Pre-Algebra Examples

$45 = \frac{9}{5} c + 32$

Step 1

Rewrite the equation as $\frac{9}{5} c + 32 = 45$ .

$\frac{9}{5} c + 32 = 45$

Step 2

Combine $\frac{9}{5}$ and $c$ .

$\frac{9 c}{5} + 32 = 45$

Step 3

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

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Step 3.1

Subtract $32$ from both sides of the equation.

$\frac{9 c}{5} = 45 - 32$

Step 3.2

Subtract $32$ from $45$ .

$\frac{9 c}{5} = 13$

Step 4

Multiply both sides of the equation by $\frac{5}{9}$ .

$\frac{5}{9} \cdot \frac{9 c}{5} = \frac{5}{9} \cdot 13$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{5}{9} \cdot \frac{9 c}{5}$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{9} \cdot \frac{9 c}{5} = \frac{5}{9} \cdot 13$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 c) = \frac{5}{9} \cdot 13$

Step 5.1.1.2

Cancel the common factor of $9$ .

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Step 5.1.1.2.1

Factor $9$ out of $9 c$ .

$\frac{1}{9} (9 (c)) = \frac{5}{9} \cdot 13$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 c) = \frac{5}{9} \cdot 13$

Step 5.1.1.2.3

Rewrite the expression.

$c = \frac{5}{9} \cdot 13$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{5}{9} \cdot 13$ .

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Step 5.2.1.1

Combine $\frac{5}{9}$ and $13$ .

$c = \frac{5 \cdot 13}{9}$

Step 5.2.1.2

Multiply $5$ by $13$ .

$c = \frac{65}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$c = \frac{65}{9}$

Decimal Form:

$c = 7.\overline{2}$

Mixed Number Form:

$c = 7 \frac{2}{9}$