Equivalent fractions worksheet with visual models and fraction comparisons.

Problem: Solve the missing fraction parts in the given worksheet on equivalent fractions.

The task involves finding the missing numerators or denominators in each fraction to make them equivalent to the given fractions. Let's solve each part step by step.

---

#### a.
Given:
$$
\frac{3}{4} = \frac{\square}{8}
$$

- The denominator changes from 4 to 8, which is a multiplication by 2.
- To keep the fractions equivalent, we must also multiply the numerator by 2.
- Therefore, $ 3 \times 2 = 6 $.

So, the missing numerator is:
$$
\frac{3}{4} = \frac{6}{8}
$$

---

#### b.
Given:
$$
\frac{4}{6} = \frac{\square}{3}
$$

- The denominator changes from 6 to 3, which is a division by 2.
- To keep the fractions equivalent, we must also divide the numerator by 2.
- Therefore, $ 4 \div 2 = 2 $.

So, the missing numerator is:
$$
\frac{4}{6} = \frac{2}{3}
$$

---

#### c.
Given:
$$
\frac{1}{2} = \frac{\square}{10}
$$

- The denominator changes from 2 to 10, which is a multiplication by 5.
- To keep the fractions equivalent, we must also multiply the numerator by 5.
- Therefore, $ 1 \times 5 = 5 $.

So, the missing numerator is:
$$
\frac{1}{2} = \frac{5}{10}
$$

---

#### d.
Given:
$$
\frac{6}{12} = \frac{\square}{6}
$$

- The denominator changes from 12 to 6, which is a division by 2.
- To keep the fractions equivalent, we must also divide the numerator by 2.
- Therefore, $ 6 \div 2 = 3 $.

So, the missing numerator is:
$$
\frac{6}{12} = \frac{3}{6}
$$

---

#### e.
Given:
$$
\frac{1}{3} = \frac{\square}{6}
$$

- The denominator changes from 3 to 6, which is a multiplication by 2.
- To keep the fractions equivalent, we must also multiply the numerator by 2.
- Therefore, $ 1 \times 2 = 2 $.

So, the missing numerator is:
$$
\frac{1}{3} = \frac{2}{6}
$$

---

#### f.
Given:
$$
\frac{1}{6} = \frac{\square}{12}
$$

- The denominator changes from 6 to 12, which is a multiplication by 2.
- To keep the fractions equivalent, we must also multiply the numerator by 2.
- Therefore, $ 1 \times 2 = 2 $.

So, the missing numerator is:
$$
\frac{1}{6} = \frac{2}{12}
$$

---

#### g.
Given:
$$
\frac{5}{10} = \frac{\square}{6}
$$

- First, simplify $ \frac{5}{10} $ to its simplest form: $ \frac{5 \div 5}{10 \div 5} = \frac{1}{2} $.
- Now, we need to find an equivalent fraction of $ \frac{1}{2} $ with a denominator of 6.
- The denominator changes from 2 to 6, which is a multiplication by 3.
- To keep the fractions equivalent, we must also multiply the numerator by 3.
- Therefore, $ 1 \times 3 = 3 $.

So, the missing numerator is:
$$
\frac{5}{10} = \frac{3}{6}
$$

---

#### h.
Given:
$$
\frac{2}{3} = \frac{\square}{9}
$$

- The denominator changes from 3 to 9, which is a multiplication by 3.
- To keep the fractions equivalent, we must also multiply the numerator by 3.
- Therefore, $ 2 \times 3 = 6 $.

So, the missing numerator is:
$$
\frac{2}{3} = \frac{6}{9}
$$

---

#### i.
Given:
$$
\frac{2}{4} = \frac{\square}{6}
$$

- First, simplify $ \frac{2}{4} $ to its simplest form: $ \frac{2 \div 2}{4 \div 2} = \frac{1}{2} $.
- Now, we need to find an equivalent fraction of $ \frac{1}{2} $ with a denominator of 6.
- The denominator changes from 2 to 6, which is a multiplication by 3.
- To keep the fractions equivalent, we must also multiply the numerator by 3.
- Therefore, $ 1 \times 3 = 3 $.

So, the missing numerator is:
$$
\frac{2}{4} = \frac{3}{6}
$$

---

#### j.
Given:
$$
\frac{1}{4} = \frac{\square}{12}
$$

- The denominator changes from 4 to 12, which is a multiplication by 3.
- To keep the fractions equivalent, we must also multiply the numerator by 3.
- Therefore, $ 1 \times 3 = 3 $.

So, the missing numerator is:
$$
\frac{1}{4} = \frac{3}{12}
$$

---

#### k.
Given:
$$
\frac{6}{9} = \frac{\square}{3}
$$

- First, simplify $ \frac{6}{9} $ to its simplest form: $ \frac{6 \div 3}{9 \div 3} = \frac{2}{3} $.
- Now, we need to find an equivalent fraction of $ \frac{2}{3} $ with a denominator of 3.
- The denominator is already 3, so the fraction is already in the desired form.

So, the missing numerator is:
$$
\frac{6}{9} = \frac{2}{3}
$$

---

#### l.
Given:
$$
\frac{2}{5} = \frac{\square}{10}
$$

- The denominator changes from 5 to 10, which is a multiplication by 2.
- To keep the fractions equivalent, we must also multiply the numerator by 2.
- Therefore, $ 2 \times 2 = 4 $.

So, the missing numerator is:
$$
\frac{2}{5} = \frac{4}{10}
$$

---

#### m.
Given:
$$
\frac{6}{8} = \frac{\square}{12}
$$

- First, simplify $ \frac{6}{8} $ to its simplest form: $ \frac{6 \div 2}{8 \div 2} = \frac{3}{4} $.
- Now, we need to find an equivalent fraction of $ \frac{3}{4} $ with a denominator of 12.
- The denominator changes from 4 to 12, which is a multiplication by 3.
- To keep the fractions equivalent, we must also multiply the numerator by 3.
- Therefore, $ 3 \times 3 = 9 $.

So, the missing numerator is:
$$
\frac{6}{8} = \frac{9}{12}
$$

---

#### n.
Given:
$$
\frac{5}{7} = \frac{\square}{14}
$$

- The denominator changes from 7 to 14, which is a multiplication by 2.
- To keep the fractions equivalent, we must also multiply the numerator by 2.
- Therefore, $ 5 \times 2 = 10 $.

So, the missing numerator is:
$$
\frac{5}{7} = \frac{10}{14}
$$

---

#### o.
Given:
$$
\frac{14}{16} = \frac{\square}{8}
$$

- First, simplify $ \frac{14}{16} $ to its simplest form: $ \frac{14 \div 2}{16 \div 2} = \frac{7}{8} $.
- Now, we need to find an equivalent fraction of $ \frac{7}{8} $ with a denominator of 8.
- The denominator is already 8, so the fraction is already in the desired form.

So, the missing numerator is:
$$
\frac{14}{16} = \frac{7}{8}
$$

---

Final Answers:

$$
\boxed{
\begin{array}{lll}
a. & \frac{3}{4} = \frac{6}{8} \\
b. & \frac{4}{6} = \frac{2}{3} \\
c. & \frac{1}{2} = \frac{5}{10} \\
d. & \frac{6}{12} = \frac{3}{6} \\
e. & \frac{1}{3} = \frac{2}{6} \\
f. & \frac{1}{6} = \frac{2}{12} \\
g. & \frac{5}{10} = \frac{3}{6} \\
h. & \frac{2}{3} = \frac{6}{9} \\
i. & \frac{2}{4} = \frac{3}{6} \\
j. & \frac{1}{4} = \frac{3}{12} \\
k. & \frac{6}{9} = \frac{2}{3} \\
l. & \frac{2}{5} = \frac{4}{10} \\
m. & \frac{6}{8} = \frac{9}{12} \\
n. & \frac{5}{7} = \frac{10}{14} \\
o. & \frac{14}{16} = \frac{7}{8} \\
\end{array}
}
$$