Pre-Algebra Examples

$\frac{9 a + 8 x}{8 a} + \frac{5 a + 6 x}{4 a} + 1$

Step 1

To write $\frac{5 a + 6 x}{4 a}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9 a + 8 x}{8 a} + \frac{5 a + 6 x}{4 a} \cdot \frac{2}{2} + 1$

Step 2

Write each expression with a common denominator of $8 a$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{5 a + 6 x}{4 a}$ by $\frac{2}{2}$ .

$\frac{9 a + 8 x}{8 a} + \frac{(5 a + 6 x) \cdot 2}{4 a \cdot 2} + 1$

Step 2.2

Multiply $2$ by $4$ .

$\frac{9 a + 8 x}{8 a} + \frac{(5 a + 6 x) \cdot 2}{8 a} + 1$

Step 3

Combine the numerators over the common denominator.

$\frac{9 a + 8 x + (5 a + 6 x) \cdot 2}{8 a} + 1$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{9 a + 8 x + 5 a \cdot 2 + 6 x \cdot 2}{8 a} + 1$

Step 4.2

Multiply $2$ by $5$ .

$\frac{9 a + 8 x + 10 a + 6 x \cdot 2}{8 a} + 1$

Step 4.3

Multiply $2$ by $6$ .

$\frac{9 a + 8 x + 10 a + 12 x}{8 a} + 1$

Step 4.4

Add $9 a$ and $10 a$ .

$\frac{19 a + 8 x + 12 x}{8 a} + 1$

Step 4.5

Add $8 x$ and $12 x$ .

$\frac{19 a + 20 x}{8 a} + 1$

Step 5

Simplify terms.

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Step 5.1

Write $1$ as a fraction with a common denominator.

$\frac{19 a + 20 x}{8 a} + \frac{8 a}{8 a}$

Step 5.2

Combine the numerators over the common denominator.

$\frac{19 a + 20 x + 8 a}{8 a}$

Step 5.3

Add $19 a$ and $8 a$ .

$\frac{27 a + 20 x}{8 a}$