Algebra Examples

$\frac{2}{3} a - (- \frac{1}{5} b - (2 a - \frac{3}{5} b) + \frac{2}{3} a) - \frac{1}{2} b$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $\frac{2}{3}$ and $a$ .

$\frac{2 a}{3} - (- \frac{1}{5} b - (2 a - \frac{3}{5} b) + \frac{2}{3} a) - \frac{1}{2} b$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Combine $b$ and $\frac{1}{5}$ .

$\frac{2 a}{3} - (- \frac{b}{5} - (2 a - \frac{3}{5} b) + \frac{2}{3} a) - \frac{1}{2} b$

Step 1.2.2

Simplify each term.

Tap for more steps...

Step 1.2.2.1

Combine $b$ and $\frac{3}{5}$ .

$\frac{2 a}{3} - (- \frac{b}{5} - (2 a - \frac{b \cdot 3}{5}) + \frac{2}{3} a) - \frac{1}{2} b$

Step 1.2.2.2

Move $3$ to the left of $b$ .

$\frac{2 a}{3} - (- \frac{b}{5} - (2 a - \frac{3 b}{5}) + \frac{2}{3} a) - \frac{1}{2} b$

Step 1.2.3

Apply the distributive property.

$\frac{2 a}{3} - (- \frac{b}{5} - (2 a) - - \frac{3 b}{5} + \frac{2}{3} a) - \frac{1}{2} b$

Step 1.2.4

Multiply $2$ by $- 1$ .

$\frac{2 a}{3} - (- \frac{b}{5} - 2 a - - \frac{3 b}{5} + \frac{2}{3} a) - \frac{1}{2} b$

Step 1.2.5

Multiply $- - \frac{3 b}{5}$ .

Tap for more steps...

Step 1.2.5.1

Multiply $- 1$ by $- 1$ .

$\frac{2 a}{3} - (- \frac{b}{5} - 2 a + 1 \frac{3 b}{5} + \frac{2}{3} a) - \frac{1}{2} b$

Step 1.2.5.2

Multiply $\frac{3 b}{5}$ by $1$ .

$\frac{2 a}{3} - (- \frac{b}{5} - 2 a + \frac{3 b}{5} + \frac{2}{3} a) - \frac{1}{2} b$

Step 1.2.6

Combine $\frac{2}{3}$ and $a$ .

$\frac{2 a}{3} - (- \frac{b}{5} - 2 a + \frac{3 b}{5} + \frac{2 a}{3}) - \frac{1}{2} b$

Step 1.3

Combine the numerators over the common denominator.

$\frac{2 a}{3} - (- 2 a + \frac{- b + 3 b}{5} + \frac{2 a}{3}) - \frac{1}{2} b$

Step 1.4

Add $- b$ and $3 b$ .

$\frac{2 a}{3} - (- 2 a + \frac{2 b}{5} + \frac{2 a}{3}) - \frac{1}{2} b$

Step 1.5

To write $- 2 a$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 a}{3} - (\frac{2 b}{5} - 2 a \cdot \frac{3}{3} + \frac{2 a}{3}) - \frac{1}{2} b$

Step 1.6

Combine $- 2 a$ and $\frac{3}{3}$ .

$\frac{2 a}{3} - (\frac{2 b}{5} + \frac{- 2 a \cdot 3}{3} + \frac{2 a}{3}) - \frac{1}{2} b$

Step 1.7

Combine the numerators over the common denominator.

$\frac{2 a}{3} - (\frac{2 b}{5} + \frac{- 2 a \cdot 3 + 2 a}{3}) - \frac{1}{2} b$

Step 1.8

Simplify each term.

Tap for more steps...

Step 1.8.1

Simplify the numerator.

Tap for more steps...

Step 1.8.1.1

Factor $2 a$ out of $- 2 a \cdot 3 + 2 a$ .

Tap for more steps...

Step 1.8.1.1.1

Factor $2 a$ out of $- 2 a \cdot 3$ .

$\frac{2 a}{3} - (\frac{2 b}{5} + \frac{2 a (- 1 \cdot 3) + 2 a}{3}) - \frac{1}{2} b$

Step 1.8.1.1.2

Factor $2 a$ out of $2 a$ .

$\frac{2 a}{3} - (\frac{2 b}{5} + \frac{2 a (- 1 \cdot 3) + 2 a (1)}{3}) - \frac{1}{2} b$

Step 1.8.1.1.3

Factor $2 a$ out of $2 a (- 1 \cdot 3) + 2 a (1)$ .

$\frac{2 a}{3} - (\frac{2 b}{5} + \frac{2 a (- 1 \cdot 3 + 1)}{3}) - \frac{1}{2} b$

Step 1.8.1.2

Multiply $- 1$ by $3$ .

$\frac{2 a}{3} - (\frac{2 b}{5} + \frac{2 a (- 3 + 1)}{3}) - \frac{1}{2} b$

Step 1.8.1.3

Add $- 3$ and $1$ .

$\frac{2 a}{3} - (\frac{2 b}{5} + \frac{2 a \cdot - 2}{3}) - \frac{1}{2} b$

Step 1.8.1.4

Multiply $- 2$ by $2$ .

$\frac{2 a}{3} - (\frac{2 b}{5} + \frac{- 4 a}{3}) - \frac{1}{2} b$

Step 1.8.2

Move the negative in front of the fraction.

$\frac{2 a}{3} - (\frac{2 b}{5} - \frac{4 a}{3}) - \frac{1}{2} b$

Step 1.9

Apply the distributive property.

$\frac{2 a}{3} - \frac{2 b}{5} - - \frac{4 a}{3} - \frac{1}{2} b$

Step 1.10

Multiply $- - \frac{4 a}{3}$ .

Tap for more steps...

Step 1.10.1

Multiply $- 1$ by $- 1$ .

$\frac{2 a}{3} - \frac{2 b}{5} + 1 \frac{4 a}{3} - \frac{1}{2} b$

Step 1.10.2

Multiply $\frac{4 a}{3}$ by $1$ .

$\frac{2 a}{3} - \frac{2 b}{5} + \frac{4 a}{3} - \frac{1}{2} b$

Step 1.11

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

$\frac{2 a}{3} - \frac{2 b}{5} + \frac{4 a}{3} - \frac{b}{2}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

$\frac{2 a + 4 a}{3} + \frac{- 2 b}{5} + \frac{- b}{2}$

Step 2.2

Add $2 a$ and $4 a$ .

$\frac{6 a}{3} + \frac{- 2 b}{5} + \frac{- b}{2}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Cancel the common factor of $6$ and $3$ .

Tap for more steps...

Step 3.1.1

Factor $3$ out of $6 a$ .

$\frac{3 (2 a)}{3} + \frac{- 2 b}{5} + \frac{- b}{2}$

Step 3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.1.2.1

Factor $3$ out of $3$ .

$\frac{3 (2 a)}{3 (1)} + \frac{- 2 b}{5} + \frac{- b}{2}$

Step 3.1.2.2

Cancel the common factor.

$\frac{3 (2 a)}{3 \cdot 1} + \frac{- 2 b}{5} + \frac{- b}{2}$

Step 3.1.2.3

Rewrite the expression.

$\frac{2 a}{1} + \frac{- 2 b}{5} + \frac{- b}{2}$

Step 3.1.2.4

Divide $2 a$ by $1$ .

$2 a + \frac{- 2 b}{5} + \frac{- b}{2}$

Step 3.2

Move the negative in front of the fraction.

$2 a - \frac{2 b}{5} + \frac{- b}{2}$

Step 3.3

Move the negative in front of the fraction.

$2 a - \frac{2 b}{5} - \frac{b}{2}$

Step 4

To write $- \frac{2 b}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 a - \frac{2 b}{5} \cdot \frac{2}{2} - \frac{b}{2}$

Step 5

To write $- \frac{b}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$2 a - \frac{2 b}{5} \cdot \frac{2}{2} - \frac{b}{2} \cdot \frac{5}{5}$

Step 6

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 6.1

Multiply $\frac{2 b}{5}$ by $\frac{2}{2}$ .

$2 a - \frac{2 b \cdot 2}{5 \cdot 2} - \frac{b}{2} \cdot \frac{5}{5}$

Step 6.2

Multiply $5$ by $2$ .

$2 a - \frac{2 b \cdot 2}{10} - \frac{b}{2} \cdot \frac{5}{5}$

Step 6.3

Multiply $\frac{b}{2}$ by $\frac{5}{5}$ .

$2 a - \frac{2 b \cdot 2}{10} - \frac{b \cdot 5}{2 \cdot 5}$

Step 6.4

Multiply $2$ by $5$ .

$2 a - \frac{2 b \cdot 2}{10} - \frac{b \cdot 5}{10}$

Step 7

Combine the numerators over the common denominator.

$2 a + \frac{- 2 b \cdot 2 - b \cdot 5}{10}$

Step 8

Simplify each term.

Tap for more steps...

Step 8.1

Simplify the numerator.

Tap for more steps...

Step 8.1.1

Factor $b$ out of $- 2 b \cdot 2 - b \cdot 5$ .

Tap for more steps...

Step 8.1.1.1

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

$2 a + \frac{b (- 2 \cdot 2) - b \cdot 5}{10}$

Step 8.1.1.2

Factor $b$ out of $- b \cdot 5$ .

$2 a + \frac{b (- 2 \cdot 2) + b (- 1 \cdot 5)}{10}$

Step 8.1.1.3

Factor $b$ out of $b (- 2 \cdot 2) + b (- 1 \cdot 5)$ .

$2 a + \frac{b (- 2 \cdot 2 - 1 \cdot 5)}{10}$

Step 8.1.2

Multiply $- 2$ by $2$ .

$2 a + \frac{b (- 4 - 1 \cdot 5)}{10}$

Step 8.1.3

Multiply $- 1$ by $5$ .

$2 a + \frac{b (- 4 - 5)}{10}$

Step 8.1.4

Subtract $5$ from $- 4$ .

$2 a + \frac{b \cdot - 9}{10}$

Step 8.2

Move $- 9$ to the left of $b$ .

$2 a + \frac{- 9 \cdot b}{10}$

Step 8.3

Move the negative in front of the fraction.

$2 a - \frac{9 b}{10}$