Simple Maths Problem

[dr_gn]

Guys/Girls, Apologies if this is in the wrong forum, but here goes: I'm helping my son with his maths for sats. He's got a work book with questions and answers. I marked this one right for him, but the answer in the book is different. The missus got the answer in the book. Here's the question:

There are two identical cakes. Person A takes 5/6 of one cake, person B takes 7/8 of the other cake. What fraction of the cakes is left?

Having thought about it, I can see how they expected it to be solved (simple subtraction of fractions), but I think it is worded badly (or at least incorrectly)

What answer would you get? Ta.

[dr_gn]

motco said:

Each cake? Average remainder? Ambiguous!

It says "cakes"...

[dr_gn]

Einion Yrth said:

tight fart said:

selym said:

Very rusty but the remainders of the cakes are 1/8 + 1/6 = 3/24 + 4/24 = 7/24

Shouldn't your maths make it 7/48?

No.

Here's how I see it:

7/24 is the remainder of one cake.

7/48 is the remainder of "the cakes" (as per the question).

Therefore the answer is 7/48.

The book wanted you to do it as a simple subtraction of fractions, and gave the answer 7/24.

[dr_gn]

brrapp said:

tight fart said:

selym said:

Very rusty but the remainders of the cakes are 1/8 + 1/6 = 3/24 + 4/24 = 7/24

Shouldn't your maths make it 7/48?

No, if you have 3 oranges in one hand and 4 oranges in the other, when you add them together you don't get 7 oranges oranges, you just get 7 oranges.
Same when you add 3 twentyfourths to 4 twentyfourths, you get 7 twentyfourths.

Apart from the fact that for this question, you've physically got 48 "slices" of cake (2 cakes x 24 slices each), and physically got 7 "slices" of cake remaining, giving an answer of 7/48 of "the cakes" remaining.

7/24 would be the remainder of one whole cake remaining.

[dr_gn]

Shaoxter said:

dr_gn said:

brrapp said:

tight fart said:

selym said:

Very rusty but the remainders of the cakes are 1/8 + 1/6 = 3/24 + 4/24 = 7/24

Shouldn't your maths make it 7/48?

No, if you have 3 oranges in one hand and 4 oranges in the other, when you add them together you don't get 7 oranges oranges, you just get 7 oranges.
Same when you add 3 twentyfourths to 4 twentyfourths, you get 7 twentyfourths.

Apart from the fact that for this question, you've physically got 48 "slices" of cake (2 cakes x 24 slices each), and physically got 7 "slices" of cake remaining, giving an answer of 7/48 of "the cakes" remaining.

The total remaining fraction of A CAKE (singular) would be 7/24

7/24 would be the remainder of one whole cake remaining.

Not sure if serious.....

Sure I'm serious:

You've got 4 out of 24 slices of one cake remaining, and 3 out of 24 slices of the other cake remaining.

Before eating any cake, you had 48 slices, not 24.

There are now 7 slices left of that original 48.

Therefore the fraction of CAKES (plural, i.e. total slices of both cakes) remaining, is 7/48.

[dr_gn]

Alex said:

selym said:

Very rusty but the remainders of the cakes are 1/8 + 1/6 = 3/24 + 4/24 = 7/24

I instinctively went with this as the correct answer, but I think the trick is that the fractions must be of the total amount of cake so, assuming the cakes are of the same size, I now think the answer is:

3/48 + 4/48 = 7/48

OP, what is the given answer?

7/24, which I think is wrong.

7/24 is the fraction of A CAKE (singular) remaining, not of THE CAKES (plural).

ETA, the question stated "there are two IDENTICAL cakes"

Edited by dr_gn on Tuesday 9th January 10:04

[dr_gn]

Shaoxter said:

Hmm my bad, I didn't spot the plural cakeS either.
I guess the essence of the question was just to ask what 1/6 + 1/8 was...

Exactly.

[dr_gn]

micky g said:

Either the question or the answer is wrong. They ask for the fraction of the 'cakes,' (plural), remaining, not the fraction of one cake.

I think the answer is wrong. The question was clear to me, but depending on who you ask, each person has a definite opinion on the answer, and interestingly, very few change their mind either way...

[dr_gn]

Planet Claire said:

selym said:

Very rusty but the remainders of the cakes are 1/8 + 1/6 = 3/24 + 4/24 = 7/24

This is correct. I think we can agree that there is 1/8 and 1/6 remaining of the two cakes. To add fractions (for us to work out the total amount remaining) we must convert to a common denominator, in this case 24 (because 6 and 8 divide exactly into 24 and thus we can find the equivalent fractions).

Therefore, 1/8 is equivalent to 3/24 and 1/6 is equivalent to 4/24. We can now add how many 24ths we have, ie 3 + 4, so the total remaining cake is 7/24.

When adding fractions with a common denominator we just add together the numerators, the common denominator stays as it is. Think about it, if we want to add 1/2 + 1/2, we know that it isn't 2/4 (1/2), it's 1 (2/2).

You've made the mistake of assuming they want the answer as a fraction of ONE CAKE (24 pieces). When what they've asked for is the fraction of BOTH CAKES, i.e. 48 pieces, and 7 remaining i.e. 7/48

[dr_gn]

essayer said:

It’s ambiguously worded but as you have 1/6 and 1/8 of a cake left

1/6 + 1/8
6/48 + 8/48 = 14/48 = 7/24

Or, consider you had “2 cake” at the beginning, 5/6 (0.833) and 7/8 (0.875) got eaten, total 1.708 leaving 0.292 cake left, which is 7/24

See you've fallen into the trap of saying 0.292 CAKE left, which, while correct in itself, Isn't what the question asked. It asked what fraction of CAKES was left.

[dr_gn]

selym said:

The 'S' is the fly in the ointment.

Even if it said "cake" it would still be ambiguous. What it should have said was "a cake". That would have made their answer correct.

[dr_gn]

What I think happens is some people read the question and once they’ve written fractions down, proceed in a mechanical way to get their answer, which turns out to be wrong because they lose the context while automatically doing the maths they’ve been taught. Others combine the maths with the context, and get it right.

[dr_gn]

Toltec said:

dr_gn said:

What I think happens is some people read the question and once they’ve written fractions down, proceed in a mechanical way to get their answer, which turns out to be wrong because they lose the context while automatically doing the maths they’ve been taught. Others combine the maths with the context, and get it right.

"The book wanted you to do it as a simple subtraction of fractions, and gave the answer 7/24."

So which is it, the answer any normal person would give or the one based on trying to weight the importance of poor grammatical phrasing?

So you expect a 10 year old - who is also being taught grammar - to make that decision?

When you say "normal" person, do you mean someone who can't tell the difference between singular and plural?

As I said, if you read the question, it's not asking for the remaining fraction of "a cake". Poor grammar or not, how can you possibly interpret it any other way than more than one cake?. It's either the wrong question, or the wrong answer, depending on what they actually wanted.

[dr_gn]

Toltec said:

Greg66 said:

dr_gn said:

There are two identical cakes. Person A takes 5/6 of one cake, person B takes 7/8 of the other cake. What fraction of the cakes is left?

If that's the question verbatim, the answer is 7/48.

Try this:

There are ten identical cakes. Person A takes 1/2 of one cake, Person B takes 1/2 of another cake. The other cakes are left untouched. What fraction of the cakes is left?

You started with ten cakes. With a bit of squashing together* you end up with 9. You have 9/10 of the cakes left.

Do the fractions thing:

You're left with 1/2 + 1/2 + 8, = 9. 9 isn't a fraction though, so you need a denominator, and that's the total number of cakes.

In the problem as presented, you're left with 1/6 of one and 1/8 of another = 7/24. You need then to divide that by the total number of cakes to get your answer, which gets you to 7/48.

Very badly worded question though, and if the set answer is 7/24 either the question setter or the marker has gone astray.


*you could say that you actually have 8 cakes left, and two bits of cake. So the answer is 8/10, and in the question as set you have no (zero) cakes left, only some bits - if you treat "cakes" and meaning "whole cakes".

I'm trying think of example where a question would be stated to get that answer in common usage. Mainly I think you would only do it if a collective noun or term could be applied.

There are two identical cakes on a plate. Person A takes 5/6 of one cake, person B takes 7/8 of the other cake. What fraction of the plate of cakes is left?

Try this one-

A farmer raises ten turkeys. One customer eats half a turkey another customer eats a third of a turkey, what fraction of the turkeys is left?

a) 11/12
b) 9/10
c) 4/5

All you have to do to correct the question is add "a" i.e. "What fraction of a cake is left?"

[dr_gn]

Greg66 said:

dr_gn said:

There are two identical cakes. Person A takes 5/6 of one cake, person B takes 7/8 of the other cake. What fraction of the cakes is left?

If that's the question verbatim, the answer is 7/48.

That is the question verbatim, and I agree about the answer.

[dr_gn]

FredClogs said:

Jesus... 4/24 + 3/24 is 7/24 not 7/48...

True, but that's not what the question asked.

[dr_gn]

V8LM said:

Alias218 said:

V8LM said:

Alias218 said:

Greg66 said:

Alias218 said:

Again, this is making the mistake of doubling the quantity.

If you go through my numbers, you are doubling up (where I put 0.291/2 - the same as your 29.1% of 200%). This, as I prove on the line below, is incorrect.

The answer is 7/24. It's all it can be.

Once again, you haven't read the question. It's not "what fraction of a cake is left?". It's "what fraction of the cakes is left?". The line of yours that starts "The two cake logic" is the line where you depart from the question and choose to answer a different question - the former one above. 7/24 is precisely the fraction of a single cake that you'd be left with. Try it.

ETA: in fact, try this (but give answers to both questions).

You've got two pizzas. Each one is divided into four equal slices.

You eat one slice.

(a) what fraction (or percentage) of a single pizza do you have left?
(b) what fraction (or percentage) of the two pizzas do you have left?

Edited by Greg66 on Thursday 11th January 19:05

(a) 7/8 - assuming you mean both combined into one big pizza. However we are not talking about 1 pizza (or cake) which is why the answer 7/48 is wrong. The question asks what remains of the cakes i.e. plural
(b) 3/4 + 4/4 = 7/4 or 1 3/4 (not 3/4 + 4/4 = 7/8 which is exactly what a lot of people, including you, have done on the cake question).

The point of fact is that we are talking about two cakes. This very fact changes the way the question is answered.

Show me how 3/4 + 4/4 = 7/8 is any different from 3/24 + 4/24 = 7/48 in the context of question (b).

Edited by Alias218 on Thursday 11th January 19:31

As written much further up, what would your answer be if 1/2 of each cake was eaten?

1 or 1/2?

Again, if combined into one cake then 2/4 or 1/2.

If taken as two cakes as per the OP's question, then 1.

ETA: As I have said previously, having two cakes changes the way you answer the question, as shown in the above example.

Edited by Alias218 on Thursday 11th January 20:22

The question was "What fraction of the cakes is left?". 1 is 1/1. 1.00. 100 * 0.01. 100%.

!00% of the cakes is [are] left? Really?

ETA: It doesn't ask what fraction of a cake is left? Or how much of a cake is left? Or what fractions of the cakes are left? The question refers to a single fraction of the total cakes. It ask what fraction [a single number] of the cakes [together, not individually] is left.

Appallingly worded question.

Edited by V8LM on Thursday 11th January 20:41

You're right that it's all about the wording, but taken in isolation (ie ignoring what the examiner might have had in mind), if you read the question, *think about it*, and then do the maths, is it badly worded, or is it that people get annoyed with themselves when they realise they've simply been careless and jumped to incorrect conclusions about what's being asked?

[dr_gn]

boyse7en said:

OK, i'm a bit lost in all the too-ing and fro-ing with various explanations and kind of lost the thread of who was arguing for which answer.

Have we finally come to a consensus that the answer is "7/48 of the cakes are left"?

Not sure if it's a consensus, but that's the right answer.

[dr_gn]

Toltec said:

dr_gn said:

Not sure if it's a consensus, but that's the right answer.

The one in the answer section of the book, yes?

No, the answer in the back of the book is for a different question.

[dr_gn]

Toltec said:

dr_gn said:

Toltec said:

dr_gn said:

Not sure if it's a consensus, but that's the right answer.

The one in the answer section of the book, yes?

No, the answer in the back of the book is for a different question.

So the answer to the question they thought they had set, but worded ambiguously, was indeed 7/24?

Worded incorrectly for the answer they gave, NOT ambiguously. Their answer was stated on page 1 of this thread BTW.

I can draw a diagram to explain it if you like, but it’s really not difficult to understand once you get beyond what you automatically tend to calculate vs. what they actually ask.