To find the total amount of all four ingredients in Hayley's trail mix, we will add the amounts together.
Here are the amounts given for each ingredient:
- Cereal: 2½ cups
- Nuts: ¾ cup
- Coconut: 1 cup
- Chocolate chips: 1½ cups
Now we will convert all quantities to improper fractions or equivalent fractions to make the addition easier:
- Cereal: \(2 \frac{1}{2} = \frac{5}{2} \)
- Nuts: \( \frac{3}{4} \)
- Coconut: \(1 = \frac{4}{4} \)
- Chocolate chips: \(1 \frac{1}{2} = \frac{3}{2} \)
Now we can add them together:
\[ \frac{5}{2} + \frac{3}{4} + \frac{4}{4} + \frac{3}{2} \]
First, we need a common denominator for \( \frac{5}{2} \), \( \frac{3}{4} \), \( \frac{4}{4} \), and \( \frac{3}{2} \). The least common denominator (LCD) is 4:
Convert each fraction:
- \( \frac{5}{2} = \frac{10}{4} \)
- \( \frac{3}{4} = \frac{3}{4} \)
- \( \frac{4}{4} = \frac{4}{4} \)
- \( \frac{3}{2} = \frac{6}{4} \)
Now add them together:
\[ \frac{10}{4} + \frac{3}{4} + \frac{4}{4} + \frac{6}{4} = \frac{10 + 3 + 4 + 6}{4} = \frac{23}{4} \]
Now convert \( \frac{23}{4} \) back to a mixed number:
\[ 23 \div 4 = 5 \text{ R } 3 \]
Thus,
\[ \frac{23}{4} = 5 \frac{3}{4} \]
So, the total amount of all four ingredients combined is:
\(\boxed{5 \frac{3}{4}} \) cups.