Four rational numbers between - 2/5 and 1/3

To find four rational numbers between \(-\frac{2}{5}\) and \(\frac{1}{3}\), we can follow these steps:

1. **Convert the fractions to a common denominator**: 
   \[
   -\frac{2}{5} \text{ and } \frac{1}{3}
   \]
   The least common denominator (LCD) of 5 and 3 is 15. 

2. **Convert the fractions**:
   \[
   -\frac{2}{5} = -\frac{2 \times 3}{5 \times 3} = -\frac{6}{15}
   \]
   \[
   \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
   \]

3. **Find four rational numbers between -6/15 and 5/15**:  
   We can choose any fractions between these two values. Here are four such numbers:
   \[
   -\frac{5}{15}, -\frac{4}{15}, \frac{1}{15}, \frac{2}{15}
   \]

4. **Verify that these numbers are between -6/15 and 5/15**:
   \[
   -\frac{6}{15} < -\frac{5}{15} < -\frac{4}{15} < \frac{1}{15} < \frac{2}{15} < \frac{5}{15}
   \]

So, four rational numbers between \(-\frac{2}{5}\) and \(\frac{1}{3}\) are:

\[
-\frac{5}{15}, -\frac{4}{15}, \frac{1}{15}, \frac{2}{15}
\]

Would you like any more details or have any questions?

Here are 5 numbered questions you might want to ask:

1. How do you convert fractions to a common denominator?
2. Can you explain how to find more rational numbers between any two given fractions?
3. What is the significance of rational numbers?
4. How do you simplify fractions?
5. What are irrational numbers and how do they differ from rational numbers?

**Tip:** When finding rational numbers between two fractions, converting them to a common denominator helps to clearly see the numbers that lie between them.

Learn how to find four rational numbers between -2/5 and 1/3 with a step-by-step solution. This problem covers key concepts in fractions and rational numbers. Suitable for students in Grades 6-8.

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