Basic Math Examples

$\frac{a + b}{5} - \frac{a - b}{12}$

Step 1

To write $\frac{a + b}{5}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{a + b}{5} \cdot \frac{12}{12} - \frac{a - b}{12}$

Step 2

To write $- \frac{a - b}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{a + b}{5} \cdot \frac{12}{12} - \frac{a - b}{12} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{a + b}{5}$ by $\frac{12}{12}$ .

$\frac{(a + b) \cdot 12}{5 \cdot 12} - \frac{a - b}{12} \cdot \frac{5}{5}$

Step 3.2

Multiply $5$ by $12$ .

$\frac{(a + b) \cdot 12}{60} - \frac{a - b}{12} \cdot \frac{5}{5}$

Step 3.3

Multiply $\frac{a - b}{12}$ by $\frac{5}{5}$ .

$\frac{(a + b) \cdot 12}{60} - \frac{(a - b) \cdot 5}{12 \cdot 5}$

Step 3.4

Multiply $12$ by $5$ .

$\frac{(a + b) \cdot 12}{60} - \frac{(a - b) \cdot 5}{60}$

Step 4

Combine the numerators over the common denominator.

$\frac{(a + b) \cdot 12 - (a - b) \cdot 5}{60}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{a \cdot 12 + b \cdot 12 - (a - b) \cdot 5}{60}$

Step 5.2

Move $12$ to the left of $a$ .

$\frac{12 \cdot a + b \cdot 12 - (a - b) \cdot 5}{60}$

Step 5.3

Move $12$ to the left of $b$ .

$\frac{12 \cdot a + 12 \cdot b - (a - b) \cdot 5}{60}$

Step 5.4

Multiply $12$ by $b$ .

$\frac{12 a + 12 b - (a - b) \cdot 5}{60}$

Step 5.5

Apply the distributive property.

$\frac{12 a + 12 b + (- a - - b) \cdot 5}{60}$

Step 5.6

Multiply $- - b$ .

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Step 5.6.1

Multiply $- 1$ by $- 1$ .

$\frac{12 a + 12 b + (- a + 1 b) \cdot 5}{60}$

Step 5.6.2

Multiply $b$ by $1$ .

$\frac{12 a + 12 b + (- a + b) \cdot 5}{60}$

Step 5.7

Apply the distributive property.

$\frac{12 a + 12 b - a \cdot 5 + b \cdot 5}{60}$

Step 5.8

Multiply $5$ by $- 1$ .

$\frac{12 a + 12 b - 5 a + b \cdot 5}{60}$

Step 5.9

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

$\frac{12 a + 12 b - 5 a + 5 \cdot b}{60}$

Step 5.10

Subtract $5 a$ from $12 a$ .

$\frac{7 a + 12 b + 5 b}{60}$

Step 5.11

Add $12 b$ and $5 b$ .

$\frac{7 a + 17 b}{60}$