Let's break down the problem step by step to determine how many days Stefan can feed Coco with the remaining oats.
### Step 1: Determine the initial amount of oats.
Stefan starts with [tex]\( 4 \frac{1}{2} \)[/tex] cups of oats.
### Step 2: Convert the mixed number to an improper fraction.
[tex]\[ 4 \frac{1}{2} \) can be converted to an improper fraction:
\[ 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \][/tex]
### Step 3: Determine the amount of oats used for granola bars.
Stefan uses [tex]\( 3 \frac{1}{4} \)[/tex] cups of oats to make the granola bars.
### Step 4: Convert the mixed number to an improper fraction.
[tex]\[ 3 \frac{1}{4} \) can be converted to an improper fraction:
\[ 3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4} \][/tex]
### Step 5: Subtract the amount of oats used from the initial amount.
[tex]\[ \frac{9}{2} - \frac{13}{4} \][/tex]
To subtract these fractions, we need a common denominator.
### Step 6: Convert both fractions to a common denominator.
The common denominator for 2 and 4 is 4.
[tex]\[ \frac{9}{2} = \frac{9 \times 2}{2 \times 2} = \frac{18}{4} \][/tex]
So now we can subtract:
[tex]\[ \frac{18}{4} - \frac{13}{4} = \frac{18 - 13}{4} = \frac{5}{4} \][/tex]
### Step 7: Determine how many days Stefan can feed Coco.
Coco needs [tex]\( \frac{1}{4} \)[/tex] cup of oats each day. We need to figure out how many [tex]\( \frac{1}{4} \)[/tex]-cup servings are in [tex]\( \frac{5}{4} \)[/tex] cups of oats.
To do this, divide the remaining oats by the daily amount:
[tex]\[ \text{Number of days} = \frac{\frac{5}{4}}{\frac{1}{4}} = \frac{5}{4} \times \frac{4}{1} = \frac{5 \times 4}{4 \times 1} = \frac{20}{4} = 5 \][/tex]
### Final Answer
Stefan can feed Coco for [tex]\(\boxed{5}\)[/tex] days with the oats he has left.
