine -\frac{3}{8}m and \frac{2}{3}m to get \frac{7}{24}m.

$$\frac{1}{2}m^{2}+\frac{7}{24}m-\frac{1}{2}$$

Expand

$$\frac{m^{2}}{2}+\frac{7m}{24}-\frac{1}{2}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{3}{4}m+1 by each term of \frac{2}{3}m-\frac{1}{2}.

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

Multiply m and m to get m^{2}.

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

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

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

Cancel out 3 in both numerator and denominator.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

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

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

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

$$\frac{1}{2}m^{2}+\frac{-3}{8}m+\frac{2}{3}m-\frac{1}{2}$$

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

$$\frac{1}{2}m^{2}-\frac{3}{8}m+\frac{2}{3}m-\frac{1}{2}$$

Combine -\frac{3}{8}m and \frac{2}{3}m to get \frac{7}{24}m.

$$\frac{1}{2}m^{2}+\frac{7}{24}m-\frac{1}{2}$$