Pre-Algebra Examples

$\frac{2}{3} \cdot (6 a + 3 b) - \frac{1}{2} \cdot (a - 2 b)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$\frac{2}{3} (6 a) + \frac{2}{3} (3 b) - \frac{1}{2} \cdot (a - 2 b)$

Step 1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.1

Factor $3$ out of $6 a$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 1.3

Multiply $2$ by $2$ .

$4 a + \frac{2}{3} (3 b) - \frac{1}{2} \cdot (a - 2 b)$

Step 1.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.4.1

Factor $3$ out of $3 b$ .

$4 a + \frac{2}{3} (3 (b)) - \frac{1}{2} \cdot (a - 2 b)$

Step 1.4.2

Cancel the common factor.

$4 a + \frac{2}{3} (3 b) - \frac{1}{2} \cdot (a - 2 b)$

Step 1.4.3

Rewrite the expression.

$4 a + 2 b - \frac{1}{2} \cdot (a - 2 b)$

Step 1.5

Apply the distributive property.

$4 a + 2 b - \frac{1}{2} a - \frac{1}{2} (- 2 b)$

Step 1.6

Combine $a$ and $\frac{1}{2}$ .

$4 a + 2 b - \frac{a}{2} - \frac{1}{2} (- 2 b)$

Step 1.7

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.7.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$4 a + 2 b - \frac{a}{2} + \frac{- 1}{2} (- 2 b)$

Step 1.7.2

Factor $2$ out of $- 2 b$ .

$4 a + 2 b - \frac{a}{2} + \frac{- 1}{2} (2 (- b))$

Step 1.7.3

Cancel the common factor.

$4 a + 2 b - \frac{a}{2} + \frac{- 1}{2} (2 (- b))$

Step 1.7.4

Rewrite the expression.

$4 a + 2 b - \frac{a}{2} - 1 (- b)$

Step 1.8

Multiply $- 1$ by $- 1$ .

$4 a + 2 b - \frac{a}{2} + 1 b$

Step 1.9

Multiply $b$ by $1$ .

$4 a + 2 b - \frac{a}{2} + b$

Step 2

To write $4 a$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 b + 4 a \cdot \frac{2}{2} - \frac{a}{2} + b$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine $4 a$ and $\frac{2}{2}$ .

$2 b + \frac{4 a \cdot 2}{2} - \frac{a}{2} + b$

Step 3.2

Combine the numerators over the common denominator.

$2 b + \frac{4 a \cdot 2 - a}{2} + b$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Factor $a$ out of $4 a \cdot 2 - a$ .

Tap for more steps...

Step 4.1.1.1

Factor $a$ out of $4 a \cdot 2$ .

$2 b + \frac{a (4 \cdot 2) - a}{2} + b$

Step 4.1.1.2

Factor $a$ out of $- a$ .

$2 b + \frac{a (4 \cdot 2) + a \cdot - 1}{2} + b$

Step 4.1.1.3

Factor $a$ out of $a (4 \cdot 2) + a \cdot - 1$ .

$2 b + \frac{a (4 \cdot 2 - 1)}{2} + b$

Step 4.1.2

Multiply $4$ by $2$ .

$2 b + \frac{a (8 - 1)}{2} + b$

Step 4.1.3

Subtract $1$ from $8$ .

$2 b + \frac{a \cdot 7}{2} + b$

Step 4.2

Move $7$ to the left of $a$ .

$2 b + \frac{7 a}{2} + b$

Step 5

Add $2 b$ and $b$ .

$3 b + \frac{7 a}{2}$