Find the Exact Value (-2/5y)-(-5/2y)

$(- \frac{2}{5} y) - (- \frac{5}{2} y)$

Simplify each term.

Combine $y$ and $\frac{2}{5}$ .

$- \frac{y \cdot 2}{5} - (- \frac{5}{2} y)$

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

$- \frac{2 \cdot y}{5} - (- \frac{5}{2} y)$

Combine $y$ and $\frac{5}{2}$ .

$- \frac{2 y}{5} - - \frac{y \cdot 5}{2}$

Move $5$ to the left of $y$ .

$- \frac{2 y}{5} - - \frac{5 \cdot y}{2}$

Multiply $- - \frac{5 y}{2}$ .

Multiply $- 1$ by $- 1$ .

$- \frac{2 y}{5} + 1 \frac{5 y}{2}$

Multiply $\frac{5 y}{2}$ by $1$ .

$- \frac{2 y}{5} + \frac{5 y}{2}$

To write $- \frac{2 y}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{2 y}{5} \cdot \frac{2}{2} + \frac{5 y}{2}$

To write $\frac{5 y}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{2 y}{5} \cdot \frac{2}{2} + \frac{5 y}{2} \cdot \frac{5}{5}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 y}{5}$ by $\frac{2}{2}$ .

$- \frac{2 y \cdot 2}{5 \cdot 2} + \frac{5 y}{2} \cdot \frac{5}{5}$

Multiply $5$ by $2$ .

$- \frac{2 y \cdot 2}{10} + \frac{5 y}{2} \cdot \frac{5}{5}$

Multiply $\frac{5 y}{2}$ by $\frac{5}{5}$ .

$- \frac{2 y \cdot 2}{10} + \frac{5 y \cdot 5}{2 \cdot 5}$

Multiply $2$ by $5$ .

$- \frac{2 y \cdot 2}{10} + \frac{5 y \cdot 5}{10}$

Combine the numerators over the common denominator.

$\frac{- 2 y \cdot 2 + 5 y \cdot 5}{10}$

Simplify the numerator.

Factor $y$ out of $- 2 y \cdot 2 + 5 y \cdot 5$ .

Factor $y$ out of $- 2 y \cdot 2$ .

$\frac{y (- 2 \cdot 2) + 5 y \cdot 5}{10}$

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

$\frac{y (- 2 \cdot 2) + y (5 \cdot 5)}{10}$

Factor $y$ out of $y (- 2 \cdot 2) + y (5 \cdot 5)$ .

$\frac{y (- 2 \cdot 2 + 5 \cdot 5)}{10}$

Multiply $- 2$ by $2$ .

$\frac{y (- 4 + 5 \cdot 5)}{10}$

Multiply $5$ by $5$ .

$\frac{y (- 4 + 25)}{10}$

Add $- 4$ and $25$ .

$\frac{y \cdot 21}{10}$

Move $21$ to the left of $y$ .

$\frac{21 y}{10}$

Find the Exact Value (-2/5y)-(-5/2y)

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