Basic Math Examples

$3 y - 2 (y + 5) - 6 \div 2$

Step 1

Find the common denominator.

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Step 1.1

Write $3 y$ as a fraction with denominator $1$ .

$\frac{3 y}{1} - 2 (y + 5) - 6 \div 2$

Step 1.2

Multiply $\frac{3 y}{1}$ by $\frac{2}{2}$ .

$\frac{3 y}{1} \cdot \frac{2}{2} - 2 (y + 5) - 6 \div 2$

Step 1.3

Multiply $\frac{3 y}{1}$ by $\frac{2}{2}$ .

$\frac{3 y \cdot 2}{2} - 2 (y + 5) - 6 \div 2$

Step 1.4

Write $- 2 (y + 5)$ as a fraction with denominator $1$ .

$\frac{3 y \cdot 2}{2} + \frac{- 2 (y + 5)}{1} - 6 \div 2$

Step 1.5

Multiply $\frac{- 2 (y + 5)}{1}$ by $\frac{2}{2}$ .

$\frac{3 y \cdot 2}{2} + \frac{- 2 (y + 5)}{1} \cdot \frac{2}{2} - 6 \div 2$

Step 1.6

Multiply $\frac{- 2 (y + 5)}{1}$ by $\frac{2}{2}$ .

$\frac{3 y \cdot 2}{2} + \frac{- 2 (y + 5) \cdot 2}{2} - 6 \div 2$

Step 2

Combine the numerators over the common denominator.

$\frac{3 y \cdot 2 - 2 (y + 5) \cdot 2 - 6}{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $3$ .

$\frac{6 y - 2 (y + 5) \cdot 2 - 6}{2}$

Step 3.2

Apply the distributive property.

$\frac{6 y + (- 2 y - 2 \cdot 5) \cdot 2 - 6}{2}$

Step 3.3

Multiply $- 2$ by $5$ .

$\frac{6 y + (- 2 y - 10) \cdot 2 - 6}{2}$

Step 3.4

Apply the distributive property.

$\frac{6 y - 2 y \cdot 2 - 10 \cdot 2 - 6}{2}$

Step 3.5

Multiply $2$ by $- 2$ .

$\frac{6 y - 4 y - 10 \cdot 2 - 6}{2}$

Step 3.6

Multiply $- 10$ by $2$ .

$\frac{6 y - 4 y - 20 - 6}{2}$

Step 4

Simplify terms.

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Step 4.1

Subtract $4 y$ from $6 y$ .

$\frac{2 y - 20 - 6}{2}$

Step 4.2

Subtract $6$ from $- 20$ .

$\frac{2 y - 26}{2}$

Step 4.3

Cancel the common factor of $2 y - 26$ and $2$ .

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Step 4.3.1

Factor $2$ out of $2 y$ .

$\frac{2 (y) - 26}{2}$

Step 4.3.2

Factor $2$ out of $- 26$ .

$\frac{2 (y) + 2 \cdot - 13}{2}$

Step 4.3.3

Factor $2$ out of $2 (y) + 2 (- 13)$ .

$\frac{2 (y - 13)}{2}$

Step 4.3.4

Cancel the common factors.

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Step 4.3.4.1

Factor $2$ out of $2$ .

$\frac{2 (y - 13)}{2 (1)}$

Step 4.3.4.2

Cancel the common factor.

$\frac{2 (y - 13)}{2 \cdot 1}$

Step 4.3.4.3

Rewrite the expression.

$\frac{y - 13}{1}$

Step 4.3.4.4

Divide $y - 13$ by $1$ .

$y - 13$