Solve 6(-4/3m+3/2n)-15(2/3n-3/5m)

$$6 ( - \frac { 4 } { 3 } m + \frac { 3 } { 2 } n ) - 15 ( \frac { 2 } { 3 } n - \frac { 3 } { 5 } m )$$

Evaluate

$$m-n$$

Solution Steps

Use the distributive property to multiply 6 by -\frac{4}{3}m+\frac{3}{2}n.

$$6\left(-\frac{4}{3}\right)m+6\times \frac{3}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Express 6\left(-\frac{4}{3}\right) as a single fraction.

$$\frac{6\left(-4\right)}{3}m+6\times \frac{3}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Multiply 6 and -4 to get -24.

$$\frac{-24}{3}m+6\times \frac{3}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Divide -24 by 3 to get -8.

$$-8m+6\times \frac{3}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Express 6\times \frac{3}{2} as a single fraction.

$$-8m+\frac{6\times 3}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Multiply 6 and 3 to get 18.

$$-8m+\frac{18}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Divide 18 by 2 to get 9.

$$-8m+9n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Use the distributive property to multiply -15 by \frac{2}{3}n-\frac{3}{5}m.

$$-8m+9n-15\times \frac{2}{3}n-15\left(-\frac{3}{5}\right)m$$

Express -15\times \frac{2}{3} as a single fraction.

$$-8m+9n+\frac{-15\times 2}{3}n-15\left(-\frac{3}{5}\right)m$$

Multiply -15 and 2 to get -30.

$$-8m+9n+\frac{-30}{3}n-15\left(-\frac{3}{5}\right)m$$

Divide -30 by 3 to get -10.

$$-8m+9n-10n-15\left(-\frac{3}{5}\right)m$$

Express -15\left(-\frac{3}{5}\right) as a single fraction.

$$-8m+9n-10n+\frac{-15\left(-3\right)}{5}m$$

Multiply -15 and -3 to get 45.

$$-8m+9n-10n+\frac{45}{5}m$$

Divide 45 by 5 to get 9.

$$-8m+9n-10n+9m$$

Combine 9n and -10n to get -n.

$$-8m-n+9m$$

Combine -8m and 9m to get m.

$$m-n$$

Expand

$$m-n$$

Solution Steps

Use the distributive property to multiply 6 by -\frac{4}{3}m+\frac{3}{2}n.

$$6\left(-\frac{4}{3}\right)m+6\times \frac{3}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Express 6\left(-\frac{4}{3}\right) as a single fraction.

$$\frac{6\left(-4\right)}{3}m+6\times \frac{3}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Multiply 6 and -4 to get -24.

$$\frac{-24}{3}m+6\times \frac{3}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Divide -24 by 3 to get -8.

$$-8m+6\times \frac{3}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Express 6\times \frac{3}{2} as a single fraction.

$$-8m+\frac{6\times 3}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Multiply 6 and 3 to get 18.

$$-8m+\frac{18}{2}n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Divide 18 by 2 to get 9.

$$-8m+9n-15\left(\frac{2}{3}n-\frac{3}{5}m\right)$$

Use the distributive property to multiply -15 by \frac{2}{3}n-\frac{3}{5}m.

$$-8m+9n-15\times \frac{2}{3}n-15\left(-\frac{3}{5}\right)m$$

Express -15\times \frac{2}{3} as a single fraction.

$$-8m+9n+\frac{-15\times 2}{3}n-15\left(-\frac{3}{5}\right)m$$

Multiply -15 and 2 to get -30.

$$-8m+9n+\frac{-30}{3}n-15\left(-\frac{3}{5}\right)m$$

Divide -30 by 3 to get -10.

$$-8m+9n-10n-15\left(-\frac{3}{5}\right)m$$

Express -15\left(-\frac{3}{5}\right) as a single fraction.

$$-8m+9n-10n+\frac{-15\left(-3\right)}{5}m$$

Multiply -15 and -3 to get 45.

$$-8m+9n-10n+\frac{45}{5}m$$

Divide 45 by 5 to get 9.

$$-8m+9n-10n+9m$$

Combine 9n and -10n to get -n.

$$-8m-n+9m$$

Combine -8m and 9m to get m.

$$m-n$$