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.
Answer
$\frac{2}{6}$, $\frac{3}{9}$, $\frac{4}{12}$
Answer for screen readers
The final answer is 2/6, 3/9, 4/12, etc.
Steps to Solve
- 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.
- 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.
- 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.
More Information
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.
Tips
A common mistake is to not multiply the numerator and denominator by the same number, which results in a fraction that is not equivalent. Always ensure both parts of the fraction are scaled by the same factor.
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