Algebra Examples

$F = \frac{9}{5} (K - 273) + 32$

Step 1

Simplify $\frac{9}{5} \cdot (K - 273) + 32$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$F = \frac{9}{5} K + \frac{9}{5} \cdot - 273 + 32$

Step 1.1.2

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

$F = \frac{9 K}{5} + \frac{9}{5} \cdot - 273 + 32$

Step 1.1.3

Multiply $\frac{9}{5} \cdot - 273$ .

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Step 1.1.3.1

Combine $\frac{9}{5}$ and $- 273$ .

$F = \frac{9 K}{5} + \frac{9 \cdot - 273}{5} + 32$

Step 1.1.3.2

Multiply $9$ by $- 273$ .

$F = \frac{9 K}{5} + \frac{- 2457}{5} + 32$

Step 1.1.4

Move the negative in front of the fraction.

$F = \frac{9 K}{5} - \frac{2457}{5} + 32$

Step 1.2

To write $32$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$F = \frac{9 K}{5} - \frac{2457}{5} + 32 \cdot \frac{5}{5}$

Step 1.3

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

$F = \frac{9 K}{5} - \frac{2457}{5} + \frac{32 \cdot 5}{5}$

Step 1.4

Combine the numerators over the common denominator.

$F = \frac{9 K}{5} + \frac{- 2457 + 32 \cdot 5}{5}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $32$ by $5$ .

$F = \frac{9 K}{5} + \frac{- 2457 + 160}{5}$

Step 1.5.2

Add $- 2457$ and $160$ .

$F = \frac{9 K}{5} + \frac{- 2297}{5}$

Step 1.6

Move the negative in front of the fraction.

$F = \frac{9 K}{5} - \frac{2297}{5}$

Step 2

To rewrite as a function of $K$ , write the equation so that $F$ is by itself on one side of the equal sign and an expression involving only $K$ is on the other side.

$f (K) = \frac{9 K}{5} - \frac{2297}{5}$