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 Post subject: Is the answer book wrong?Posted: Fri Oct 16, 2020 7:44 pm

Joined: Thu Oct 18, 2012 10:41 am
Posts: 482
Alia ate 1/3 of a pizza for lunch. Later she ate 2/5 of the remaining pizza as a snack. How much of the pizza did she eat altogether?

A. 3/8
B. 3/5
C. 11/15
D. 4/5
E. 3/15

Answer sheet says C 11/15, but I agree with DC!

Can anyone explain why it's C please?

TIA

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 Post subject: Re: Is the answer book wrong?Posted: Fri Oct 16, 2020 7:47 pm

Joined: Mon May 16, 2011 2:05 pm
Posts: 6885

I think you’ve missed that she are 2/5 of the remaining pizza. So you need to work out what 2/5 of 2/3 is, to work out how much is eaten then work out how much is left.

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 Post subject: Re: Is the answer book wrong?Posted: Fri Oct 16, 2020 7:55 pm

Joined: Thu Oct 18, 2012 10:41 am
Posts: 482
These are our steps:

Ate 1/3 = 5/15

Ate 2/5 of remaining, so 2/5 x 2/3 = 4/15

Altogether ate 5/15 + 4/15 = 9/15 = 3/5

Am I missing something

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 Post subject: Re: Is the answer book wrong?Posted: Fri Oct 16, 2020 8:28 pm

Joined: Thu May 01, 2008 6:27 pm
Posts: 5125
Location: london
Yes

1/3 = 5 /15 so she has already eaten 5/15

Remaining is 10/15

2/5 of this is 6/15 (x both x 3)

so 5/15 + 6/15 = 11/15

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 Post subject: Re: Is the answer book wrong?Posted: Fri Oct 16, 2020 9:06 pm

Joined: Wed May 09, 2007 3:09 pm
Posts: 1204
Location: Solihull, West Midlands

Imagine the pizza had been precut into 15 slices

First she eats 1/3 of them ie 5 slices - there are now 10 slices left

Then she eats 2/5 of the 10 slices ie 4 slices (4/10 and 2/5 are equivalent fractions)

She's eaten 9 altogether which is 9/15 or 3/5 of the original pizza

You can see how they choose the "wrong" answers too to catch out the common mistakes

A: from incorrectly adding 1/3 + 2/5 (adding tops & bottoms of the fractions)
C: This would be correct if adding 1/3 +2/5 properly as you would convert both to 15ths 5/15 + 6/15, so without the words "of the remaining pizza"
D: ? not sure
E: adding 1+2 and multiplying the denominators together

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 Post subject: Re: Is the answer book wrong?Posted: Fri Oct 16, 2020 9:21 pm

Joined: Thu May 01, 2008 6:27 pm
Posts: 5125
Location: london
Thanks Solimum. So glad I don't have to to this any more!

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 Post subject: Re: Is the answer book wrong?Posted: Fri Oct 16, 2020 10:53 pm

Joined: Wed May 09, 2007 3:09 pm
Posts: 1204
Location: Solihull, West Midlands
One concept which is difficult to grasp with fractions is that the innocuous word "of" means "multiply"

so 2/5 OF 2/3 means 2/5 x 2/3 and multiplying fractions is the "easy" one, (2x2)/(5x3)

I think where you went astray mad is
Quote:
Remaining is 10/15

2/5 of this is 6/15 (x both x 3)

What you've done there is express 2/5 as its equivalent fraction 6/15 by multiplying top & bottom by 3

But the 15ths here are different from the original 15ths: it's as if you divided the 2/3 of the original pizza into 15 new slices and had 6 of those - those are smaller than the imaginary 15 slices of the original pizza.

It would be much easier to explain with real pizza.....

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 Post subject: Re: Is the answer book wrong?Posted: Sat Oct 17, 2020 6:55 am

Joined: Thu May 01, 2008 6:27 pm
Posts: 5125
Location: london
Haha or less wine

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 Post subject: Re: Is the answer book wrong?Posted: Sat Oct 17, 2020 8:18 am

Joined: Thu Oct 18, 2012 10:41 am
Posts: 482
Thanks all

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