Pre-Algebra Examples

$\frac{7}{\frac{1}{5}} = \frac{20}{x}$

Step 1

Rewrite the equation as $\frac{20}{x} = \frac{7}{\frac{1}{5}}$ .

$\frac{20}{x} = \frac{7}{\frac{1}{5}}$

Step 2

Factor each term.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{20}{x} = 7 \cdot 5$

Step 2.2

Multiply $7$ by $5$ .

$\frac{20}{x} = 35$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

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

$x, 1$

Step 3.2

The LCM of one and any expression is the expression.

$x$

Step 4

Multiply each term in $\frac{20}{x} = 35$ by $x$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{20}{x} = 35$ by $x$ .

$\frac{20}{x} x = 35 x$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{20}{x} x = 35 x$

Step 4.2.1.2

Rewrite the expression.

$20 = 35 x$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $35 x = 20$ .

$35 x = 20$

Step 5.2

Divide each term in $35 x = 20$ by $35$ and simplify.

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Step 5.2.1

Divide each term in $35 x = 20$ by $35$ .

$\frac{35 x}{35} = \frac{20}{35}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $35$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{35 x}{35} = \frac{20}{35}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{20}{35}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Cancel the common factor of $20$ and $35$ .

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Step 5.2.3.1.1

Factor $5$ out of $20$ .

$x = \frac{5 (4)}{35}$

Step 5.2.3.1.2

Cancel the common factors.

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Step 5.2.3.1.2.1

Factor $5$ out of $35$ .

$x = \frac{5 \cdot 4}{5 \cdot 7}$

Step 5.2.3.1.2.2

Cancel the common factor.

$x = \frac{5 \cdot 4}{5 \cdot 7}$

Step 5.2.3.1.2.3

Rewrite the expression.

$x = \frac{4}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{7}$

Decimal Form:

$x = 0.\overline{571428}$