Algebra Examples

$K = \frac{5}{9} (F + 459.67)$

Step 1

Rewrite the equation as $\frac{5}{9} \cdot (F + 459.67) = K$ .

$\frac{5}{9} \cdot (F + 459.67) = K$

Step 2

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

$\frac{9}{5} (\frac{5}{9} \cdot (F + 459.67)) = \frac{9}{5} K$

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

Simplify $\frac{9}{5} (\frac{5}{9} \cdot (F + 459.67))$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{9}{5} (\frac{5}{9} F + \frac{5}{9} \cdot 459.67) = \frac{9}{5} K$

Step 3.1.1.2

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

$\frac{9}{5} (\frac{5 F}{9} + \frac{5}{9} \cdot 459.67) = \frac{9}{5} K$

Step 3.1.1.3

Multiply $\frac{5}{9} \cdot 459.67$ .

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Step 3.1.1.3.1

Combine $\frac{5}{9}$ and $459.67$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{5 \cdot 459.67}{9}) = \frac{9}{5} K$

Step 3.1.1.3.2

Multiply $5$ by $459.67$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{2298.35}{9}) = \frac{9}{5} K$

Step 3.1.1.4

Divide $2298.35$ by $9$ .

$\frac{9}{5} (\frac{5 F}{9} + 255.37\overline{2}) = \frac{9}{5} K$

Step 3.1.1.5

Apply the distributive property.

$\frac{9}{5} \cdot \frac{5 F}{9} + \frac{9}{5} \cdot 255.37\overline{2} = \frac{9}{5} K$

Step 3.1.1.6

Cancel the common factor of $9$ .

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Step 3.1.1.6.1

Cancel the common factor.

$\frac{9}{5} \cdot \frac{5 F}{9} + \frac{9}{5} \cdot 255.37\overline{2} = \frac{9}{5} K$

Step 3.1.1.6.2

Rewrite the expression.

$\frac{1}{5} (5 F) + \frac{9}{5} \cdot 255.37\overline{2} = \frac{9}{5} K$

Step 3.1.1.7

Cancel the common factor of $5$ .

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Step 3.1.1.7.1

Factor $5$ out of $5 F$ .

$\frac{1}{5} (5 (F)) + \frac{9}{5} \cdot 255.37\overline{2} = \frac{9}{5} K$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{1}{5} (5 F) + \frac{9}{5} \cdot 255.37\overline{2} = \frac{9}{5} K$

Step 3.1.1.7.3

Rewrite the expression.

$F + \frac{9}{5} \cdot 255.37\overline{2} = \frac{9}{5} K$

Step 3.1.1.8

Multiply $\frac{9}{5} \cdot 255.37\overline{2}$ .

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Step 3.1.1.8.1

Combine $\frac{9}{5}$ and $255.37\overline{2}$ .

$F + \frac{9 \cdot 255.37\overline{2}}{5} = \frac{9}{5} K$

Step 3.1.1.8.2

Multiply $9$ by $255.37\overline{2}$ .

$F + \frac{2298.35}{5} = \frac{9}{5} K$

Step 3.1.1.9

Divide $2298.35$ by $5$ .

$F + 459.67 = \frac{9}{5} K$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

$F + 459.67 = \frac{9 K}{5}$

Step 4

Subtract $459.67$ from both sides of the equation.

$F = \frac{9 K}{5} - 459.67$