Algebra Examples

$F = \frac{5}{9} C + 32$ for $C$

Step 1

Rewrite the equation as $\frac{5}{9} C + 32 = F$ .

$\frac{5}{9} C + 32 = F$

Step 2

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

$\frac{5 C}{9} + 32 = F$

Step 3

Subtract $32$ from both sides of the equation.

$\frac{5 C}{9} = F - 32$

Step 4

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

$\frac{9}{5} \cdot \frac{5 C}{9} = \frac{9}{5} (F - 32)$

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 $\frac{9}{5} \cdot \frac{5 C}{9}$ .

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Step 5.1.1.1

Cancel the common factor of $9$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{9}{5} \cdot \frac{5 C}{9} = \frac{9}{5} (F - 32)$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 C) = \frac{9}{5} (F - 32)$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $5 C$ .

$\frac{1}{5} (5 (C)) = \frac{9}{5} (F - 32)$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 C) = \frac{9}{5} (F - 32)$

Step 5.1.1.2.3

Rewrite the expression.

$C = \frac{9}{5} (F - 32)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{9}{5} (F - 32)$ .

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Step 5.2.1.1

Apply the distributive property.

$C = \frac{9}{5} F + \frac{9}{5} \cdot - 32$

Step 5.2.1.2

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

$C = \frac{9 F}{5} + \frac{9}{5} \cdot - 32$

Step 5.2.1.3

Multiply $\frac{9}{5} \cdot - 32$ .

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Step 5.2.1.3.1

Combine $\frac{9}{5}$ and $- 32$ .

$C = \frac{9 F}{5} + \frac{9 \cdot - 32}{5}$

Step 5.2.1.3.2

Multiply $9$ by $- 32$ .

$C = \frac{9 F}{5} + \frac{- 288}{5}$

Step 5.2.1.4

Move the negative in front of the fraction.

$C = \frac{9 F}{5} - \frac{288}{5}$