Which of the following fractions `(3)/(8), (4)/(5), (31)/(40), (9)/(20)` and `(7)/(10)` is greater than `(1)/(2)` and less than `(3)/(4)` ?

Options

A. `(4)/(5)`
B. `(7)/(10)`
C. `(31)/(40)`
D. `(9)/(20)`

Answer

To determine which of the given fractions is greater than \( \frac{1}{2} \) and less than \( \frac{3}{4} \), we will follow these steps:

### Step 1: Convert the fractions to decimal form
We will convert each fraction to its decimal equivalent to easily compare them with \( \frac{1}{2} \) and \( \frac{3}{4} \).

1. \( \frac{3}{8} = 0.375 \)
2. \( \frac{4}{5} = 0.8 \)
3. \( \frac{31}{40} = 0.775 \)
4. \( \frac{9}{20} = 0.45 \)
5. \( \frac{7}{10} = 0.7 \)

### Step 2: Identify the decimal values of \( \frac{1}{2} \) and \( \frac{3}{4} \)
Next, we will convert \( \frac{1}{2} \) and \( \frac{3}{4} \) into decimal form:

- \( \frac{1}{2} = 0.5 \)
- \( \frac{3}{4} = 0.75 \)

### Step 3: Compare the decimal values
Now we will check which of the fractions fall between \( 0.5 \) and \( 0.75 \):

- \( 0.375 \) (from \( \frac{3}{8} \)) is less than \( 0.5 \)
- \( 0.8 \) (from \( \frac{4}{5} \)) is greater than \( 0.75 \)
- \( 0.775 \) (from \( \frac{31}{40} \)) is greater than \( 0.75 \)
- \( 0.45 \) (from \( \frac{9}{20} \)) is less than \( 0.5 \)
- \( 0.7 \) (from \( \frac{7}{10} \)) is between \( 0.5 \) and \( 0.75 \)

### Step 4: Conclusion
The only fraction that is greater than \( \frac{1}{2} \) and less than \( \frac{3}{4} \) is \( \frac{7}{10} \).

### Final Answer
The fraction that is greater than \( \frac{1}{2} \) and less than \( \frac{3}{4} \) is \( \frac{7}{10} \).

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