Basic Math Examples

$\frac{a + b}{2} + \frac{a - b}{5}$

Step 1

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Multiply $2$ by $5$ .

$\frac{(a + b) \cdot 5}{10} + \frac{a - b}{5} \cdot \frac{2}{2}$

Step 3.3

Multiply $\frac{a - b}{5}$ by $\frac{2}{2}$ .

$\frac{(a + b) \cdot 5}{10} + \frac{(a - b) \cdot 2}{5 \cdot 2}$

Step 3.4

Multiply $5$ by $2$ .

$\frac{(a + b) \cdot 5}{10} + \frac{(a - b) \cdot 2}{10}$

Step 4

Combine the numerators over the common denominator.

$\frac{(a + b) \cdot 5 + (a - b) \cdot 2}{10}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{a \cdot 5 + b \cdot 5 + (a - b) \cdot 2}{10}$

Step 5.2

Move $5$ to the left of $a$ .

$\frac{5 \cdot a + b \cdot 5 + (a - b) \cdot 2}{10}$

Step 5.3

Move $5$ to the left of $b$ .

$\frac{5 \cdot a + 5 \cdot b + (a - b) \cdot 2}{10}$

Step 5.4

Multiply $5$ by $b$ .

$\frac{5 a + 5 b + (a - b) \cdot 2}{10}$

Step 5.5

Apply the distributive property.

$\frac{5 a + 5 b + a \cdot 2 - b \cdot 2}{10}$

Step 5.6

Move $2$ to the left of $a$ .

$\frac{5 a + 5 b + 2 \cdot a - b \cdot 2}{10}$

Step 5.7

Multiply $2$ by $- 1$ .

$\frac{5 a + 5 b + 2 \cdot a - 2 b}{10}$

Step 5.8

Add $5 a$ and $2 a$ .

$\frac{7 a + 5 b - 2 b}{10}$

Step 5.9

Subtract $2 b$ from $5 b$ .

$\frac{7 a + 3 b}{10}$