Finite Math Examples

$\frac{\frac{7}{y}}{\frac{1}{4} - \frac{2}{y}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{7}{y} \cdot \frac{1}{\frac{1}{4} - \frac{2}{y}}$

Step 2

Simplify the denominator.

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Step 2.1

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{7}{y} \cdot \frac{1}{\frac{1}{4} \cdot \frac{y}{y} - \frac{2}{y}}$

Step 2.2

To write $- \frac{2}{y}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7}{y} \cdot \frac{1}{\frac{1}{4} \cdot \frac{y}{y} - \frac{2}{y} \cdot \frac{4}{4}}$

Step 2.3

Write each expression with a common denominator of $4 y$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{1}{4}$ by $\frac{y}{y}$ .

$\frac{7}{y} \cdot \frac{1}{\frac{y}{4 y} - \frac{2}{y} \cdot \frac{4}{4}}$

Step 2.3.2

Multiply $\frac{2}{y}$ by $\frac{4}{4}$ .

$\frac{7}{y} \cdot \frac{1}{\frac{y}{4 y} - \frac{2 \cdot 4}{y \cdot 4}}$

Step 2.3.3

Reorder the factors of $y \cdot 4$ .

$\frac{7}{y} \cdot \frac{1}{\frac{y}{4 y} - \frac{2 \cdot 4}{4 y}}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7}{y} \cdot \frac{1}{\frac{y - 2 \cdot 4}{4 y}}$

Step 2.5

Multiply $- 2$ by $4$ .

$\frac{7}{y} \cdot \frac{1}{\frac{y - 8}{4 y}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{7}{y} (1 \frac{4 y}{y - 8})$

Step 4

Multiply $\frac{4 y}{y - 8}$ by $1$ .

$\frac{7}{y} \cdot \frac{4 y}{y - 8}$

Step 5

Cancel the common factor of $y$ .

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Step 5.1

Factor $y$ out of $4 y$ .

$\frac{7}{y} \cdot \frac{y \cdot 4}{y - 8}$

Step 5.2

Cancel the common factor.

$\frac{7}{y} \cdot \frac{y \cdot 4}{y - 8}$

Step 5.3

Rewrite the expression.

$7 \frac{4}{y - 8}$

Step 6

Combine $7$ and $\frac{4}{y - 8}$ .

$\frac{7 \cdot 4}{y - 8}$

Step 7

Multiply $7$ by $4$ .

$\frac{28}{y - 8}$