Solve for F K=5/9(F-32)+273.15

$K = \frac{5}{9} (F - 32) + 273.15$

Step 1

Rewrite the equation as $\frac{5}{9} \cdot (F - 32) + 273.15 = K$ .

$\frac{5}{9} \cdot (F - 32) + 273.15 = K$

Step 2

Simplify $\frac{5}{9} \cdot (F - 32) + 273.15$ .

Simplify each term.

Apply the distributive property.

$\frac{5}{9} F + \frac{5}{9} \cdot - 32 + 273.15 = K$

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

$\frac{5 F}{9} + \frac{5}{9} \cdot - 32 + 273.15 = K$

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

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

$\frac{5 F}{9} + \frac{5 \cdot - 32}{9} + 273.15 = K$

Multiply $5$ by $- 32$ .

$\frac{5 F}{9} + \frac{- 160}{9} + 273.15 = K$

Move the negative in front of the fraction.

$\frac{5 F}{9} - \frac{160}{9} + 273.15 = K$

To write $273.15$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{5 F}{9} - \frac{160}{9} + 273.15 \cdot \frac{9}{9} = K$

Combine $273.15$ and $\frac{9}{9}$ .

$\frac{5 F}{9} - \frac{160}{9} + \frac{273.15 \cdot 9}{9} = K$

Combine the numerators over the common denominator.

$\frac{5 F}{9} + \frac{- 160 + 273.15 \cdot 9}{9} = K$

Combine the numerators over the common denominator.

$\frac{5 F - 160 + 273.15 \cdot 9}{9} = K$

Simplify the expression.

Multiply $273.15$ by $9$ .

$\frac{5 F - 160 + 2458.35}{9} = K$

Add $- 160$ and $2458.35$ .

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

Factor $0.05$ out of $5 F + 2298.35$ .

Factor $0.05$ out of $5 F$ .

$\frac{0.05 (100 F) + 2298.35}{9} = K$

Factor $0.05$ out of $2298.35$ .

$\frac{0.05 (100 F) + 0.05 (45967)}{9} = K$

Factor $0.05$ out of $0.05 (100 F) + 0.05 (45967)$ .

$\frac{0.05 (100 F + 45967)}{9} = K$

Factor $9$ out of $9$ .

$\frac{0.05 (100 F + 45967)}{9 (1)} = K$

Separate fractions.

$\frac{0.05}{9} \cdot \frac{100 F + 45967}{1} = K$

Simplify the expression.

Divide $0.05$ by $9$ .

$0.00\overline{5} \frac{100 F + 45967}{1} = K$

Divide $100 F + 45967$ by $1$ .

$0.00\overline{5} (100 F + 45967) = K$

Apply the distributive property.

$0.00\overline{5} (100 F) + 0.00\overline{5} \cdot 45967 = K$

Multiply.

Multiply $100$ by $0.00\overline{5}$ .

$0.\overline{5} F + 0.00\overline{5} \cdot 45967 = K$

Multiply $0.00\overline{5}$ by $45967$ .

$0.\overline{5} F + 255.37222222 = K$

Step 3

Subtract $255.37222222$ from both sides of the equation.

$0.\overline{5} F = K - 255.37222222$

Step 4

Divide each term in $0.\overline{5} F = K - 255.37222222$ by $0.\overline{5}$ and simplify.

Divide each term in $0.\overline{5} F = K - 255.37222222$ by $0.\overline{5}$ .

$\frac{0.\overline{5} F}{0.\overline{5}} = \frac{K}{0.\overline{5}} + \frac{- 255.37222222}{0.\overline{5}}$

Simplify the left side.

Cancel the common factor of $0.\overline{5}$ .

Cancel the common factor.

$\frac{0.\overline{5} F}{0.\overline{5}} = \frac{K}{0.\overline{5}} + \frac{- 255.37222222}{0.\overline{5}}$

Divide $F$ by $1$ .

$F = \frac{K}{0.\overline{5}} + \frac{- 255.37222222}{0.\overline{5}}$

Simplify the right side.

Simplify each term.

Multiply by $1$ .

$F = \frac{1 K}{0.\overline{5}} + \frac{- 255.37222222}{0.\overline{5}}$

Factor $0.\overline{5}$ out of $0.\overline{5}$ .

$F = \frac{1 K}{0.\overline{5} (1)} + \frac{- 255.37222222}{0.\overline{5}}$

Separate fractions.

$F = \frac{1}{0.\overline{5}} \cdot \frac{K}{1} + \frac{- 255.37222222}{0.\overline{5}}$

Divide $1$ by $0.\overline{5}$ .

$F = 1.8 \frac{K}{1} + \frac{- 255.37222222}{0.\overline{5}}$

Divide $K$ by $1$ .

$F = 1.8 K + \frac{- 255.37222222}{0.\overline{5}}$

Divide $- 255.37222222$ by $0.\overline{5}$ .

$F = 1.8 K - 459.67$

Solve for F K=5/9(F-32)+273.15

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