Basic Math Examples

$\frac{y}{7} - \frac{y - 8}{9}$

Step 1

To write $\frac{y}{7}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{y}{7} \cdot \frac{9}{9} - \frac{y - 8}{9}$

Step 2

To write $- \frac{y - 8}{9}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{y}{7} \cdot \frac{9}{9} - \frac{y - 8}{9} \cdot \frac{7}{7}$

Step 3

Write each expression with a common denominator of $63$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{y}{7}$ by $\frac{9}{9}$ .

$\frac{y \cdot 9}{7 \cdot 9} - \frac{y - 8}{9} \cdot \frac{7}{7}$

Step 3.2

Multiply $7$ by $9$ .

$\frac{y \cdot 9}{63} - \frac{y - 8}{9} \cdot \frac{7}{7}$

Step 3.3

Multiply $\frac{y - 8}{9}$ by $\frac{7}{7}$ .

$\frac{y \cdot 9}{63} - \frac{(y - 8) \cdot 7}{9 \cdot 7}$

Step 3.4

Multiply $9$ by $7$ .

$\frac{y \cdot 9}{63} - \frac{(y - 8) \cdot 7}{63}$

Step 4

Combine the numerators over the common denominator.

$\frac{y \cdot 9 - (y - 8) \cdot 7}{63}$

Step 5

Simplify the numerator.

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Step 5.1

Move $9$ to the left of $y$ .

$\frac{9 \cdot y - (y - 8) \cdot 7}{63}$

Step 5.2

Apply the distributive property.

$\frac{9 y + (- y - - 8) \cdot 7}{63}$

Step 5.3

Multiply $- 1$ by $- 8$ .

$\frac{9 y + (- y + 8) \cdot 7}{63}$

Step 5.4

Apply the distributive property.

$\frac{9 y - y \cdot 7 + 8 \cdot 7}{63}$

Step 5.5

Multiply $7$ by $- 1$ .

$\frac{9 y - 7 y + 8 \cdot 7}{63}$

Step 5.6

Multiply $8$ by $7$ .

$\frac{9 y - 7 y + 56}{63}$

Step 5.7

Subtract $7 y$ from $9 y$ .

$\frac{2 y + 56}{63}$

Step 5.8

Factor $2$ out of $2 y + 56$ .

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Step 5.8.1

Factor $2$ out of $2 y$ .

$\frac{2 (y) + 56}{63}$

Step 5.8.2

Factor $2$ out of $56$ .

$\frac{2 y + 2 \cdot 28}{63}$

Step 5.8.3

Factor $2$ out of $2 y + 2 \cdot 28$ .

$\frac{2 (y + 28)}{63}$