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The problem asks to simplify the fraction \( \frac{10}{16} \) to its lowest terms and find an equivalent fraction that has a denominator of 32.

### Step 1: Simplify \( \frac{10}{16} \)
To simplify \( \frac{10}{16} \), we need to find the greatest common divisor (GCD) of 10 and 16, which is 2. Now, divide both the numerator and the denominator by 2:

\[
\frac{10}{16} = \frac{10 \div 2}{16 \div 2} = \frac{5}{8}
\]

### Step 2: Find an equivalent fraction with a denominator of 32
We need to rewrite \( \frac{5}{8} \) as a fraction with a denominator of 32. To do this, multiply both the numerator and denominator by 4:

\[
\frac{5}{8} = \frac{5 \times 4}{8 \times 4} = \frac{20}{32}
\]

### Answer:
The correct simplified fraction is \( \frac{5}{8} \), and the equivalent fraction with a denominator of 32 is \( \frac{20}{32} \).

Thus, the correct answer from the options is:
- \( \frac{5}{8} , \frac{20}{32} \)

Would you like more details or explanations? 

Here are 5 related questions:
1. How do you determine the greatest common divisor (GCD)?
2. Why is finding an equivalent fraction important in certain cases?
3. Can \( \frac{5}{8} \) be simplified further or is it already in its lowest terms?
4. How can you check if two fractions are equivalent?
5. What are some real-world examples where equivalent fractions are used?

**Tip:** When simplifying fractions, always check for the greatest common divisor to make sure the fraction is in its simplest form.

Simplify 10/16 to lowest terms and find an equivalent fraction that has a denominator of 32.

Learn how to simplify 10/16 to its lowest terms and find an equivalent fraction with a denominator of 32. This solution involves simplifying fractions using the GCD and finding equivalent fractions through multiplication. Suitable for Grades 6-8.

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