Sure, let's walk through how we determine the new amounts for each ingredient if Mrs. Hughes wants to make only two-thirds of the original recipe. Here are the original amounts of each ingredient:
1. Chicken Broth: [tex]\(2 \frac{2}{3}\)[/tex] cups
2. Chicken: [tex]\(1 \frac{1}{2}\)[/tex] cups
3. Rice: [tex]\(\frac{3^6}{4}\)[/tex] cups
Mrs. Hughes wants to make only two-thirds of the recipe, so we will need to multiply each amount by [tex]\(\frac{2}{3}\)[/tex]. Let's do the conversions:
### Chicken Broth
First, convert the mixed number [tex]\(2 \frac{2}{3}\)[/tex] to an improper fraction:
[tex]\[ 2 \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \][/tex]
Now, find two-thirds of this amount:
[tex]\[ \frac{8}{3} \times \frac{2}{3} = \frac{16}{9} \][/tex]
Convert [tex]\(\frac{16}{9}\)[/tex] to a decimal to be more understandable:
[tex]\[ \frac{16}{9} \approx 1.77777 \][/tex]
Thus, Mrs. Hughes would need approximately 1.78 cups of chicken broth.
### Chicken
Next, convert the mixed number [tex]\(1 \frac{1}{2}\)[/tex] to an improper fraction:
[tex]\[ 1 \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \][/tex]
Now, find two-thirds of this amount:
[tex]\[ \frac{3}{2} \times \frac{2}{3} = \frac{6}{6} = 1 \][/tex]
So, Mrs. Hughes would need 1 cup of chicken.
### Rice
Calculate [tex]\(\frac{3^6}{4}\)[/tex]:
[tex]\[ 3^6 = 729 \][/tex]
[tex]\[ \frac{729}{4} = 182.25 \][/tex]
Now, find two-thirds of this amount:
[tex]\[ 182.25 \times \frac{2}{3} = 121.5 \][/tex]
So, Mrs. Hughes would need 121.5 cups of rice.
### Summary
To make two-thirds of the original recipe, Mrs. Hughes needs:
- Approximately 1.78 cups of chicken broth,
- 1 cup of chicken, and
- 121.5 cups of rice.
