Basic Math Examples

$9 - y = 2 \frac{1}{2}$

Step 1

Simplify the right side.

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Step 1.1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$9 - y = 2 + \frac{1}{2}$

Step 1.1.2

Add $2$ and $\frac{1}{2}$ .

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Step 1.1.2.1

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

$9 - y = 2 \cdot \frac{2}{2} + \frac{1}{2}$

Step 1.1.2.2

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

$9 - y = \frac{2 \cdot 2}{2} + \frac{1}{2}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$9 - y = \frac{2 \cdot 2 + 1}{2}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $2$ .

$9 - y = \frac{4 + 1}{2}$

Step 1.1.2.4.2

Add $4$ and $1$ .

$9 - y = \frac{5}{2}$

Step 2

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

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Step 2.1

Subtract $9$ from both sides of the equation.

$- y = \frac{5}{2} - 9$

Step 2.2

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- y = \frac{5}{2} - 9 \cdot \frac{2}{2}$

Step 2.3

Combine $- 9$ and $\frac{2}{2}$ .

$- y = \frac{5}{2} + \frac{- 9 \cdot 2}{2}$

Step 2.4

Combine the numerators over the common denominator.

$- y = \frac{5 - 9 \cdot 2}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 9$ by $2$ .

$- y = \frac{5 - 18}{2}$

Step 2.5.2

Subtract $18$ from $5$ .

$- y = \frac{- 13}{2}$

Step 2.6

Move the negative in front of the fraction.

$- y = - \frac{13}{2}$

Step 3

Divide each term in $- y = - \frac{13}{2}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = - \frac{13}{2}$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- \frac{13}{2}}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- \frac{13}{2}}{- 1}$

Step 3.2.2

Divide $y$ by $1$ .

$y = \frac{- \frac{13}{2}}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

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

Step 3.3.2

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 6.5$

Mixed Number Form:

$y = 6 \frac{1}{2}$