Worksheet on identifying equivalent fractions using number lines.

Let's solve each problem step by step using the number lines provided. The goal is to find the equivalent fraction for each given fraction by observing where the point lies on the number line and matching it with the corresponding value on the second number line.

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1) $\frac{1}{3} = \ ?$

- On the top number line, the point is at $\frac{1}{3}$.
- The bottom number line is divided into sixths: $0, \frac{1}{6}, \frac{2}{6}, \frac{3}{6}, \frac{4}{6}, \frac{5}{6}, \frac{6}{6}$.
- We need to find which fraction in sixths is equal to $\frac{1}{3}$.

We know:
$$
\frac{1}{3} = \frac{2}{6}
$$

✔ So, the answer is:
$\frac{2}{6}$

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2) $\frac{3}{15} = \ ?$

- On the top number line, the point is at $\frac{3}{15}$.
- The bottom number line is divided into fifths: $0, \frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5}, \frac{5}{5}$.

Now simplify $\frac{3}{15}$:
$$
\frac{3}{15} = \frac{1}{5}
$$

So, $\frac{3}{15}$ is equivalent to $\frac{1}{5}$.

✔ Answer: $\frac{1}{5}$

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3) $\frac{2}{4} = \ ?$

- On the top number line, the point is at $\frac{2}{4}$.
- The bottom number line is divided into sixteenths: $0, \frac{1}{16}, \frac{2}{16}, ..., \frac{16}{16}$.

We know:
$$
\frac{2}{4} = \frac{1}{2}
$$

Now, find what $\frac{1}{2}$ is in sixteenths:
$$
\frac{1}{2} = \frac{8}{16}
$$

So, $\frac{2}{4} = \frac{8}{16}$

✔ Answer: $\frac{8}{16}$

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4) $\frac{12}{14} = \ ?$

- On the top number line, the point is at $\frac{12}{14}$.
- The bottom number line is divided into sevenths: $0, \frac{1}{7}, \frac{2}{7}, ..., \frac{7}{7}$.

Simplify $\frac{12}{14}$:
$$
\frac{12}{14} = \frac{6}{7}
$$

So, $\frac{12}{14} = \frac{6}{7}$

✔ Answer: $\frac{6}{7}$

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✔ Final Answers:

1) $\frac{1}{3} = \boxed{\frac{2}{6}}$
2) $\frac{3}{15} = \boxed{\frac{1}{5}}$
3) $\frac{2}{4} = \boxed{\frac{8}{16}}$
4) $\frac{12}{14} = \boxed{\frac{6}{7}}$

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🔍 Explanation Summary:

Each problem uses number lines to visually show that two fractions are equivalent (same point on the number line). To find the equivalent fraction:

- Identify the position of the given fraction on the top number line.
- Match that same point on the bottom number line (with different denominators).
- Write down the fraction from the bottom line.

This reinforces understanding of equivalent fractions through visual representation and simplification.