Basic Math Examples

$\frac{a - 1}{5} - \frac{a + 3}{3}$

Step 1

To write $\frac{a - 1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{a - 1}{5} \cdot \frac{3}{3} - \frac{a + 3}{3}$

Step 2

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

$\frac{a - 1}{5} \cdot \frac{3}{3} - \frac{a + 3}{3} \cdot \frac{5}{5}$

Step 3

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

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Step 3.1

Multiply $\frac{a - 1}{5}$ by $\frac{3}{3}$ .

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

Step 3.2

Multiply $5$ by $3$ .

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

Step 3.3

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

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

Step 3.4

Multiply $3$ by $5$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

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

Step 5.2

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

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

Step 5.3

Multiply $- 1$ by $3$ .

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

Step 5.4

Apply the distributive property.

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

Step 5.5

Multiply $- 1$ by $3$ .

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

Step 5.6

Apply the distributive property.

$\frac{3 a - 3 - a \cdot 5 - 3 \cdot 5}{15}$

Step 5.7

Multiply $5$ by $- 1$ .

$\frac{3 a - 3 - 5 a - 3 \cdot 5}{15}$

Step 5.8

Multiply $- 3$ by $5$ .

$\frac{3 a - 3 - 5 a - 15}{15}$

Step 5.9

Subtract $5 a$ from $3 a$ .

$\frac{- 2 a - 3 - 15}{15}$

Step 5.10

Subtract $15$ from $- 3$ .

$\frac{- 2 a - 18}{15}$

Step 5.11

Factor $2$ out of $- 2 a - 18$ .

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Step 5.11.1

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

$\frac{2 (- a) - 18}{15}$

Step 5.11.2

Factor $2$ out of $- 18$ .

$\frac{2 (- a) + 2 (- 9)}{15}$

Step 5.11.3

Factor $2$ out of $2 (- a) + 2 (- 9)$ .

$\frac{2 (- a - 9)}{15}$

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- a$ .

$\frac{2 (- (a) - 9)}{15}$

Step 6.2

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{2 (- (a) - 1 (9))}{15}$

Step 6.3

Factor $- 1$ out of $- (a) - 1 (9)$ .

$\frac{2 (- (a + 9))}{15}$

Step 6.4

Simplify the expression.

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Step 6.4.1

Rewrite $- (a + 9)$ as $- 1 (a + 9)$ .

$\frac{2 (- 1 (a + 9))}{15}$

Step 6.4.2

Move the negative in front of the fraction.

$- \frac{2 (a + 9)}{15}$