To solve this problem, we need to express the rate of calories to grams in the simplest fractional form.
Given:
- 550 calories
- 100 grams
We start by writing the fraction as:
[tex]\[
\frac{550 \text{ calories}}{100 \text{ grams}}
\][/tex]
Next, our goal is to simplify this fraction. To simplify any fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. For the numbers 550 and 100, the GCD is 50.
We divide both the numerator and the denominator by their GCD (which is 50):
[tex]\[
\frac{550 \div 50}{100 \div 50} = \frac{11}{2}
\][/tex]
Thus, the simplified fraction is:
[tex]\[
\frac{11 \text{ calories}}{2 \text{ grams}}
\][/tex]
Given the answer choices:
1. [tex]\(\frac{2 \text{ grams}}{11 \text { calories}}\)[/tex]
2. [tex]\(\frac{11 \text{ calories}}{2 \text{ grams}}\)[/tex]
3. [tex]\(\frac{550 \text{ calories}}{100 \text{ grams}}\)[/tex]
4. [tex]\(\frac{11}{2}\)[/tex]
From our simplified fraction, we see that the correct answer is:
[tex]\[
\frac{11 \text{ calories}}{2 \text{ grams}}
\][/tex]
Therefore, the correct choice is:
[tex]\[
\frac{11 \text{ calories}}{2 \text{ grams}}
\][/tex]
