Answer: 8/3 cup
Explanation:
To find out how much sugar Theresa would need to make 2 4/5 batches of cookies, we first need to determine the total amount of sugar required for one batch of cookies.
The recipe states that one batch uses 1 1/3 cup of sugar. To add the fractions, we need to find a common denominator. The denominator for 3 and 5 is 15.
Converting 1 to fifteenths:
1 = 15/15
Adding 15/15 to 1/3:
15/15 + 1/3 = 15/15 + 5/15 = 20/15
Therefore, one batch of cookies requires 20/15 cups of sugar.
Now, to calculate the total amount of sugar needed for 2 4/5 batches, we multiply the amount for one batch by the number of batches:
(20/15) * (2 4/5)
To multiply a whole number with a fraction, we first convert the whole number to a fraction by giving it the same denominator as the fraction part:
2 = 2/1
Now, we multiply:
(20/15) * (2/1) = (20 * 2) / (15 * 1) = 40/15
The fraction 40/15 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 5:
40/15 = (40 ÷ 5) / (15 ÷ 5) = 8/3
Therefore, Theresa would need 8/3 cups of sugar to make 2 4/5 batches of cookies.