Final answer:
Sherry used 4/8 cup of sugar, which can be converted into eighths (4/8) to match the original amount (7/8 cup). By dividing 4/8 by 7/8 and simplifying, we find out that Sherry used 4/7 of her total sugar to make sweet tea.
Step-by-step explanation:
The student is asking about the operation with fractions in the context of a practical application involving measuring cups of sugar. To determine what fraction of the sugar Sherry used to make sweet tea, you have to perform a simple division since the original quantity and the amount used are both expressed as fractions of a cup.
Sherry started with 7/8 cup of sugar and then used 1/2 cup of it. To find out what fraction of her sugar was used, we calculate the following:
Convert 1/2 cup into eighths to match the denominator of Sherry's original amount of sugar, which results in 4/8 cup.
Divide the 4/8 cup by the original amount, which is 7/8 cup. The fraction that represents the sugar used is 4/8 divided by 7/8.
To divide fractions, we multiply by the reciprocal. So we multiply 4/8 cup by the reciprocal of 7/8 cup, which is 8/7. Therefore, the calculation is 4/8 × 8/7 = 32/56, which simplifies to 4/7 after dividing both numerator and denominator by 8.
Thus, Sherry used 4/7 of her total sugar to make sweet tea.