The value of which one of the following fractions falls in between `(2)/(5)and (7)/(8)` ?

Options

A. `8/9`
B. `6/7`
C. `(12)/(13)`
D. `(4)/(7)`

Answer

To determine which fraction falls between \( \frac{2}{5} \) and \( \frac{7}{8} \), we will first convert these fractions to decimal form for easier comparison.

### Step 1: Convert \( \frac{2}{5} \) to decimal
\[ \frac{2}{5} = 0.4 \]

**Hint:** To convert a fraction to a decimal, divide the numerator by the denominator.

### Step 2: Convert \( \frac{7}{8} \) to decimal
\[ \frac{7}{8} = 0.875 \]

**Hint:** Use long division or a calculator to find the decimal equivalent of the fraction.

### Step 3: Identify the range
Now we know:
- \( \frac{2}{5} = 0.4 \)
- \( \frac{7}{8} = 0.875 \)

We are looking for fractions that fall between \( 0.4 \) and \( 0.875 \).

**Hint:** The range is between the two decimal values we calculated.

### Step 4: Test potential fractions
We will test the following fractions to see if their decimal values fall within the range \( (0.4, 0.875) \):
1. \( \frac{4}{7} \)
2. \( \frac{6}{7} \)
3. \( \frac{8}{9} \)
4. \( \frac{12}{13} \)

### Step 5: Convert each fraction to decimal
1. **For \( \frac{4}{7} \)**:
\[ \frac{4}{7} \approx 0.571 \]
(This value is between \( 0.4 \) and \( 0.875 \))

2. **For \( \frac{6}{7} \)**:
\[ \frac{6}{7} \approx 0.857 \]
(This value is also between \( 0.4 \) and \( 0.875 \))

3. **For \( \frac{8}{9} \)**:
\[ \frac{8}{9} \approx 0.889 \]
(This value is greater than \( 0.875 \))

4. **For \( \frac{12}{13} \)**:
\[ \frac{12}{13} \approx 0.923 \]
(This value is also greater than \( 0.875 \))

### Step 6: Conclusion
The fractions \( \frac{4}{7} \) and \( \frac{6}{7} \) both fall between \( \frac{2}{5} \) and \( \frac{7}{8} \).

**Final Answer:** The values of \( \frac{4}{7} \) and \( \frac{6}{7} \) fall between \( \frac{2}{5} \) and \( \frac{7}{8} \).