To determine which of the three children has a fraction of chocolate candies equal to [tex]\(\frac{1}{4}\)[/tex], we need to find the ratio of chocolate candies to the total candies for each child and compare it to [tex]\(\frac{1}{4}\)[/tex].
Let's break this down step-by-step:
### Jan
- Total candies: [tex]\(54\)[/tex]
- Chocolate candies: [tex]\(12\)[/tex]
The ratio of chocolate candies to total candies for Jan is:
[tex]\[ \text{Jan's ratio} = \frac{12}{54} \][/tex]
Simplifying [tex]\( \frac{12}{54} \)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 6, we get:
[tex]\[ \text{Jan's ratio} = \frac{12 \div 6}{54 \div 6} = \frac{2}{9} \][/tex]
### Lorena
- Total candies: [tex]\(60\)[/tex]
- Chocolate candies: [tex]\(15\)[/tex]
The ratio of chocolate candies to total candies for Lorena is:
[tex]\[ \text{Lorena's ratio} = \frac{15}{60} \][/tex]
Simplifying [tex]\( \frac{15}{60} \)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 15, we get:
[tex]\[ \text{Lorena's ratio} = \frac{15 \div 15}{60 \div 15} = \frac{1}{4} \][/tex]
### Luis
- Total candies: [tex]\(40\)[/tex]
- Chocolate candies: [tex]\(11\)[/tex]
The ratio of chocolate candies to total candies for Luis is:
[tex]\[ \text{Luis's ratio} = \frac{11}{40} \][/tex]
### Comparison with [tex]\(\frac{1}{4}\)[/tex]
Now, we compare the ratios we found with the given ratio [tex]\(\frac{1}{4}\)[/tex]:
- Jan's ratio is [tex]\( \frac{2}{9} \)[/tex], which is not equal to [tex]\( \frac{1}{4} \)[/tex].
- Lorena's ratio is [tex]\( \frac{1}{4} \)[/tex], which is exactly the required ratio.
- Luis's ratio is [tex]\( \frac{11}{40} \)[/tex], which is not equal to [tex]\( \frac{1}{4} \)[/tex].
Thus, only Lorena has a fraction of chocolate candies equal to [tex]\(\frac{1}{4}\)[/tex] of her total candies.
