Question

A certain recipe for trail mix only calls for 44 cups of almonds and 11 cup of chocolate chips. Write a part-to-part ratio of almonds to chocolate chips. Then write a part-to-whole ratio of almonds to the total cups of trail mix. Finally, write a fraction in simplest terms to express the proportion of almonds to the whole.

Answer 1

To find the requested ratios and fraction, let's start with the information given in the recipe:

- Cups of almonds: 44
- Cups of chocolate chips: 11

### Part-to-Part Ratio of Almonds to Chocolate Chips
The part-to-part ratio of almonds to chocolate chips is written as:
\[
\text{Ratio of almonds to chocolate chips} = \frac{44}{11}
\]
To simplify:
\[
\frac{44}{11} = 4
\]
So the part-to-part ratio of almonds to chocolate chips is \( 4:1 \).

### Part-to-Whole Ratio of Almonds to Total Cups of Trail Mix
First, we find the total amount of trail mix, which is the sum of the cups of almonds and chocolate chips:
\[
\text{Total cups of trail mix} = 44 + 11 = 55
\]
Now, the part-to-whole ratio of almonds to the total cups of trail mix is written as:
\[
\text{Ratio of almonds to total trail mix} = \frac{44}{55}
\]
This would be simplified as follows:
\[
\frac{44}{55} = \frac{4}{5}
\]
So the part-to-whole ratio of almonds to the total cup of trail mix is \( 4:5 \).

### Fraction in Simplest Terms to Express the Proportion of Almonds to the Whole
The fraction representing the proportion of almonds to the whole trail mix has already been simplified:
\[
\frac{44}{55} = \frac{4}{5}
\]
Thus, the fraction in simplest terms to express the proportion of almonds to the whole is \( \frac{4}{5} \).

### Summary
1. Part-to-part ratio: \( 4:1 \)
2. Part-to-whole ratio: \( 4:5 \)
3. Fraction in simplest terms: \( \frac{4}{5} \)