Basic Math Examples

$\frac{7 y}{63} - \frac{9}{2}$

Step 1

Cancel the common factor of $7$ and $63$ .

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Step 1.1

Factor $7$ out of $7 y$ .

$\frac{7 (y)}{63} - \frac{9}{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $7$ out of $63$ .

$\frac{7 y}{7 \cdot 9} - \frac{9}{2}$

Step 1.2.2

Cancel the common factor.

$\frac{7 y}{7 \cdot 9} - \frac{9}{2}$

Step 1.2.3

Rewrite the expression.

$\frac{y}{9} - \frac{9}{2}$

Step 2

To write $\frac{y}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y}{9} \cdot \frac{2}{2} - \frac{9}{2}$

Step 3

To write $- \frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{y}{9} \cdot \frac{2}{2} - \frac{9}{2} \cdot \frac{9}{9}$

Step 4

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{y}{9}$ by $\frac{2}{2}$ .

$\frac{y \cdot 2}{9 \cdot 2} - \frac{9}{2} \cdot \frac{9}{9}$

Step 4.2

Multiply $9$ by $2$ .

$\frac{y \cdot 2}{18} - \frac{9}{2} \cdot \frac{9}{9}$

Step 4.3

Multiply $\frac{9}{2}$ by $\frac{9}{9}$ .

$\frac{y \cdot 2}{18} - \frac{9 \cdot 9}{2 \cdot 9}$

Step 4.4

Multiply $2$ by $9$ .

$\frac{y \cdot 2}{18} - \frac{9 \cdot 9}{18}$

Step 5

Combine the numerators over the common denominator.

$\frac{y \cdot 2 - 9 \cdot 9}{18}$

Step 6

Simplify the numerator.

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Step 6.1

Move $2$ to the left of $y$ .

$\frac{2 \cdot y - 9 \cdot 9}{18}$

Step 6.2

Multiply $- 9$ by $9$ .

$\frac{2 y - 81}{18}$