Pre-Algebra Examples

$\frac{5}{9} \cdot (f - 32) = 25$

Step 1

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

$\frac{9}{5} (\frac{5}{9} \cdot (f - 32)) = \frac{9}{5} \cdot 25$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

$\frac{9}{5} (\frac{5}{9} f + \frac{5}{9} \cdot - 32) = \frac{9}{5} \cdot 25$

Step 2.1.1.2

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

$\frac{9}{5} (\frac{5 f}{9} + \frac{5}{9} \cdot - 32) = \frac{9}{5} \cdot 25$

Step 2.1.1.3

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

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Step 2.1.1.3.1

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

$\frac{9}{5} (\frac{5 f}{9} + \frac{5 \cdot - 32}{9}) = \frac{9}{5} \cdot 25$

Step 2.1.1.3.2

Multiply $5$ by $- 32$ .

$\frac{9}{5} (\frac{5 f}{9} + \frac{- 160}{9}) = \frac{9}{5} \cdot 25$

Step 2.1.1.4

Move the negative in front of the fraction.

$\frac{9}{5} (\frac{5 f}{9} - \frac{160}{9}) = \frac{9}{5} \cdot 25$

Step 2.1.1.5

Apply the distributive property.

$\frac{9}{5} \cdot \frac{5 f}{9} + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 25$

Step 2.1.1.6

Cancel the common factor of $9$ .

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Step 2.1.1.6.1

Cancel the common factor.

$\frac{9}{5} \cdot \frac{5 f}{9} + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 25$

Step 2.1.1.6.2

Rewrite the expression.

$\frac{1}{5} (5 f) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 25$

Step 2.1.1.7

Cancel the common factor of $5$ .

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Step 2.1.1.7.1

Factor $5$ out of $5 f$ .

$\frac{1}{5} (5 (f)) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 25$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{1}{5} (5 f) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 25$

Step 2.1.1.7.3

Rewrite the expression.

$f + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot 25$

Step 2.1.1.8

Cancel the common factor of $9$ .

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Step 2.1.1.8.1

Move the leading negative in $- \frac{160}{9}$ into the numerator.

$f + \frac{9}{5} \cdot \frac{- 160}{9} = \frac{9}{5} \cdot 25$

Step 2.1.1.8.2

Cancel the common factor.

$f + \frac{9}{5} \cdot \frac{- 160}{9} = \frac{9}{5} \cdot 25$

Step 2.1.1.8.3

Rewrite the expression.

$f + \frac{1}{5} \cdot - 160 = \frac{9}{5} \cdot 25$

Step 2.1.1.9

Cancel the common factor of $5$ .

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Step 2.1.1.9.1

Factor $5$ out of $- 160$ .

$f + \frac{1}{5} \cdot (5 (- 32)) = \frac{9}{5} \cdot 25$

Step 2.1.1.9.2

Cancel the common factor.

$f + \frac{1}{5} \cdot (5 \cdot - 32) = \frac{9}{5} \cdot 25$

Step 2.1.1.9.3

Rewrite the expression.

$f - 32 = \frac{9}{5} \cdot 25$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{9}{5} \cdot 25$ .

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Step 2.2.1.1

Cancel the common factor of $5$ .

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Step 2.2.1.1.1

Factor $5$ out of $25$ .

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

Step 2.2.1.1.2

Cancel the common factor.

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

Step 2.2.1.1.3

Rewrite the expression.

$f - 32 = 9 \cdot 5$

Step 2.2.1.2

Multiply $9$ by $5$ .

$f - 32 = 45$

Step 3

Move all terms not containing $f$ to the right side of the equation.

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Step 3.1

Add $32$ to both sides of the equation.

$f = 45 + 32$

Step 3.2

Add $45$ and $32$ .

$f = 77$