Simple Maths Problem

[micky g]

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

[kowalski655]

Cake that's left over????? No such thing

[Alex]

dr_gn said:

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.

Indeed, so we are left with 7/24ths of a cake, but 7/48ths of the cakes.

[selym]

dr_gn said:

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.

Which is 7/24. Why oh why do they need to put the element in doubt in these questions?

[Planet Claire]

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).

[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

[essayer]

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

[micky g]

The denominator should be x2 as this represents the whole amount of cake that you are wanting to calculate the fraction remaining. Do you guys work in climate science?

[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.

[selym]

The 'S' is the fly in the ointment.

[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.

[TwigtheWonderkid]

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).

When I read it, I instinctively went for this. Without this thread, I would have answered 7/24 without giving it another thought.

[Alex]

Planet Claire said:

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).

If those were our cakes, we'd have 1 (2/2) cake left, which would be 1/2 of our original 2 cakes.

[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.

[Toltec]

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?

[essayer]

Hm, I don't buy it.
I interpret "Fraction of the cakes" as 'the remaining amounts of both cakes expressed as a single fraction", as per standard GCSE questions on the topic.

[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.

[Toltec]

dr_gn said:

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.

Exactly my point.

[V8LM]

The cakes are identical - otherwise the answer can only be 1/6 of one and 1/8 of the other.

With that information think of it as 1/2 eaten by one person and 1/2 by another: What fraction of (a) cake is left is 1/2 + 1/2 = 1. So 7/24 in the question.

But the question about was what fraction of THE cakes (the total) is left. We have half of one and half of the other, so we have two halves of two cakes (1/2 + 1/2) / (1 + 1) = 1/2. In the question this is 7/48.

Edited by V8LM on Wednesday 10th January 07:28