# What fraction is equivalent to 1/3?

#### Understand the Problem

The question is asking for fractions that have the same value as 1/3, which involves finding other fractions that simplify to this same ratio.

$\frac{2}{6}$, $\frac{3}{9}$, $\frac{4}{12}$

The final answer is 2/6, 3/9, 4/12, etc.

#### Steps to Solve

1. Understand Equivalent Fractions

Equivalent fractions are fractions that represent the same part of a whole despite having different numerators and denominators. To form an equivalent fraction of $\frac{1}{3}$, we can multiply both the numerator (top number) and the denominator (bottom number) by the same non-zero integer.

1. Multiply Numerator and Denominator by the Same Number

For example, let's multiply both the numerator and the denominator by 2:

$$\frac{1 \times 2}{3 \times 2} = \frac{2}{6}$$

This shows that $\frac{2}{6}$ is equivalent to $\frac{1}{3}$. We can do this for any integer to form more equivalent fractions.

1. Formulate More Equivalent Fractions

Let's try multiplying by 3 and 4:

$$\frac{1 \times 3}{3 \times 3} = \frac{3}{9}$$

$$\frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$

Thus, $\frac{3}{9}$ and $\frac{4}{12}$ are also equivalent to $\frac{1}{3}$.

The final answer is 2/6, 3/9, 4/12, etc.

Any fraction that can be simplified to $\frac{1}{3}$ is considered equivalent to $\frac{1}{3}$. Multiplying the numerator and the denominator by the same non-zero integer will lead to equivalent fractions.