Pre-Algebra Examples

$175.5 = 19 \frac{1}{2} \cdot x$

Step 1

Simplify the right side.

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Step 1.1

Simplify $19 \frac{1}{2} \cdot x$ .

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Step 1.1.1

Convert $19 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$175.5 = (19 + \frac{1}{2}) \cdot x$

Step 1.1.1.2

Add $19$ and $\frac{1}{2}$ .

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Step 1.1.1.2.1

To write $19$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$175.5 = (19 \cdot \frac{2}{2} + \frac{1}{2}) \cdot x$

Step 1.1.1.2.2

Combine $19$ and $\frac{2}{2}$ .

$175.5 = (\frac{19 \cdot 2}{2} + \frac{1}{2}) \cdot x$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$175.5 = \frac{19 \cdot 2 + 1}{2} \cdot x$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $19$ by $2$ .

$175.5 = \frac{38 + 1}{2} \cdot x$

Step 1.1.1.2.4.2

Add $38$ and $1$ .

$175.5 = \frac{39}{2} \cdot x$

Step 1.1.2

Combine $\frac{39}{2}$ and $x$ .

$175.5 = \frac{39 x}{2}$

Step 2

Rewrite the equation as $\frac{39 x}{2} = 175.5$ .

$\frac{39 x}{2} = 175.5$

Step 3

Multiply both sides of the equation by $\frac{2}{39}$ .

$\frac{2}{39} \cdot \frac{39 x}{2} = \frac{2}{39} \cdot 175.5$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{2}{39} \cdot \frac{39 x}{2}$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2}{39} \cdot \frac{39 x}{2} = \frac{2}{39} \cdot 175.5$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{39} (39 x) = \frac{2}{39} \cdot 175.5$

Step 4.1.1.2

Cancel the common factor of $39$ .

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Step 4.1.1.2.1

Factor $39$ out of $39 x$ .

$\frac{1}{39} (39 (x)) = \frac{2}{39} \cdot 175.5$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{39} (39 x) = \frac{2}{39} \cdot 175.5$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{2}{39} \cdot 175.5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{2}{39} \cdot 175.5$ .

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Step 4.2.1.1

Multiply $\frac{2}{39} \cdot 175.5$ .

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Step 4.2.1.1.1

Combine $\frac{2}{39}$ and $175.5$ .

$x = \frac{2 \cdot 175.5}{39}$

Step 4.2.1.1.2

Multiply $2$ by $175.5$ .

$x = \frac{351}{39}$

Step 4.2.1.2

Divide $351$ by $39$ .

$x = 9$