Basic Math Examples

$(\frac{3 a - 5}{9}) - (\frac{2 a + 7}{6})$

Step 1

To write $\frac{3 a - 5}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 a - 5}{9} \cdot \frac{2}{2} - \frac{2 a + 7}{6}$

Step 2

To write $- \frac{2 a + 7}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 a - 5}{9} \cdot \frac{2}{2} - \frac{2 a + 7}{6} \cdot \frac{3}{3}$

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 $\frac{3 a - 5}{9}$ by $\frac{2}{2}$ .

$\frac{(3 a - 5) \cdot 2}{9 \cdot 2} - \frac{2 a + 7}{6} \cdot \frac{3}{3}$

Step 3.2

Multiply $9$ by $2$ .

$\frac{(3 a - 5) \cdot 2}{18} - \frac{2 a + 7}{6} \cdot \frac{3}{3}$

Step 3.3

Multiply $\frac{2 a + 7}{6}$ by $\frac{3}{3}$ .

$\frac{(3 a - 5) \cdot 2}{18} - \frac{(2 a + 7) \cdot 3}{6 \cdot 3}$

Step 3.4

Multiply $6$ by $3$ .

$\frac{(3 a - 5) \cdot 2}{18} - \frac{(2 a + 7) \cdot 3}{18}$

Step 4

Combine the numerators over the common denominator.

$\frac{(3 a - 5) \cdot 2 - (2 a + 7) \cdot 3}{18}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{3 a \cdot 2 - 5 \cdot 2 - (2 a + 7) \cdot 3}{18}$

Step 5.2

Multiply $2$ by $3$ .

$\frac{6 a - 5 \cdot 2 - (2 a + 7) \cdot 3}{18}$

Step 5.3

Multiply $- 5$ by $2$ .

$\frac{6 a - 10 - (2 a + 7) \cdot 3}{18}$

Step 5.4

Apply the distributive property.

$\frac{6 a - 10 + (- (2 a) - 1 \cdot 7) \cdot 3}{18}$

Step 5.5

Multiply $2$ by $- 1$ .

$\frac{6 a - 10 + (- 2 a - 1 \cdot 7) \cdot 3}{18}$

Step 5.6

Multiply $- 1$ by $7$ .

$\frac{6 a - 10 + (- 2 a - 7) \cdot 3}{18}$

Step 5.7

Apply the distributive property.

$\frac{6 a - 10 - 2 a \cdot 3 - 7 \cdot 3}{18}$

Step 5.8

Multiply $3$ by $- 2$ .

$\frac{6 a - 10 - 6 a - 7 \cdot 3}{18}$

Step 5.9

Multiply $- 7$ by $3$ .

$\frac{6 a - 10 - 6 a - 21}{18}$

Step 5.10

Subtract $6 a$ from $6 a$ .

$\frac{0 - 10 - 21}{18}$

Step 5.11

Subtract $10$ from $0$ .

$\frac{- 10 - 21}{18}$

Step 5.12

Subtract $21$ from $- 10$ .

$\frac{- 31}{18}$

Step 6

Move the negative in front of the fraction.

$- \frac{31}{18}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{31}{18}$

Decimal Form:

$- 1.7\overline{2}$

Mixed Number Form:

$- 1 \frac{13}{18}$