Let's solve the problem step by step.

Problem Summary:

• Initial purchase: 21 ½ gallons of lemonade.
• Additional purchase by the teacher: 5 ¼ gallons of lemonade.
• Leftover lemonade at the end of the day: 1 ¾ gallons of lemonade.
• Question: How much lemonade was consumed during the day?

Step-by-Step Solution:

1. Convert mixed numbers to improper fractions:

   • $21 \frac{1}{2}$ = $\frac{43}{2}$ gallons.
   • $5 \frac{1}{4}$ = $\frac{21}{4}$ gallons.
   • $1 \frac{3}{4}$ = $\frac{7}{4}$ gallons.

2. Total lemonade available:

   • Add the initial purchase and the teacher’s additional purchase: $\frac{43}{2} + \frac{21}{4}$ First, find a common denominator (4): $\frac{43}{2} = \frac{86}{4}$ Now add: $\frac{86}{4} + \frac{21}{4} = \frac{107}{4}$ Total lemonade available = $\frac{107}{4}$ gallons.

3. Lemonade consumed: The school has 1 ¾ gallons left at the end of the day, or $\frac{7}{4}$ gallons. To find out how much lemonade was consumed, subtract the leftover from the total lemonade available: $\frac{107}{4} - \frac{7}{4} = \frac{100}{4} = 25 \text{ gallons}.$

Answer:

The amount of lemonade consumed during the day is 25 gallons.

Would you like further details or have any questions about the process?

Here are 5 related questions you can explore:

1. How do you convert between mixed numbers and improper fractions?
2. How do you find a common denominator when adding fractions?
3. How can you verify your subtraction of fractions in this problem?
4. What is the significance of improper fractions in real-world problems?
5. How would the solution change if there was no leftover lemonade?

Tip: Always ensure that your fractions have the same denominator when adding or subtracting them to avoid errors.