Find the rational numbers between 3/7 and 5/3

To find the rational numbers between \( \frac{3}{7} \) and \( \frac{5}{3} \), we can follow these steps:

### Step 1: Convert to Decimals
First, convert both fractions to decimal form to understand the range:
- \( \frac{3}{7} \approx 0.4286 \)
- \( \frac{5}{3} \approx 1.6667 \)

So, we are looking for rational numbers between 0.4286 and 1.6667.

### Step 2: Identify Rational Numbers
Rational numbers are numbers that can be expressed as a fraction of two integers. Examples of such numbers between 0.4286 and 1.6667 include:

1. \( \frac{1}{2} = 0.5 \)
2. \( \frac{2}{3} = 0.6667 \)
3. \( \frac{3}{4} = 0.75 \)
4. \( \frac{4}{5} = 0.8 \)
5. \( \frac{7}{6} = 1.1667 \)

These are just a few examples of rational numbers between \( \frac{3}{7} \) and \( \frac{5}{3} \).

### Step 3: Generate More Examples
You can generate more rational numbers by finding fractions within the given range, for example:
- \( \frac{5}{7} \approx 0.7143 \)
- \( \frac{9}{8} = 1.125 \)
- \( \frac{6}{5} = 1.2 \)

These numbers provide a variety of rational numbers within the specified range.

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Do you want more details on this method or have any questions?

Here are 5 related questions to deepen your understanding:
1. How can you find a fraction between two given fractions?
2. What are the steps to convert a repeating decimal into a fraction?
3. How do you identify if a number is rational or irrational?
4. What is the difference between rational and irrational numbers?
5. How can you find all the rational numbers between two given decimals?

**Tip:** Remember, there are infinitely many rational numbers between any two given numbers!

Discover how to find rational numbers between the fractions 3/7 and 5/3, converting them to decimals and identifying several examples. Explore key concepts like rational numbers, fractions, and the density of rational numbers. Ideal for students in Grades 6-8.

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