What fractions are equal to 8/12?

Understand the Problem

The question is asking for fractions that are equivalent to 8/12. To find equivalent fractions, we can multiply both the numerator and denominator of 8/12 by the same non-zero integer.

Answer

Some equivalent fractions for $\frac{8}{12}$ are $\frac{16}{24}$, $\frac{24}{36}$, and $\frac{32}{48}$.

Steps to Solve

Determine a Non-Zero Integer to Use for Multiplication

Choose a non-zero integer to multiply both the numerator (8) and the denominator (12). For example, let's use the integer 2.

Multiply the Numerator and Denominator

Multiply both the numerator and denominator by the chosen integer:

$$ \frac{8 \times 2}{12 \times 2} = \frac{16}{24} $$

Choose a Different Non-Zero Integer

Next, use another integer, such as 3, and repeat the process:

$$ \frac{8 \times 3}{12 \times 3} = \frac{24}{36} $$

Find More Equivalent Fractions

Continue this process with different integers. For example, with the integer 4:

$$ \frac{8 \times 4}{12 \times 4} = \frac{32}{48} $$

List the Equivalent Fractions Obtained

After calculating with different integers, list the equivalent fractions. In our examples, we found:

$ \frac{16}{24} $
$ \frac{24}{36} $
$ \frac{32}{48} $

Generalize the Concept

You can generalize that any equivalent fraction can be found using the formula:

$$ \frac{8n}{12n} $$

where $n$ is any non-zero integer.

Some equivalent fractions for $\frac{8}{12}$ are $\frac{16}{24}$, $\frac{24}{36}$, and $\frac{32}{48}$.

More Information

Equivalent fractions are created by multiplying both the numerator and denominator by the same integer. The concept highlights the idea that different fractions can represent the same value.

Tips

Forgetting to multiply both the numerator and the denominator by the same integer, which would result in non-equivalent fractions.
Choosing zero as the integer to multiply by, which is not allowed because it would create a fraction with a numerator of zero (e.g., $ \frac{0}{0} $).

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