https://file.aiquickdraw.com/mathbot/file/1726880041932c38b8zn6.jpg

The question in the image asks: 

**Which of these products are equivalent?**

1. \(\left(\frac{7}{4}\right) \times \left(\frac{15}{4}\right)\)
2. \(\left(\frac{21}{2}\right) \times \left(\frac{5}{8}\right)\)
3. \(\left(\frac{7}{2}\right) \times \left(\frac{3}{4}\right) \times \left(\frac{5}{2}\right)\)

Let's evaluate each expression to determine equivalence:

### Expression I: 
\[
\left(\frac{7}{4}\right) \times \left(\frac{15}{4}\right) = \frac{7 \times 15}{4 \times 4} = \frac{105}{16}
\]

### Expression II:
\[
\left(\frac{21}{2}\right) \times \left(\frac{5}{8}\right) = \frac{21 \times 5}{2 \times 8} = \frac{105}{16}
\]

### Expression III:
\[
\left(\frac{7}{2}\right) \times \left(\frac{3}{4}\right) \times \left(\frac{5}{2}\right) = \frac{7 \times 3 \times 5}{2 \times 4 \times 2} = \frac{105}{16}
\]

### Conclusion:
All three expressions yield the same result: \(\frac{105}{16}\).

So, the correct answer is **D: I, II, and III**.

Do you need further details or have any questions?

Here are some related questions for further exploration:
1. How do you multiply fractions with different denominators?
2. What are the steps to simplify products of fractions?
3. How can you check for equivalence between two fraction products?
4. What happens if one or more fractions are improper fractions?
5. Can these techniques be applied to division of fractions?

**Tip:** When multiplying fractions, simplify any common factors in the numerator and denominator before performing the multiplication to make calculations easier.

Which of these products are equivalent? I. (7/4) × (15/4), II. (21/2) × (5/8), III. (7/2) × (3/4) × (5/2)

Learn how to identify equivalent products of fraction multiplication by comparing multiple expressions. Explore multiplication of fractions with improper fractions and determine if the resulting products are the same. Suitable for Grades 6-8 students, this problem involves calculating and simplifying products of fractions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation