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### 13) Choose the fraction that is equivalent to the given fraction:

**Given fraction:**  
\[
\frac{4}{10}
\]

**Options:**  
- (A) \(\frac{2}{5}\)
- (B) \(\frac{3}{8}\)
- (C) \(\frac{8}{20}\)

**Solution:**  
To find an equivalent fraction, we need a fraction that simplifies to \(\frac{4}{10}\) or has the same value when the numerator and denominator are multiplied or divided by the same number.

\[
\frac{4}{10} = \frac{2}{5} \quad (\text{by dividing numerator and denominator by 2})
\]

So, option (A) \(\frac{2}{5}\) is equivalent to \(\frac{4}{10}\).

**Answer for Question 13:** (A) \(\frac{2}{5}\)

### 14) Using the product rule, see if the fraction is equivalent or not equivalent:

**Given fractions to compare:**  
\[
\frac{7}{9} \text{ and } \frac{21}{36}
\]

**Solution:**  
To determine if two fractions are equivalent using the cross-multiplication (product) rule, we check if:

\[
7 \times 36 = 9 \times 21
\]

Calculating both sides:

\[
7 \times 36 = 252, \quad 9 \times 21 = 189
\]

Since \(252 \neq 189\), the fractions \(\frac{7}{9}\) and \(\frac{21}{36}\) are **not equivalent**.

**Answer for Question 14:** Not equivalent

### 15) Using the product rule, see if the fraction is equivalent or not equivalent:

**Given fractions to compare:**  
\[
\frac{3}{4} \text{ and } \frac{6}{8}
\]

**Solution:**  
Using the cross-multiplication (product) rule, we check if:

\[
3 \times 8 = 4 \times 6
\]

Calculating both sides:

\[
3 \times 8 = 24, \quad 4 \times 6 = 24
\]

Since \(24 = 24\), the fractions \(\frac{3}{4}\) and \(\frac{6}{8}\) are **equivalent**.

**Answer for Question 15:** Equivalent

---

Would you like more details on any of these solutions, or do you have any specific questions?

Here are 5 related questions to explore further:
1. How do you simplify a fraction to its simplest form?
2. What is the cross-multiplication (product) rule for checking equivalent fractions?
3. How can you find multiple equivalent fractions for a given fraction?
4. What are some common mistakes to avoid when determining if fractions are equivalent?
5. How do you compare fractions with different denominators?

**Tip:** When checking for equivalent fractions, remember that you can multiply or divide the numerator and the denominator by the same non-zero number without changing the value of the fraction.

Choose the fraction that is equivalent to the given fraction 4/10. Using the product rule, see if the fraction 7/9 is equivalent or not equivalent to 21/36. Using the product rule, see if the fraction 3/4 is equivalent or not equivalent to 6/8.

Solve problems involving equivalent fractions and cross-multiplication. Learn how to determine if fractions are equivalent using the product rule. Suitable for students in Grades 5-7.

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