Pre-Algebra Examples

$\frac{0.1}{x} = \frac{1.1}{110}$

Step 1

Divide $1.1$ by $110$ .

$\frac{0.1}{x} = 0.01$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

Step 2.2

The LCM of one and any expression is the expression.

$x$

Step 3

Multiply each term in $\frac{0.1}{x} = 0.01$ by $x$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{0.1}{x} = 0.01$ by $x$ .

$\frac{0.1}{x} x = 0.01 x$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.1$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.1}{x} x = 0.01 x$

Step 3.2.1.2

Rewrite the expression.

$\frac{1}{x} \cdot \frac{x}{10} = 0.01 x$

Step 3.2.2

Cancel the common factor of $x$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{1}{x} \cdot \frac{x}{10} = 0.01 x$

Step 3.2.2.2

Rewrite the expression.

$\frac{1}{10} = 0.01 x$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $0.01 x = \frac{1}{10}$ .

$0.01 x = \frac{1}{10}$

Step 4.2

Divide each term in $0.01 x = \frac{1}{10}$ by $0.01$ and simplify.

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Step 4.2.1

Divide each term in $0.01 x = \frac{1}{10}$ by $0.01$ .

$\frac{0.01 x}{0.01} = \frac{\frac{1}{10}}{0.01}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $0.01$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{0.01 x}{0.01} = \frac{\frac{1}{10}}{0.01}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{10}}{0.01}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{10} \cdot \frac{1}{0.01}$

Step 4.2.3.2

Cancel the common factor of $0.01$ .

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Step 4.2.3.2.1

Factor $0.01$ out of $1$ .

$x = \frac{0.01 (100)}{10} \cdot \frac{1}{0.01}$

Step 4.2.3.2.2

Cancel the common factor.

$x = \frac{0.01 \cdot 100}{10} \cdot \frac{1}{0.01}$

Step 4.2.3.2.3

Rewrite the expression.

$x = \frac{100}{10}$

Step 4.2.3.3

Divide $100$ by $10$ .

$x = 10$