Answer: Kayla sold 1/12 gallons more than Ethan.
Explanation:
Let's start by finding out how much lemonade Kayla sold. We know that together, Ethan and Kayla sold 1 1/4 gallons, which is the same as 5/4 gallons. We also know that Ethan sold 2/3 gallons. Therefore, we can find how much Kayla sold by subtracting Ethan's sales from the total sales:
Kayla's sales = Total sales - Ethan's sales
Kayla's sales = 5/4 - 2/3
To subtract these fractions, we need to find a common denominator. The smallest common multiple of 4 and 3 is 12, so we can rewrite the fractions with 12 as the denominator:
Kayla's sales = (5/4)(3/3) - (2/3)(4/4)
Kayla's sales = 15/12 - 8/12
Kayla's sales = 7/12
Therefore, Kayla sold 7/12 gallons of lemonade. Now, we need to compare this to Ethan's sales. We can convert Ethan's sales to twelfths to make it easier to compare:
Ethan's sales = (2/3)(4/4) = 8/12
Now we can see that Kayla sold more lemonade than Ethan. The difference in sales is:
Kayla's sales - Ethan's sales = 7/12 - 8/12
Kayla's sales - Ethan's sales = -1/12
The result is negative, which means that Ethan sold 1/12 gallons less than Kayla. Therefore, Kayla sold 1/12 gallons more than Ethan.