Pre-Algebra Examples

$1 : 5 = 2 : 10$

Step 1

Convert the ratio to a fraction by making the left side of the ratio the numerator and the right side the denominator.

$\frac{1}{5} = 2 : 10$

Step 2

Convert the ratio to a fraction by making the left side of the ratio the numerator and the right side the denominator.

$\frac{1}{5} = \frac{2}{10}$

Step 3

Cancel the common factor of $2$ and $10$ .

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Step 3.1

Factor $2$ out of $2$ .

$\frac{1}{5} = \frac{2 (1)}{10}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $10$ .

$\frac{1}{5} = \frac{2 \cdot 1}{2 \cdot 5}$

Step 3.2.2

Cancel the common factor.

$\frac{1}{5} = \frac{2 \cdot 1}{2 \cdot 5}$

Step 3.2.3

Rewrite the expression.

$\frac{1}{5} = \frac{1}{5}$

Step 4

Since $\frac{1}{5} = \frac{1}{5}$ , the equation will always be true.

Always true

Step 5

Since the fractional versions of the ratios are equal, the ratios are equivalent.

$1 : 5 = 2 : 10$