Which of the following fraction is greater than `(3)/(4)` but less greater than `(5)/(6)?` than ?

Options

A. `(2)/(3)`
B. `(1)/(2)`
C. `(4)/(5)`
D. `(9)/(10)`

Answer

To determine which of the given fractions is greater than \( \frac{3}{4} \) but less than \( \frac{5}{6} \), we will follow these steps:

### Step 1: Convert the fractions to decimal form
First, we convert \( \frac{3}{4} \) and \( \frac{5}{6} \) to decimal form for easier comparison.

- \( \frac{3}{4} = 0.75 \)
- \( \frac{5}{6} \approx 0.833 \)

### Step 2: Analyze the options
Now, we will convert each of the given options to decimal form:

1. \( \frac{2}{3} \approx 0.6667 \)
2. \( \frac{1}{2} = 0.5 \)
3. \( \frac{4}{5} = 0.8 \)
4. \( \frac{9}{10} = 0.9 \)

### Step 3: Compare the decimals
Now we will compare each decimal value with \( 0.75 \) and \( 0.833 \):

- \( 0.6667 \) (from \( \frac{2}{3} \)): This is less than \( 0.75 \).
- \( 0.5 \) (from \( \frac{1}{2} \)): This is also less than \( 0.75 \).
- \( 0.8 \) (from \( \frac{4}{5} \)): This is greater than \( 0.75 \) and less than \( 0.833 \).
- \( 0.9 \) (from \( \frac{9}{10} \)): This is greater than \( 0.833 \).

### Step 4: Conclusion
The only fraction that is greater than \( \frac{3}{4} \) and less than \( \frac{5}{6} \) is \( \frac{4}{5} \).

### Final Answer
The fraction that is greater than \( \frac{3}{4} \) but less than \( \frac{5}{6} \) is \( \frac{4}{5} \).

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