The two consecutive integers between which the fraction `5/7` lies are

Options

A. 5 and 6
B. 0 and 1
C. 5 and 7
D. 6 and 7

Answer

To find the two consecutive integers between which the fraction \( \frac{5}{7} \) lies, we can follow these steps:

### Step 1: Convert the Fraction to Decimal
First, we need to convert the fraction \( \frac{5}{7} \) into a decimal. We can do this by performing the division of 5 by 7.

\[ 5 \div 7 = 0.714285714285... \]

For simplicity, we can round this to two decimal places:

\[ \frac{5}{7} \approx 0.71 \]

### Step 2: Identify the Consecutive Integers
Next, we need to determine the two consecutive integers that the decimal \( 0.71 \) lies between.

The integers immediately surrounding \( 0.71 \) are:

- The integer just below \( 0.71 \) is \( 0 \)
- The integer just above \( 0.71 \) is \( 1 \)

### Step 3: Conclusion
Thus, the two consecutive integers between which \( \frac{5}{7} \) lies are:

\[ 0 \text{ and } 1 \]

### Final Answer
The two consecutive integers between which the fraction \( \frac{5}{7} \) lies are \( 0 \) and \( 1 \).

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