Basic Math Examples

$\frac{y}{5} - \frac{y}{8}$

Step 1

To write $\frac{y}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{y}{5} \cdot \frac{8}{8} - \frac{y}{8}$

Step 2

To write $- \frac{y}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{y}{5} \cdot \frac{8}{8} - \frac{y}{8} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{y}{5}$ by $\frac{8}{8}$ .

$\frac{y \cdot 8}{5 \cdot 8} - \frac{y}{8} \cdot \frac{5}{5}$

Step 3.2

Multiply $5$ by $8$ .

$\frac{y \cdot 8}{40} - \frac{y}{8} \cdot \frac{5}{5}$

Step 3.3

Multiply $\frac{y}{8}$ by $\frac{5}{5}$ .

$\frac{y \cdot 8}{40} - \frac{y \cdot 5}{8 \cdot 5}$

Step 3.4

Multiply $8$ by $5$ .

$\frac{y \cdot 8}{40} - \frac{y \cdot 5}{40}$

Step 4

Combine the numerators over the common denominator.

$\frac{y \cdot 8 - y \cdot 5}{40}$

Step 5

Rewrite $\frac{y \cdot 8 - y \cdot 5}{40}$ in a factored form.

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Step 5.1

Factor $y$ out of $y \cdot 8 - y \cdot 5$ .

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Step 5.1.1

Factor $y$ out of $y \cdot 8$ .

$\frac{y (8) - y \cdot 5}{40}$

Step 5.1.2

Factor $y$ out of $- y \cdot 5$ .

$\frac{y (8) + y (- 1 \cdot 5)}{40}$

Step 5.1.3

Factor $y$ out of $y (8) + y (- 1 \cdot 5)$ .

$\frac{y (8 - 1 \cdot 5)}{40}$

Step 5.2

Multiply $- 1$ by $5$ .

$\frac{y (8 - 5)}{40}$

Step 5.3

Subtract $5$ from $8$ .

$\frac{y \cdot 3}{40}$