Question

You need to divide
5
4
​
cup of chocolate chips by
5
4
​
to find 1 cup of chocolate chips. To keep the ratio the same, you also need to divide
7
1
​
cup of pecans by
5
4
​
. Start by writing
7
1
​
÷
5
4
​
as a multiplication expression.
÷
5
4
​

÷
5
4
​

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

7
1
​

1 ?
7
1
​
÷
5
4
​


=
•

Answer 1

To write the division \( 7 \frac{1}{2} \div \frac{5}{4} \) as a multiplication expression, you can use the reciprocal of the divisor. Here’s how to do it step by step:

1. **Convert \( 7 \frac{1}{2} \) to an improper fraction**:
\[ 7 \frac{1}{2} = 7 \times 2 + 1 = 14 + 1 = 15 \text{ and keep 2 as the denominator} = \frac{15}{2} \]

2. **Write the division as multiplication by the reciprocal**:
\[ 7 \frac{1}{2} \div \frac{5}{4} = \frac{15}{2} \times \frac{4}{5} \]

Thus, you can express the division \( 7 \frac{1}{2} \div \frac{5}{4} \) as:

\[
\frac{15}{2} \times \frac{4}{5}
\]

Next, carry out the multiplication:

3. **Multiply the fractions**:
\[ \frac{15 \times 4}{2 \times 5} = \frac{60}{10} \]

4. **Simplify the result**:
\[ \frac{60}{10} = 6 \]

So, \( 7 \frac{1}{2} \div \frac{5}{4} = 6 \).

Now we can summarize the information in a table for the recipe:

\[
\begin{array}{|c|c|}
\hline
\text{Chocolate Chips (cups)} & \text{Pecans (cups)} \\
\hline
\frac{5}{4} & 6 \\
\hline
\end{array}
\]

Thus, to maintain the same ratio of chocolate chips to pecans, you would use **6 cups of pecans** when you use **1 cup of chocolate chips**.