Final answer:
Jake ate 1/2 of the candy bar. After Jeffery ate 1/3 and gave away 1/2 of the whole candy bar, 3/6 or 1/2 of the candy bar was left, which Jake then consumed.
Step-by-step explanation:
Finding the Fraction Jake Ate
Jeffery ate 1/3 of a candy bar and then gave away 1/2 of the whole candy bar to his friend. To determine what fraction of the candy bar Jake ate, we first need to find out how much of the candy bar was left after Jeffery ate his part and gave some to his friend. Initially, consider the candy bar as a whole, which is 1 or 3/3. When Jeffery ate 1/3, 2/3 of the candy bar was left. However, Jeffery then gave away 1/2 of the whole candy bar, not just what was left after he ate. Therefore, to find out how much he gave away, we need to calculate 1/2 of the whole candy bar, which is 1/2 of 3/3, resulting in 3/6 or simplified to 1/2.
Now, subtract the part Jeffery gave away from the total:
- Entire candy bar: 3/3 or 1
- Jeffery's friend's portion (1/2): 3/6
We find the common denominator for 3/3 and 3/6, which is 6, and express the entire candy bar as 6/6. Subtracting the friend's portion, we get:
- 6/6 (entire bar) - 3/6 (friend's portion) = 3/6
Now, we know that Jake ate the remaining 3/6 of the candy bar. This fraction can be simplified by dividing both numerator and denominator by 3:
- Jake's portion: 3/6 = 1/2