Rational number `(-19)/2` lies between consecutive integers____

Options

A. `-2` and -1
B. `-7` and -8
C. `-6` and -7
D. `-9` and -10

Answer

To determine between which consecutive integers the rational number \(-\frac{19}{2}\) lies, we can follow these steps:

### Step 1: Convert the Rational Number to Decimal Form
First, we need to convert \(-\frac{19}{2}\) into decimal form by performing the division.

\[ -\frac{19}{2} = -19 \div 2 \]

### Step 2: Perform the Division
Now, we perform the division:

\[ -19 \div 2 = -9.5 \]

### Step 3: Identify the Consecutive Integers
Next, we need to find the consecutive integers that surround \(-9.5\). The integers just below and above \(-9.5\) are:

- The integer just below \(-9.5\) is \(-10\).
- The integer just above \(-9.5\) is \(-9\).

### Step 4: Conclusion
Thus, the rational number \(-\frac{19}{2}\) lies between the consecutive integers \(-10\) and \(-9\).

### Final Answer
The rational number \(-\frac{19}{2}\) lies between consecutive integers \(-10\) and \(-9\).

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