SOLUTION: In each of the following parts, the people named shared all of a large candy bar. Make a drawing and give your reasoning in finding what fraction of the bar each person ate. a) Tom

Question 1190543: In each of the following parts, the people named shared all of a large candy bar. Make a drawing and give your reasoning in finding what fraction of the bar each person ate. a) Tome ate 2/3 as much as Ulysses ate. b) Vicky ate 3/4 as much as Willie, who ate half as much as Xavier. e) Yolanda ate 1/3 of the bar, Zeb ate 3/4 of what Yolanda left, and then Arnie ate the rest.
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
**a) Tome and Ulysses**
* **Drawing:** Imagine the candy bar divided into 5 equal pieces. Ulysses eats 3 of those pieces, and Tome eats 2.
* **Reasoning:** Since Tome ate 2/3 as much as Ulysses, we can represent their shares as a ratio of 2:3. This means the candy bar needs to be divided into 2 + 3 = 5 equal parts.
* **Fractions:** Ulysses ate 3/5 of the candy bar, and Tome ate 2/5 of the candy bar.
**b) Vicky, Willie, and Xavier**
* **Drawing:** Picture the candy bar divided into 8 equal pieces. Xavier eats 4 pieces, Willie eats 2 pieces, and Vicky eats 1.5 pieces (imagine splitting one piece in half).
* **Reasoning:** We're given that Willie ate half as much as Xavier. Let's say Xavier ate 4 pieces (it's easiest to work with whole numbers). This means Willie ate 4 / 2 = 2 pieces. Vicky ate 3/4 as much as Willie, so she ate (3/4) * 2 = 1.5 pieces. In total, they ate 4 + 2 + 1.5 = 7.5 pieces. To make this work with fractions, we can double the number of pieces to 16. Now Xavier has 8, Willie has 4, and Vicky has 3.
* **Fractions:** Xavier ate 8/16 (or 1/2) of the candy bar, Willie ate 4/16 (or 1/4) of the candy bar, and Vicky ate 3/16 of the candy bar.
**c) Yolanda, Zeb, and Arnie**
* **Drawing:** Divide the candy bar into thirds. Yolanda eats one-third. Then divide the remaining two-thirds into quarters. Zeb eats three of those quarters. The remaining quarter is for Arnie.
* **Reasoning:** Yolanda ate 1/3 of the bar, leaving 1 - 1/3 = 2/3 remaining. Zeb ate 3/4 of the remaining portion, so he ate (3/4) * (2/3) = 1/2 of the whole candy bar. Arnie ate the rest, which is 1 - 1/3 - 1/2 = 1/6 of the candy bar.
* **Fractions:** Yolanda ate 1/3 of the candy bar, Zeb ate 1/2 of the candy bar, and Arnie ate 1/6 of the candy bar.
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