John eats 2/5 of a bar of chocolate. Linda eats 4/9 of what remains.
What fraction of the bar of chocolate have they eaten between them?

Is this correct?

1-2/5=3/5 (Which is what was eaten by John)

4/9 of 3/5=4/15 (She ate 4/15)

4/15 + 3/5 = 13/15 Which is the answer.. I am not sure if this is correct. Please help!

Hello Joherba

If John ate 2/5 bar, than 1-2/5=3/5 bar remains.

If Linda ate 4/9 of 3/5 bar, than 5/9 of 3/5 remains = 5/9 x 3/5 = 15/45 = 1/3 bar remains.

So John and Linda ate together 2/3 bar.

Or as per your calculation :

Remains 1 - 2/5 - 4/15 = 15/15 - 6/15 - 4/15 = 5/15 = 1/3 (bar).

You mixed up what they ate and what remained!

Quote:

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Originally Posted by sarnian

Hello Joherba

If John ate 2/5 bar, than 1-2/5=3/5 bar remains.

If Linda ate 4/9 of 3/5 bar, than 5/9 of 3/5 remains = 5/9 x 3/5 = 15/45 = 1/3 bar remains.

So John and Linda ate together 2/3 bar.

Or as per your calculation :

Remains 1 - 2/5 - 4/15 = 15/15 - 6/15 - 4/15 = 5/15 = 1/3 (bar).

You mixed up what they ate and what remained!

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Thanks for your help, I just do not understand why you multiply 5/9 with 3/5?

Quote:

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Originally Posted by Joherba

Thanks for your help, I just do not understand why you multiply 5/9 with 3/5?

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Hello Joherba

Because you yourself calculated first how much bar remained after John ate, and I continued that line of thought. Also because the question was 'what fraction of the bar of chocolate have they eaten between them?'. Well : what remains is 1 minus all that is eaten.

In my reply I provided you the 2 different ways to get to the proper answer !

1) John ate 2/5 bar. Linda ate 4/9 of what remained (i.e. of 3/5 bar). So Linda ate 4/9 x 3/5 bar = 12/45 bar = 4/15 bar.
So together they ate 2/5 + 4/15 = 6/15 + 4/15 = 10/15 = 2/3 (bar).

2) John ate 2/5 bar. Remains 3/5 bar. Linda ate 4/9 of that, and so remains 5/9 x 3/5 bar = 15/45 bar= 1/3 bar. So they ate between them 1 - 1/3 bar = 2/3 bar.

The dual calculation just confirms that the calculation was carried out properly.

Quote:

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Originally Posted by sarnian

Hello Joherba

Because you yourself calculated first how much bar remained after John ate, and I continued that line of thought. Also because the question was 'what fraction of the bar of chocolate have they eaten between them?'. Well : what remains is 1 minus all that is eaten.

In my reply I provided you the 2 different ways to get to the proper answer !

1) John ate 2/5 bar. Linda ate 4/9 of what remained (i.e. of 3/5 bar). So Linda ate 4/9 x 3/5 bar = 12/45 bar = 4/15 bar.
So together they ate 2/5 + 4/15 = 6/15 + 4/15 = 10/15 = 2/3 (bar).

2) John ate 2/5 bar. Remains 3/5 bar. Linda ate 4/9 of that, and so remains 5/9 x 3/5 bar = 15/45 bar= 1/3 bar. So they ate between them 1 - 1/3 bar = 2/3 bar.

The dual calculation just confirms that the calculation was carried out properly.

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Thank you very much for your help! I appreciate it... :)