Basic Math Examples

$13.5 - \frac{1}{2} y + \frac{1}{3} y = 11$

Step 1

Simplify $13.5 - \frac{1}{2} y + \frac{1}{3} y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$13.5 - \frac{y}{2} + \frac{1}{3} y = 11$

Step 1.1.2

Combine $\frac{1}{3}$ and $y$ .

$13.5 - \frac{y}{2} + \frac{y}{3} = 11$

Step 1.2

To write $- \frac{y}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$13.5 - \frac{y}{2} \cdot \frac{3}{3} + \frac{y}{3} = 11$

Step 1.3

To write $\frac{y}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$13.5 - \frac{y}{2} \cdot \frac{3}{3} + \frac{y}{3} \cdot \frac{2}{2} = 11$

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

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

$13.5 - \frac{y \cdot 3}{2 \cdot 3} + \frac{y}{3} \cdot \frac{2}{2} = 11$

Step 1.4.2

Multiply $2$ by $3$ .

$13.5 - \frac{y \cdot 3}{6} + \frac{y}{3} \cdot \frac{2}{2} = 11$

Step 1.4.3

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

$13.5 - \frac{y \cdot 3}{6} + \frac{y \cdot 2}{3 \cdot 2} = 11$

Step 1.4.4

Multiply $3$ by $2$ .

$13.5 - \frac{y \cdot 3}{6} + \frac{y \cdot 2}{6} = 11$

Step 1.5

Combine the numerators over the common denominator.

$13.5 + \frac{- y \cdot 3 + y \cdot 2}{6} = 11$

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $y$ out of $- y \cdot 3 + y \cdot 2$ .

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Step 1.6.1.1.1

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

$13.5 + \frac{y (- 1 \cdot 3) + y \cdot 2}{6} = 11$

Step 1.6.1.1.2

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

$13.5 + \frac{y (- 1 \cdot 3) + y (2)}{6} = 11$

Step 1.6.1.1.3

Factor $y$ out of $y (- 1 \cdot 3) + y (2)$ .

$13.5 + \frac{y (- 1 \cdot 3 + 2)}{6} = 11$

Step 1.6.1.2

Multiply $- 1$ by $3$ .

$13.5 + \frac{y (- 3 + 2)}{6} = 11$

Step 1.6.1.3

Add $- 3$ and $2$ .

$13.5 + \frac{y \cdot - 1}{6} = 11$

Step 1.6.2

Move $- 1$ to the left of $y$ .

$13.5 + \frac{- 1 \cdot y}{6} = 11$

Step 1.6.3

Move the negative in front of the fraction.

$13.5 - \frac{y}{6} = 11$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Subtract $13.5$ from both sides of the equation.

$- \frac{y}{6} = 11 - 13.5$

Step 2.2

Subtract $13.5$ from $11$ .

$- \frac{y}{6} = - 2.5$

Step 3

Multiply both sides of the equation by $- 6$ .

$- 6 (- \frac{y}{6}) = - 6 \cdot - 2.5$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 6 (- \frac{y}{6})$ .

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Step 4.1.1.1

Cancel the common factor of $6$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{y}{6}$ into the numerator.

$- 6 \frac{- y}{6} = - 6 \cdot - 2.5$

Step 4.1.1.1.2

Factor $6$ out of $- 6$ .

$6 (- 1) \frac{- y}{6} = - 6 \cdot - 2.5$

Step 4.1.1.1.3

Cancel the common factor.

$6 \cdot - 1 \frac{- y}{6} = - 6 \cdot - 2.5$

Step 4.1.1.1.4

Rewrite the expression.

$- - y = - 6 \cdot - 2.5$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 6 \cdot - 2.5$

Step 4.1.1.2.2

Multiply $y$ by $1$ .

$y = - 6 \cdot - 2.5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 6$ by $- 2.5$ .

$y = 15$