Pre-Algebra Examples

$70 = 100 \cdot (\frac{16}{x})$

Step 1

Rewrite the equation as $100 \cdot \frac{16}{x} = 70$ .

$100 \cdot \frac{16}{x} = 70$

Step 2

Multiply $100 \frac{16}{x}$ .

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Step 2.1

Combine $100$ and $\frac{16}{x}$ .

$\frac{100 \cdot 16}{x} = 70$

Step 2.2

Multiply $100$ by $16$ .

$\frac{1600}{x} = 70$

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 $\frac{1600}{x} = 70$ by $x$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{1600}{x} = 70$ by $x$ .

$\frac{1600}{x} x = 70 x$

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.

$\frac{1600}{x} x = 70 x$

Step 4.2.1.2

Rewrite the expression.

$1600 = 70 x$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $70 x = 1600$ .

$70 x = 1600$

Step 5.2

Divide each term in $70 x = 1600$ by $70$ and simplify.

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Step 5.2.1

Divide each term in $70 x = 1600$ by $70$ .

$\frac{70 x}{70} = \frac{1600}{70}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $70$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{70 x}{70} = \frac{1600}{70}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1600}{70}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Cancel the common factor of $1600$ and $70$ .

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Step 5.2.3.1.1

Factor $10$ out of $1600$ .

$x = \frac{10 (160)}{70}$

Step 5.2.3.1.2

Cancel the common factors.

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Step 5.2.3.1.2.1

Factor $10$ out of $70$ .

$x = \frac{10 \cdot 160}{10 \cdot 7}$

Step 5.2.3.1.2.2

Cancel the common factor.

$x = \frac{10 \cdot 160}{10 \cdot 7}$

Step 5.2.3.1.2.3

Rewrite the expression.

$x = \frac{160}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{160}{7}$

Decimal Form:

$x = 22.85714285 \dots$

Mixed Number Form:

$x = 22 \frac{6}{7}$