Basic Math Examples

$\frac{5 y - 3}{12 y} - \frac{2 + y}{5 y}$

Step 1

To write $\frac{5 y - 3}{12 y}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 y - 3}{12 y} \cdot \frac{5}{5} - \frac{2 + y}{5 y}$

Step 2

To write $- \frac{2 + y}{5 y}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{5 y - 3}{12 y} \cdot \frac{5}{5} - \frac{2 + y}{5 y} \cdot \frac{12}{12}$

Step 3

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

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Step 3.1

Multiply $\frac{5 y - 3}{12 y}$ by $\frac{5}{5}$ .

$\frac{(5 y - 3) \cdot 5}{12 y \cdot 5} - \frac{2 + y}{5 y} \cdot \frac{12}{12}$

Step 3.2

Multiply $5$ by $12$ .

$\frac{(5 y - 3) \cdot 5}{60 y} - \frac{2 + y}{5 y} \cdot \frac{12}{12}$

Step 3.3

Multiply $\frac{2 + y}{5 y}$ by $\frac{12}{12}$ .

$\frac{(5 y - 3) \cdot 5}{60 y} - \frac{(2 + y) \cdot 12}{5 y \cdot 12}$

Step 3.4

Multiply $12$ by $5$ .

$\frac{(5 y - 3) \cdot 5}{60 y} - \frac{(2 + y) \cdot 12}{60 y}$

Step 4

Combine the numerators over the common denominator.

$\frac{(5 y - 3) \cdot 5 - (2 + y) \cdot 12}{60 y}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{5 y \cdot 5 - 3 \cdot 5 - (2 + y) \cdot 12}{60 y}$

Step 5.2

Multiply $5$ by $5$ .

$\frac{25 y - 3 \cdot 5 - (2 + y) \cdot 12}{60 y}$

Step 5.3

Multiply $- 3$ by $5$ .

$\frac{25 y - 15 - (2 + y) \cdot 12}{60 y}$

Step 5.4

Apply the distributive property.

$\frac{25 y - 15 + (- 1 \cdot 2 - y) \cdot 12}{60 y}$

Step 5.5

Multiply $- 1$ by $2$ .

$\frac{25 y - 15 + (- 2 - y) \cdot 12}{60 y}$

Step 5.6

Apply the distributive property.

$\frac{25 y - 15 - 2 \cdot 12 - y \cdot 12}{60 y}$

Step 5.7

Multiply $- 2$ by $12$ .

$\frac{25 y - 15 - 24 - y \cdot 12}{60 y}$

Step 5.8

Multiply $12$ by $- 1$ .

$\frac{25 y - 15 - 24 - 12 y}{60 y}$

Step 5.9

Subtract $12 y$ from $25 y$ .

$\frac{13 y - 15 - 24}{60 y}$

Step 5.10

Subtract $24$ from $- 15$ .

$\frac{13 y - 39}{60 y}$

Step 5.11

Factor $13$ out of $13 y - 39$ .

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Step 5.11.1

Factor $13$ out of $13 y$ .

$\frac{13 (y) - 39}{60 y}$

Step 5.11.2

Factor $13$ out of $- 39$ .

$\frac{13 y + 13 \cdot - 3}{60 y}$

Step 5.11.3

Factor $13$ out of $13 y + 13 \cdot - 3$ .

$\frac{13 (y - 3)}{60 y}$