Pre-Algebra Examples

$- \frac{y}{5} + \frac{y}{7}$

Step 1

To write $- \frac{y}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{y}{5} \cdot \frac{7}{7} + \frac{y}{7}$

Step 2

To write $\frac{y}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{y}{5} \cdot \frac{7}{7} + \frac{y}{7} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{y}{5}$ by $\frac{7}{7}$ .

$- \frac{y \cdot 7}{5 \cdot 7} + \frac{y}{7} \cdot \frac{5}{5}$

Step 3.2

Multiply $5$ by $7$ .

$- \frac{y \cdot 7}{35} + \frac{y}{7} \cdot \frac{5}{5}$

Step 3.3

Multiply $\frac{y}{7}$ by $\frac{5}{5}$ .

$- \frac{y \cdot 7}{35} + \frac{y \cdot 5}{7 \cdot 5}$

Step 3.4

Multiply $7$ by $5$ .

$- \frac{y \cdot 7}{35} + \frac{y \cdot 5}{35}$

Step 4

Combine the numerators over the common denominator.

$\frac{- y \cdot 7 + y \cdot 5}{35}$

Step 5

Rewrite $\frac{- y \cdot 7 + y \cdot 5}{35}$ in a factored form.

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Step 5.1

Factor $- y$ out of $- y \cdot 7 + y \cdot 5$ .

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Step 5.1.1

Reorder the expression.

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Step 5.1.1.1

Move $y$ .

$\frac{- 1 \cdot 7 y + y \cdot 5}{35}$

Step 5.1.1.2

Reorder $y$ and $5$ .

$\frac{- 1 \cdot 7 y + 5 \cdot y}{35}$

Step 5.1.2

Factor $- y$ out of $- 1 \cdot 7 y$ .

$\frac{- y (7) + 5 \cdot y}{35}$

Step 5.1.3

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

$\frac{- y (7) - y (- 5)}{35}$

Step 5.1.4

Factor $- y$ out of $- y (7) - y (- 5)$ .

$\frac{- y (7 - 5)}{35}$

Step 5.2

Subtract $5$ from $7$ .

$\frac{- y \cdot 2}{35}$

Step 5.3

Multiply $2$ by $- 1$ .

$\frac{- 2 y}{35}$