https://file.aiquickdraw.com/mathbot/file/1729685258150mj3r3att.jpg

The image contains two math problems focused on comparing and ordering fractions. Let's break down each one.

### Problem 1: Ordering Fractions (Small to Large)
The fractions are:
\[
\frac{3}{4}, \frac{5}{8}, \frac{8}{9}
\]
We need to arrange them from smallest to largest. To compare these fractions, we can either find a common denominator or convert them to decimal form.

- \(\frac{3}{4} = 0.75\)
- \(\frac{5}{8} = 0.625\)
- \(\frac{8}{9} \approx 0.888\)

Now we can see the order from smallest to largest:
\[
\frac{5}{8}, \frac{3}{4}, \frac{8}{9}
\]

The correct answer in the image for this problem is the first option:
\[
\boxed{\frac{5}{8}, \frac{3}{4}, \frac{8}{9}}
\]

---

### Problem 2: Ordering Fractions (Increasing Order)
The fractions are:
\[
\frac{1}{3}, \frac{1}{6}, \frac{5}{2}, \frac{3}{2}
\]
We need to arrange these fractions in increasing order. First, we convert them to decimals:

- \(\frac{1}{3} \approx 0.333\)
- \(\frac{1}{6} \approx 0.167\)
- \(\frac{5}{2} = 2.5\)
- \(\frac{3}{2} = 1.5\)

Now, we can arrange them from smallest to largest:
\[
\frac{1}{6}, \frac{1}{3}, \frac{3}{2}, \frac{5}{2}
\]

The correct option in the image for this problem is **C**.

---

Would you like more details on any of these solutions? Here are 5 related questions you might find useful:

1. How do you compare fractions without converting to decimals?
2. What is a common denominator and how do you find it?
3. How can you estimate fractions quickly?
4. What are proper fractions, improper fractions, and mixed numbers?
5. What are the methods for simplifying fractions?

**Tip**: Always try to simplify fractions before comparing them—it often makes the process quicker and more intuitive!

Sắp xếp các phân số sau theo thứ tự từ nhỏ đến lớn: \(\frac{3}{4}, \frac{5}{8}, \frac{8}{9}\). Sắp xếp các phân số theo thứ tự tăng dần: \(\frac{1}{3}, \frac{1}{6}, \frac{5}{2}, \frac{3}{2}\)

Learn how to compare and order fractions like \(\frac{3}{4}, \frac{5}{8}, \frac{8}{9}\) and \(\frac{1}{3}, \frac{1}{6}, \frac{5}{2}, \frac{3}{2}\) by converting them to decimals or finding common denominators. Suitable for students in Grades 5-7.

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