Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- \frac{3 + 2 a}{5} + \frac{2}{3} a + \frac{2}{3} \cdot - 2$

Step 1.2

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

$- \frac{3 + 2 a}{5} + \frac{2 a}{3} + \frac{2}{3} \cdot - 2$

Step 1.3

Multiply $\frac{2}{3} \cdot - 2$ .

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Step 1.3.1

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

$- \frac{3 + 2 a}{5} + \frac{2 a}{3} + \frac{2 \cdot - 2}{3}$

Step 1.3.2

Multiply $2$ by $- 2$ .

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

Step 1.4

Move the negative in front of the fraction.

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

Step 2

To write $- \frac{3 + 2 a}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

To write $\frac{2 a}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3 + 2 a}{5}$ by $\frac{3}{3}$ .

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

Step 4.2

Multiply $5$ by $3$ .

$- \frac{(3 + 2 a) \cdot 3}{15} + \frac{2 a}{3} \cdot \frac{5}{5} - \frac{4}{3}$

Step 4.3

Multiply $\frac{2 a}{3}$ by $\frac{5}{5}$ .

$- \frac{(3 + 2 a) \cdot 3}{15} + \frac{2 a \cdot 5}{3 \cdot 5} - \frac{4}{3}$

Step 4.4

Multiply $3$ by $5$ .

$- \frac{(3 + 2 a) \cdot 3}{15} + \frac{2 a \cdot 5}{15} - \frac{4}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{- (3 + 2 a) \cdot 3 + 2 a \cdot 5}{15} - \frac{4}{3}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{(- 1 \cdot 3 - (2 a)) \cdot 3 + 2 a \cdot 5}{15} - \frac{4}{3}$

Step 6.2

Multiply $- 1$ by $3$ .

$\frac{(- 3 - (2 a)) \cdot 3 + 2 a \cdot 5}{15} - \frac{4}{3}$

Step 6.3

Multiply $2$ by $- 1$ .

$\frac{(- 3 - 2 a) \cdot 3 + 2 a \cdot 5}{15} - \frac{4}{3}$

Step 6.4

Apply the distributive property.

$\frac{- 3 \cdot 3 - 2 a \cdot 3 + 2 a \cdot 5}{15} - \frac{4}{3}$

Step 6.5

Multiply $- 3$ by $3$ .

$\frac{- 9 - 2 a \cdot 3 + 2 a \cdot 5}{15} - \frac{4}{3}$

Step 6.6

Multiply $3$ by $- 2$ .

$\frac{- 9 - 6 a + 2 a \cdot 5}{15} - \frac{4}{3}$

Step 6.7

Multiply $5$ by $2$ .

$\frac{- 9 - 6 a + 10 a}{15} - \frac{4}{3}$

Step 6.8

Add $- 6 a$ and $10 a$ .

$\frac{- 9 + 4 a}{15} - \frac{4}{3}$

Step 7

To write $- \frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{- 9 + 4 a}{15} - \frac{4}{3} \cdot \frac{5}{5}$

Step 8

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{4}{3}$ by $\frac{5}{5}$ .

$\frac{- 9 + 4 a}{15} - \frac{4 \cdot 5}{3 \cdot 5}$

Step 8.2

Multiply $3$ by $5$ .

$\frac{- 9 + 4 a}{15} - \frac{4 \cdot 5}{15}$

Step 9

Combine the numerators over the common denominator.

$\frac{- 9 + 4 a - 4 \cdot 5}{15}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $- 4$ by $5$ .

$\frac{- 9 + 4 a - 20}{15}$

Step 10.2

Subtract $20$ from $- 9$ .

$\frac{4 a - 29}{15}$