Basic Math Examples

$130 = \frac{1}{2} \cdot (y (6 + 7))$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (y (6 + 7)) = 130$ .

$\frac{1}{2} \cdot (y (6 + 7)) = 130$

Step 2

Multiply both sides of the equation by $\frac{1}{\frac{1}{2} (6 + 7)}$ .

$\frac{1}{\frac{1}{2} (6 + 7)} (\frac{1}{2} \cdot (y (6 + 7))) = \frac{1}{\frac{1}{2} (6 + 7)} \cdot 130$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $\frac{1}{2} \cdot (6 + 7)$ .

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Step 3.1.1.1

Factor $\frac{1}{2} \cdot (6 + 7)$ out of $\frac{1}{2} \cdot (y (6 + 7))$ .

$\frac{1}{\frac{1}{2} (6 + 7)} (\frac{1}{2} (6 + 7) (y)) = \frac{1}{\frac{1}{2} (6 + 7)} \cdot 130$

Step 3.1.1.2

Cancel the common factor.

$\frac{1}{\frac{1}{2} (6 + 7)} (\frac{1}{2} (6 + 7) y) = \frac{1}{\frac{1}{2} (6 + 7)} \cdot 130$

Step 3.1.1.3

Rewrite the expression.

$y = \frac{1}{\frac{1}{2} (6 + 7)} \cdot 130$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{1}{\frac{1}{2} (6 + 7)} \cdot 130$ .

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Step 3.2.1.1

Add $6$ and $7$ .

$y = \frac{1}{\frac{1}{2} \cdot 13} \cdot 130$

Step 3.2.1.2

Combine $\frac{1}{2}$ and $13$ .

$y = \frac{1}{\frac{13}{2}} \cdot 130$

Step 3.2.1.3

Multiply the numerator by the reciprocal of the denominator.

$y = 1 (\frac{2}{13}) \cdot 130$

Step 3.2.1.4

Multiply $\frac{2}{13}$ by $1$ .

$y = \frac{2}{13} \cdot 130$

Step 3.2.1.5

Cancel the common factor of $13$ .

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Step 3.2.1.5.1

Factor $13$ out of $130$ .

$y = \frac{2}{13} \cdot (13 (10))$

Step 3.2.1.5.2

Cancel the common factor.

$y = \frac{2}{13} \cdot (13 \cdot 10)$

Step 3.2.1.5.3

Rewrite the expression.

$y = 2 \cdot 10$

Step 3.2.1.6

Multiply $2$ by $10$ .

$y = 20$