Basic Math Examples

$\frac{5}{9} \cdot (f - 32) = - 14$

Step 1

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

$\frac{9}{5} (\frac{5}{9} \cdot (f - 32)) = \frac{9}{5} \cdot - 14$

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.

$\frac{9}{5} (\frac{5}{9} f + \frac{5}{9} \cdot - 32) = \frac{9}{5} \cdot - 14$

Step 2.1.1.2

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

$\frac{9}{5} (\frac{5 f}{9} + \frac{5}{9} \cdot - 32) = \frac{9}{5} \cdot - 14$

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 $- 32$ .

$\frac{9}{5} (\frac{5 f}{9} + \frac{5 \cdot - 32}{9}) = \frac{9}{5} \cdot - 14$

Step 2.1.1.3.2

Multiply $5$ by $- 32$ .

$\frac{9}{5} (\frac{5 f}{9} + \frac{- 160}{9}) = \frac{9}{5} \cdot - 14$

Step 2.1.1.4

Move the negative in front of the fraction.

$\frac{9}{5} (\frac{5 f}{9} - \frac{160}{9}) = \frac{9}{5} \cdot - 14$

Step 2.1.1.5

Apply the distributive property.

$\frac{9}{5} \cdot \frac{5 f}{9} + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot - 14$

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.

$\frac{9}{5} \cdot \frac{5 f}{9} + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot - 14$

Step 2.1.1.6.2

Rewrite the expression.

$\frac{1}{5} (5 f) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot - 14$

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 $5 f$ .

$\frac{1}{5} (5 (f)) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot - 14$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{1}{5} (5 f) + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot - 14$

Step 2.1.1.7.3

Rewrite the expression.

$f + \frac{9}{5} (- \frac{160}{9}) = \frac{9}{5} \cdot - 14$

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.

$f + \frac{9}{5} \cdot \frac{- 160}{9} = \frac{9}{5} \cdot - 14$

Step 2.1.1.8.2

Cancel the common factor.

$f + \frac{9}{5} \cdot \frac{- 160}{9} = \frac{9}{5} \cdot - 14$

Step 2.1.1.8.3

Rewrite the expression.

$f + \frac{1}{5} \cdot - 160 = \frac{9}{5} \cdot - 14$

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 $- 160$ .

$f + \frac{1}{5} \cdot (5 (- 32)) = \frac{9}{5} \cdot - 14$

Step 2.1.1.9.2

Cancel the common factor.

$f + \frac{1}{5} \cdot (5 \cdot - 32) = \frac{9}{5} \cdot - 14$

Step 2.1.1.9.3

Rewrite the expression.

$f - 32 = \frac{9}{5} \cdot - 14$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{9}{5} \cdot - 14$ .

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Step 2.2.1.1

Multiply $\frac{9}{5} \cdot - 14$ .

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Step 2.2.1.1.1

Combine $\frac{9}{5}$ and $- 14$ .

$f - 32 = \frac{9 \cdot - 14}{5}$

Step 2.2.1.1.2

Multiply $9$ by $- 14$ .

$f - 32 = \frac{- 126}{5}$

Step 2.2.1.2

Move the negative in front of the fraction.

$f - 32 = - \frac{126}{5}$

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.

$f = - \frac{126}{5} + 32$

Step 3.2

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

$f = - \frac{126}{5} + 32 \cdot \frac{5}{5}$

Step 3.3

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

$f = - \frac{126}{5} + \frac{32 \cdot 5}{5}$

Step 3.4

Combine the numerators over the common denominator.

$f = \frac{- 126 + 32 \cdot 5}{5}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $32$ by $5$ .

$f = \frac{- 126 + 160}{5}$

Step 3.5.2

Add $- 126$ and $160$ .

$f = \frac{34}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$f = \frac{34}{5}$

Decimal Form:

$f = 6.8$

Mixed Number Form:

$f = 6 \frac{4}{5}$