Question

Amar’e used ⅔ of a package of cornbread mix. He will use equal parts of the leftover mix to make 2 batches of cornbread. What fraction of the original package will he use for each batch?
Answer:





Aurora is going to use all of the following ingredients to make a trail mix. 2 ½ pounds of dried apples, 4 pounds of pecans, and 1 ½ pounds of raisins. How many ½ pound packages can she make?
Answer:

Answer 1

Let's solve the first question regarding Amar’e and the cornbread mix:

1. Amar’e used \( \frac{2}{3} \) of a package of cornbread mix.
2. Therefore, the leftover mix is:
\[
1 - \frac{2}{3} = \frac{1}{3}
\]
3. He will use this leftover mix to make 2 batches of cornbread. Therefore, the amount of mix used for each batch is:
\[
\frac{1}{3} \div 2 = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}
\]
So, Amar’e will use \( \frac{1}{6} \) of the original package for each batch.

**Answer:** \( \frac{1}{6} \)

Now, let's solve the second question regarding Aurora making trail mix:

1. Aurora has the following amounts of ingredients:
- Dried apples: \( 2 \frac{1}{2} \) pounds
- Pecans: \( 4 \) pounds
- Raisins: \( 1 \frac{1}{2} \) pounds

2. First, convert the mixed numbers to improper fractions:
- Dried apples: \( 2 \frac{1}{2} = \frac{5}{2} \)
- Pecans: \( 4 = \frac{4}{1} \)
- Raisins: \( 1 \frac{1}{2} = \frac{3}{2} \)

3. Next, find the total weight of the ingredients:
\[
\frac{5}{2} + 4 + \frac{3}{2}
\]
Convert the integer 4 to a fraction:
\[
4 = \frac{8}{2}
\]
So, the total weight is:
\[
\frac{5}{2} + \frac{8}{2} + \frac{3}{2} = \frac{5 + 8 + 3}{2} = \frac{16}{2} = 8 \text{ pounds}
\]

4. Now, determine how many \( \frac{1}{2} \) pound packages she can make:
\[
8 \div \frac{1}{2} = 8 \times 2 = 16
\]

**Answer:** 16 packages