Basic Math Examples

$\frac{3 g - 1}{9} - \frac{g + 1}{6}$

Step 1

To write $\frac{3 g - 1}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 g - 1}{9} \cdot \frac{2}{2} - \frac{g + 1}{6}$

Step 2

To write $- \frac{g + 1}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 g - 1}{9} \cdot \frac{2}{2} - \frac{g + 1}{6} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3 g - 1}{9}$ by $\frac{2}{2}$ .

$\frac{(3 g - 1) \cdot 2}{9 \cdot 2} - \frac{g + 1}{6} \cdot \frac{3}{3}$

Step 3.2

Multiply $9$ by $2$ .

$\frac{(3 g - 1) \cdot 2}{18} - \frac{g + 1}{6} \cdot \frac{3}{3}$

Step 3.3

Multiply $\frac{g + 1}{6}$ by $\frac{3}{3}$ .

$\frac{(3 g - 1) \cdot 2}{18} - \frac{(g + 1) \cdot 3}{6 \cdot 3}$

Step 3.4

Multiply $6$ by $3$ .

$\frac{(3 g - 1) \cdot 2}{18} - \frac{(g + 1) \cdot 3}{18}$

Step 4

Combine the numerators over the common denominator.

$\frac{(3 g - 1) \cdot 2 - (g + 1) \cdot 3}{18}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{3 g \cdot 2 - 1 \cdot 2 - (g + 1) \cdot 3}{18}$

Step 5.2

Multiply $2$ by $3$ .

$\frac{6 g - 1 \cdot 2 - (g + 1) \cdot 3}{18}$

Step 5.3

Multiply $- 1$ by $2$ .

$\frac{6 g - 2 - (g + 1) \cdot 3}{18}$

Step 5.4

Apply the distributive property.

$\frac{6 g - 2 + (- g - 1 \cdot 1) \cdot 3}{18}$

Step 5.5

Multiply $- 1$ by $1$ .

$\frac{6 g - 2 + (- g - 1) \cdot 3}{18}$

Step 5.6

Apply the distributive property.

$\frac{6 g - 2 - g \cdot 3 - 1 \cdot 3}{18}$

Step 5.7

Multiply $3$ by $- 1$ .

$\frac{6 g - 2 - 3 g - 1 \cdot 3}{18}$

Step 5.8

Multiply $- 1$ by $3$ .

$\frac{6 g - 2 - 3 g - 3}{18}$

Step 5.9

Subtract $3 g$ from $6 g$ .

$\frac{3 g - 2 - 3}{18}$

Step 5.10

Subtract $3$ from $- 2$ .

$\frac{3 g - 5}{18}$