Pre-Algebra Examples

$\frac{1^{\frac{1}{8}}}{4.5} = \frac{2 \frac{7}{16}}{x}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{1^{\frac{1}{8}}}{4.5}$ .

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Step 1.1.1

One to any power is one.

$\frac{1}{4.5} = \frac{2 \frac{7}{16}}{x}$

Step 1.1.2

Divide $1$ by $4.5$ .

$0.\overline{2} = \frac{2 \frac{7}{16}}{x}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\frac{2 \frac{7}{16}}{x}$ .

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Step 2.1.1

Convert $2 \frac{7}{16}$ to an improper fraction.

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Step 2.1.1.1

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

$0.\overline{2} = \frac{2 + \frac{7}{16}}{x}$

Step 2.1.1.2

Add $2$ and $\frac{7}{16}$ .

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Step 2.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$0.\overline{2} = \frac{2 \cdot \frac{16}{16} + \frac{7}{16}}{x}$

Step 2.1.1.2.2

Combine $2$ and $\frac{16}{16}$ .

$0.\overline{2} = \frac{\frac{2 \cdot 16}{16} + \frac{7}{16}}{x}$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$0.\overline{2} = \frac{\frac{2 \cdot 16 + 7}{16}}{x}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $2$ by $16$ .

$0.\overline{2} = \frac{\frac{32 + 7}{16}}{x}$

Step 2.1.1.2.4.2

Add $32$ and $7$ .

$0.\overline{2} = \frac{\frac{39}{16}}{x}$

Step 2.1.2

Multiply the numerator by the reciprocal of the denominator.

$0.\overline{2} = \frac{39}{16} \cdot \frac{1}{x}$

Step 2.1.3

Multiply $\frac{39}{16}$ by $\frac{1}{x}$ .

$0.\overline{2} = \frac{39}{16 x}$

Step 3

Rewrite the equation as $\frac{39}{16 x} = 0.\overline{2}$ .

$\frac{39}{16 x} = 0.\overline{2}$

Step 4

Find the LCD of the terms in the equation.

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Step 4.1

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

$16 x, 1$

Step 4.2

The LCM of one and any expression is the expression.

$16 x$

Step 5

Multiply each term in $\frac{39}{16 x} = 0.\overline{2}$ by $16 x$ to eliminate the fractions.

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Step 5.1

Multiply each term in $\frac{39}{16 x} = 0.\overline{2}$ by $16 x$ .

$\frac{39}{16 x} (16 x) = 0.\overline{2} (16 x)$

Step 5.2

Simplify the left side.

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Step 5.2.1

Rewrite using the commutative property of multiplication.

$16 \frac{39}{16 x} x = 0.\overline{2} (16 x)$

Step 5.2.2

Cancel the common factor of $16$ .

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Step 5.2.2.1

Factor $16$ out of $16 x$ .

$16 \frac{39}{16 (x)} x = 0.\overline{2} (16 x)$

Step 5.2.2.2

Cancel the common factor.

$16 \frac{39}{16 x} x = 0.\overline{2} (16 x)$

Step 5.2.2.3

Rewrite the expression.

$\frac{39}{x} x = 0.\overline{2} (16 x)$

Step 5.2.3

Cancel the common factor of $x$ .

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Step 5.2.3.1

Cancel the common factor.

$\frac{39}{x} x = 0.\overline{2} (16 x)$

Step 5.2.3.2

Rewrite the expression.

$39 = 0.\overline{2} (16 x)$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply $16$ by $0.\overline{2}$ .

$39 = 3.\overline{5} x$

Step 6

Solve the equation.

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Step 6.1

Rewrite the equation as $3.\overline{5} x = 39$ .

$3.\overline{5} x = 39$

Step 6.2

Divide each term in $3.\overline{5} x = 39$ by $3.\overline{5}$ and simplify.

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Step 6.2.1

Divide each term in $3.\overline{5} x = 39$ by $3.\overline{5}$ .

$\frac{3.\overline{5} x}{3.\overline{5}} = \frac{39}{3.\overline{5}}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $3.\overline{5}$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{3.\overline{5} x}{3.\overline{5}} = \frac{39}{3.\overline{5}}$

Step 6.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{39}{3.\overline{5}}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $39$ by $3.\overline{5}$ .

$x = 10.96875$