Basic Math Examples

$\frac{\frac{1}{12} - \frac{4}{y}}{\frac{7}{15 y - y}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{1}{12} - \frac{4}{y}) \frac{15 y - y}{7}$

Step 2

Subtract $y$ from $15 y$ .

$(\frac{1}{12} - \frac{4}{y}) \frac{14 y}{7}$

Step 3

To write $\frac{1}{12}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$(\frac{1}{12} \cdot \frac{y}{y} - \frac{4}{y}) \frac{14 y}{7}$

Step 4

To write $- \frac{4}{y}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$(\frac{1}{12} \cdot \frac{y}{y} - \frac{4}{y} \cdot \frac{12}{12}) \frac{14 y}{7}$

Step 5

Write each expression with a common denominator of $12 y$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{1}{12}$ by $\frac{y}{y}$ .

$(\frac{y}{12 y} - \frac{4}{y} \cdot \frac{12}{12}) \frac{14 y}{7}$

Step 5.2

Multiply $\frac{4}{y}$ by $\frac{12}{12}$ .

$(\frac{y}{12 y} - \frac{4 \cdot 12}{y \cdot 12}) \frac{14 y}{7}$

Step 5.3

Reorder the factors of $y \cdot 12$ .

$(\frac{y}{12 y} - \frac{4 \cdot 12}{12 y}) \frac{14 y}{7}$

Step 6

Combine the numerators over the common denominator.

$\frac{y - 4 \cdot 12}{12 y} \cdot \frac{14 y}{7}$

Step 7

Multiply $- 4$ by $12$ .

$\frac{y - 48}{12 y} \cdot \frac{14 y}{7}$

Step 8

Cancel the common factor of $2 y$ .

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Step 8.1

Factor $2 y$ out of $12 y$ .

$\frac{y - 48}{2 y (6)} \cdot \frac{14 y}{7}$

Step 8.2

Factor $2 y$ out of $14 y$ .

$\frac{y - 48}{2 y (6)} \cdot \frac{2 y (7)}{7}$

Step 8.3

Cancel the common factor.

$\frac{y - 48}{2 y \cdot 6} \cdot \frac{2 y \cdot 7}{7}$

Step 8.4

Rewrite the expression.

$\frac{y - 48}{6} \cdot \frac{7}{7}$

Step 9

Multiply $\frac{y - 48}{6}$ by $\frac{7}{7}$ .

$\frac{(y - 48) \cdot 7}{6 \cdot 7}$

Step 10

Multiply $6$ by $7$ .

$\frac{(y - 48) \cdot 7}{42}$

Step 11

Cancel the common factor of $7$ and $42$ .

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Step 11.1

Factor $7$ out of $(y - 48) \cdot 7$ .

$\frac{7 \cdot (y - 48)}{42}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $7$ out of $42$ .

$\frac{7 \cdot (y - 48)}{7 \cdot 6}$

Step 11.2.2

Cancel the common factor.

$\frac{7 \cdot (y - 48)}{7 \cdot 6}$

Step 11.2.3

Rewrite the expression.

$\frac{y - 48}{6}$