Solve for f k=5/9(f-32)+273

$k = \frac{5}{9} (f - 32) + 273$

Rewrite the equation as $\frac{5}{9} \cdot (f - 32) + 273 = k$ .

$\frac{5}{9} \cdot (f - 32) + 273 = k$

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

Simplify each term.

Apply the distributive property.

$\frac{5}{9} f + \frac{5}{9} \cdot - 32 + 273 = k$

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

$\frac{5 f}{9} + \frac{5}{9} \cdot - 32 + 273 = k$

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

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

$\frac{5 f}{9} + \frac{5 \cdot - 32}{9} + 273 = k$

Multiply $5$ by $- 32$ .

$\frac{5 f}{9} + \frac{- 160}{9} + 273 = k$

Move the negative in front of the fraction.

$\frac{5 f}{9} - \frac{160}{9} + 273 = k$

To write $273$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{5 f}{9} - \frac{160}{9} + 273 \cdot \frac{9}{9} = k$

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

$\frac{5 f}{9} - \frac{160}{9} + \frac{273 \cdot 9}{9} = k$

Combine the numerators over the common denominator.

$\frac{5 f}{9} + \frac{- 160 + 273 \cdot 9}{9} = k$

Simplify the numerator.

Multiply $273$ by $9$ .

$\frac{5 f}{9} + \frac{- 160 + 2457}{9} = k$

Add $- 160$ and $2457$ .

$\frac{5 f}{9} + \frac{2297}{9} = k$

Subtract $\frac{2297}{9}$ from both sides of the equation.

$\frac{5 f}{9} = k - \frac{2297}{9}$

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

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

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $9$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{5} (5 f) = \frac{9}{5} (k - \frac{2297}{9})$

Cancel the common factor of $5$ .

Factor $5$ out of $5 f$ .

$\frac{1}{5} (5 (f)) = \frac{9}{5} (k - \frac{2297}{9})$

Cancel the common factor.

$\frac{1}{5} (5 f) = \frac{9}{5} (k - \frac{2297}{9})$

Rewrite the expression.

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

Simplify the right side.

Simplify $\frac{9}{5} (k - \frac{2297}{9})$ .

Apply the distributive property.

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

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

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

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{2297}{9}$ into the numerator.

$f = \frac{9 k}{5} + \frac{9}{5} \cdot \frac{- 2297}{9}$

Cancel the common factor.

$f = \frac{9 k}{5} + \frac{9}{5} \cdot \frac{- 2297}{9}$

Rewrite the expression.

$f = \frac{9 k}{5} + \frac{1}{5} \cdot - 2297$

Combine $\frac{1}{5}$ and $- 2297$ .

$f = \frac{9 k}{5} + \frac{- 2297}{5}$

Move the negative in front of the fraction.

$f = \frac{9 k}{5} - \frac{2297}{5}$

Solve for f k=5/9(f-32)+273

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