Basic Math Examples

$- \frac{5}{3} \cdot (y - 5) - \frac{1}{9} y$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- \frac{5}{3} y - \frac{5}{3} \cdot - 5 - \frac{1}{9} y$

Step 1.2

Combine $y$ and $\frac{5}{3}$ .

$- \frac{y \cdot 5}{3} - \frac{5}{3} \cdot - 5 - \frac{1}{9} y$

Step 1.3

Multiply $- \frac{5}{3} \cdot - 5$ .

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Step 1.3.1

Multiply $- 5$ by $- 1$ .

$- \frac{y \cdot 5}{3} + 5 (\frac{5}{3}) - \frac{1}{9} y$

Step 1.3.2

Combine $5$ and $\frac{5}{3}$ .

$- \frac{y \cdot 5}{3} + \frac{5 \cdot 5}{3} - \frac{1}{9} y$

Step 1.3.3

Multiply $5$ by $5$ .

$- \frac{y \cdot 5}{3} + \frac{25}{3} - \frac{1}{9} y$

Step 1.4

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

$- \frac{5 y}{3} + \frac{25}{3} - \frac{1}{9} y$

Step 1.5

Combine $y$ and $\frac{1}{9}$ .

$- \frac{5 y}{3} + \frac{25}{3} - \frac{y}{9}$

Step 2

To write $- \frac{5 y}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{5 y}{3} \cdot \frac{3}{3} - \frac{y}{9} + \frac{25}{3}$

Step 3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 y}{3}$ by $\frac{3}{3}$ .

$- \frac{5 y \cdot 3}{3 \cdot 3} - \frac{y}{9} + \frac{25}{3}$

Step 3.2

Multiply $3$ by $3$ .

$- \frac{5 y \cdot 3}{9} - \frac{y}{9} + \frac{25}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 5 y \cdot 3 - y}{9} + \frac{25}{3}$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Factor $y$ out of $- 5 y \cdot 3 - y$ .

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Step 5.1.1.1

Factor $y$ out of $- 5 y \cdot 3$ .

$\frac{y (- 5 \cdot 3) - y}{9} + \frac{25}{3}$

Step 5.1.1.2

Factor $y$ out of $- y$ .

$\frac{y (- 5 \cdot 3) + y \cdot - 1}{9} + \frac{25}{3}$

Step 5.1.1.3

Factor $y$ out of $y (- 5 \cdot 3) + y \cdot - 1$ .

$\frac{y (- 5 \cdot 3 - 1)}{9} + \frac{25}{3}$

Step 5.1.2

Multiply $- 5$ by $3$ .

$\frac{y (- 15 - 1)}{9} + \frac{25}{3}$

Step 5.1.3

Subtract $1$ from $- 15$ .

$\frac{y \cdot - 16}{9} + \frac{25}{3}$

Step 5.2

Move $- 16$ to the left of $y$ .

$\frac{- 16 \cdot y}{9} + \frac{25}{3}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{16 y}{9} + \frac{25}{3}$