Basic Math Examples

$- \frac{5}{3} \cdot (y - 12) - \frac{1}{9}$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- \frac{5}{3} y - \frac{5}{3} \cdot - 12 - \frac{1}{9}$

Step 1.2

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

$- \frac{y \cdot 5}{3} - \frac{5}{3} \cdot - 12 - \frac{1}{9}$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$- \frac{y \cdot 5}{3} + \frac{- 5}{3} \cdot - 12 - \frac{1}{9}$

Step 1.3.2

Factor $3$ out of $- 12$ .

$- \frac{y \cdot 5}{3} + \frac{- 5}{3} \cdot (3 (- 4)) - \frac{1}{9}$

Step 1.3.3

Cancel the common factor.

$- \frac{y \cdot 5}{3} + \frac{- 5}{3} \cdot (3 \cdot - 4) - \frac{1}{9}$

Step 1.3.4

Rewrite the expression.

$- \frac{y \cdot 5}{3} - 5 \cdot - 4 - \frac{1}{9}$

Step 1.4

Multiply $- 5$ by $- 4$ .

$- \frac{y \cdot 5}{3} + 20 - \frac{1}{9}$

Step 1.5

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

$- \frac{5 y}{3} + 20 - \frac{1}{9}$

Step 2

To write $20$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{5 y}{3} + 20 \cdot \frac{9}{9} - \frac{1}{9}$

Step 3

Combine $20$ and $\frac{9}{9}$ .

$- \frac{5 y}{3} + \frac{20 \cdot 9}{9} - \frac{1}{9}$

Step 4

Combine the numerators over the common denominator.

$- \frac{5 y}{3} + \frac{20 \cdot 9 - 1}{9}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $20$ by $9$ .

$- \frac{5 y}{3} + \frac{180 - 1}{9}$

Step 5.2

Subtract $1$ from $180$ .

$- \frac{5 y}{3} + \frac{179}{9}$