Write the rational number whose numerator is `4 xx (-7) ` and denominator is `(3-7) xx (15 - 11).`

Options

A. `(16)/(28)`
B. `(8)/(13)`
C. `(13)/(8)`
D. `(-28)/(-16)`

Answer

To find the rational number whose numerator is \(4 \times (-7)\) and denominator is \((3 - 7) \times (15 - 11)\), we will follow these steps:

### Step 1: Calculate the Numerator
The numerator is given as:
\[ 4 \times (-7) \]
Calculating this:
\[ 4 \times (-7) = -28 \]
So, the numerator is \(-28\).

### Step 2: Calculate the Denominator
The denominator is given as:
\[ (3 - 7) \times (15 - 11) \]
First, we calculate \(3 - 7\):
\[ 3 - 7 = -4 \]
Next, we calculate \(15 - 11\):
\[ 15 - 11 = 4 \]
Now, we multiply these two results:
\[ (-4) \times 4 = -16 \]
So, the denominator is \(-16\).

### Step 3: Write the Rational Number
Now we can write the rational number as:
\[ \frac{-28}{-16} \]

### Step 4: Simplify the Rational Number
Since both the numerator and denominator are negative, we can cancel the negative signs:
\[ \frac{-28}{-16} = \frac{28}{16} \]
Now, we simplify \(\frac{28}{16}\):
Both 28 and 16 can be divided by 4:
\[ \frac{28 \div 4}{16 \div 4} = \frac{7}{4} \]

### Final Answer
The rational number is:
\[ \frac{7}{4} \]

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