Question

A recipe for trail mix calls for
5
4
​
cup of chocolate chips for every
7
1
​
cup of pecans. How many cups of pecans are needed to make the trail mix with 1 cup of chocolate chips?
You’re trying to solve
5
4
​
÷ ?=1. Remember, dividing any number by itself has a quotient of 1. What number can you divide
5
4
​
cup of chocolate chips by to find 1 cup of chocolate chips?

÷
Chocolate chips (cups) Pecans (cups)
5
4
​

7
1
​

1 ?

Answer 1

To find out how many cups of pecans are needed to make the trail mix using 1 cup of chocolate chips, we can set up a proportion:

Given:
- 5/4 cups of chocolate chips for every 7/1 cups of pecans.

We're trying to find how many cups of pecans (let's call it \(x\)) correspond to 1 cup of chocolate chips.

Set up the proportion as follows:

\[
\frac{5/4}{7/1} = \frac{1}{x}
\]

Cross-multiplying gives:

\[
(5/4) \cdot x = 7
\]

Now, to solve for \(x\):

\[
x = \frac{7}{5/4}
\]

Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite it as:

\[
x = 7 \cdot \frac{4}{5}
\]

\[
x = \frac{28}{5}
\]

\[
x = 5.6
\]

Thus, you will need **5.6 cups of pecans** for 1 cup of chocolate chips in your trail mix.