# Thread: % problem

1. ## % problem

Karen has a banana. She eats 2/3 of it and then gives the rest to her younger brother, Jamal. Jamal eats 2/3 of what he was given and then gives the rest to his baby sister, Kia. Kia eats half of what she was given and then throws the rest away. What fraction of the banana was thrown away?

2. Originally Posted by nancymcwilliams
if you add those three fractions up you get 1 and 1/3 that is more than 1 banana. is that right? or perhaps I am not understanding.
2/3 x eaten, 1/3 x remains.

2/3 (1/3 x) eaten, 1/3 (1/3 x) = 1/9 x remains.

1/2 (1/9 x) eaten, 1/2 (1/9 x) remains and gets thrown out.

So 1/18 of the banana gets thrown out.

Note: 2/3 x + 2/9 x + 1/18 x = 17/18 x. Add the bit that gets thrown out and you have 1 x.

3. ## still confused

now I am even more confused. Help!

4. Originally Posted by nancymcwilliams
now I am even more confused. Help!
What are you confused about?

Think of x as the unknown length of the banana. I have gone through a series of steps showing how much length gets eaten and how much length remains at each step.

Where are you confused? 1/18 of the banana gets thrown out.

5. Originally Posted by nancymcwilliams
if you add those three fractions up you get 1 and 1/3 that is more than 1 banana. is that right? or perhaps I am not understanding.
Obviously it cannot add up to more banana than there was. Jameson made a small typo that carrried through the rest of that solution. I have addressed that in post #6.

6. if jamal ate 2/9 the shoudnt kia have eaten

1/ 2 of 2/9 or 1 /2 times 2/9, which equals 1/9?

7. Originally Posted by nancymcwilliams
if jamal ate 2/9 the shoudnt kia have eaten

1/ 2 of 2/9 or 1 /2 times 2/9, which equals 1/9?
NO.

Jamal ate 2/3 of what was given to him. What's was given to him was 1/3 of the banana. Therefore Jamal eats (2/3)(1/3 x) = 2/9 x.

Obviously Jamal does not eat the remaining 1/3 of what was given to him. Therefore Jamal does not eat 1/3 (1/3 x) = 1/9 x.

What Jamal does not eat gets given to Kia. Therefore Kia gets given 1/9 x. Kia eats 1/2 of this, that is, 1/2 (1/9 x) = 1/18 x.

Obviously Kia does not eat the remaining 1/2 of what was given to her. Therefore Kia does not eat 1/2 (1/9 x) = 1/18 x.

So 1/18 of the banana is thrown away.