Let's break down the problem step-by-step to determine how many smaller cups can be filled with lemonade from the large container and how much lemonade will be left over.
1. Convert the Amounts to Improper Fractions or Decimals:
- The large container contains [tex]\( 41 \frac{2}{3} \)[/tex] cups of lemonade.
[tex]\[
41 \frac{2}{3} = 41 + \frac{2}{3} \approx 41.6667 \text{ cups}
\][/tex]
- Each smaller cup holds [tex]\( 3 \frac{1}{8} \)[/tex] cups of lemonade.
[tex]\[
3 \frac{1}{8} = 3 + \frac{1}{8} = 3.125 \text{ cups}
\][/tex]
2. Calculate the Number of Smaller Cups that can be Filled:
- To find out how many full smaller cups can be filled, we perform the division of the total lemonade by the capacity of each smaller cup.
[tex]\[
\text{Number of smaller cups} = \frac{41.6667}{3.125} \approx 13
\][/tex]
So, 13 full smaller cups can be filled.
3. Calculate the Leftover Lemonade:
- To find the leftover lemonade, we can use the modulus operation:
[tex]\[
\text{Leftover lemonade} = 41.6667 \mod 3.125 \approx 1.0417 \text{ cups}
\][/tex]
Putting it all together:
- The large container, which initially holds [tex]\( 41 \frac{2}{3} \)[/tex] cups of lemonade, can fill 13 smaller cups.
- After filling these 13 smaller cups, there will be approximately [tex]\( 1.0417 \)[/tex] cups of lemonade left over.
Therefore, the solution is:
- Number of smaller cups filled: [tex]\( 13 \)[/tex]
- Leftover lemonade: [tex]\( 1.0417 \)[/tex] cups
