Solve 1/2(a-2b)-1/3(3a-b)=

$$\frac { 1 } { 2 } ( a - 2 b ) - \frac { 1 } { 3 } ( 3 a - b ) =$$

Evaluate

$$-\frac{a}{2}-\frac{2b}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by a-2b.

$$\frac{1}{2}a+\frac{1}{2}\left(-2\right)b-\frac{1}{3}\left(3a-b\right)$$

Multiply \frac{1}{2} and -2 to get \frac{-2}{2}.

$$\frac{1}{2}a+\frac{-2}{2}b-\frac{1}{3}\left(3a-b\right)$$

Divide -2 by 2 to get -1.

$$\frac{1}{2}a-b-\frac{1}{3}\left(3a-b\right)$$

Use the distributive property to multiply -\frac{1}{3} by 3a-b.

$$\frac{1}{2}a-b-\frac{1}{3}\times 3a-\frac{1}{3}\left(-1\right)b$$

Cancel out 3 and 3.

$$\frac{1}{2}a-b-a-\frac{1}{3}\left(-1\right)b$$

Multiply -\frac{1}{3} and -1 to get \frac{1}{3}.

$$\frac{1}{2}a-b-a+\frac{1}{3}b$$

Combine \frac{1}{2}a and -a to get -\frac{1}{2}a.

$$-\frac{1}{2}a-b+\frac{1}{3}b$$

Combine -b and \frac{1}{3}b to get -\frac{2}{3}b.

$$-\frac{1}{2}a-\frac{2}{3}b$$

Expand

$$-\frac{a}{2}-\frac{2b}{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by a-2b.

$$\frac{1}{2}a+\frac{1}{2}\left(-2\right)b-\frac{1}{3}\left(3a-b\right)$$

Multiply \frac{1}{2} and -2 to get \frac{-2}{2}.

$$\frac{1}{2}a+\frac{-2}{2}b-\frac{1}{3}\left(3a-b\right)$$

Divide -2 by 2 to get -1.

$$\frac{1}{2}a-b-\frac{1}{3}\left(3a-b\right)$$

Use the distributive property to multiply -\frac{1}{3} by 3a-b.

$$\frac{1}{2}a-b-\frac{1}{3}\times 3a-\frac{1}{3}\left(-1\right)b$$

Cancel out 3 and 3.

$$\frac{1}{2}a-b-a-\frac{1}{3}\left(-1\right)b$$

Multiply -\frac{1}{3} and -1 to get \frac{1}{3}.

$$\frac{1}{2}a-b-a+\frac{1}{3}b$$

Combine \frac{1}{2}a and -a to get -\frac{1}{2}a.

$$-\frac{1}{2}a-b+\frac{1}{3}b$$

Combine -b and \frac{1}{3}b to get -\frac{2}{3}b.

$$-\frac{1}{2}a-\frac{2}{3}b$$