Simple Maths Problem

[tight fart]

There are two cakes, chocolate & vanilla cut into 24 slices each. Person A takes 20 slices of chocolate cake, person B takes 21 of the vanila cake. What of the cakes is left?

[FredClogs]

Terribly worded.question, I'd get my kid to put down both possible answers, i.e the amount left of each cake and the combined amount of cake left with an explanation as to why she'd given two answers.

[Jinx]

5/6 - small obviously a standard sponge type cake probably Victoria but I haven't ruled out lemon drizzle.

7/8 - larger given the number of portions so I'm inclined to assume a gateau of some kind.

Total cake left - 2 portions but not for long

[anonymous-user]

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".

[Toltec]

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

[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.

[Toltec]

dr_gn 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.

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

Was it the expected answer, i.e the one the question setter wanted you to get?

[FredClogs]

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

[Alias218]

1/6 remains of one cake, 1/8 of the other.

We need to find a common denominator: 6*8=48.

Now the numerators need to be adjusted to match the new denominators: 6 goes into 48 eight times so the 1 becomes an 8 for 8/48 (the same as 1/6)

8 goes into 48 six times so the 1 becomes a 6 for 6/48 (the same as 1/8).

Add these together: 8/48 + 6/48= 14/48 (the denominator does not change).

Cancel down: 7/24.

And there is your answer.

So the answer, depending on how you view the question, is either 1/6 and 1/8 or 7/24.

[liner33]

This is fairly typical maths question , its just a complicated way of saying

What is 1/6 + 1/8 ?

We ALL that that kind of basic sum at school

[boyse7en]

FredClogs said:

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

Don't you start! I was just getting my head round this...

I've gone with the answer being 7/24 of a cake, or 7/48 of the cakes

[Toltec]

boyse7en said:

FredClogs said:

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

Don't you start! I was just getting my head round this...

I've gone with the answer being 7/24 of a cake, or 7/48 of the cakes

If someone asks how much fuel you have left do you say a quarter of a tank, fifteen litres or a quarter of the gallons I started with?

[boyse7en]

Alias218 said:

1/6 remains of one cake, 1/8 of the other.

We need to find a common denominator: 6*8=48.

Now the numerators need to be adjusted to match the new denominators: 6 goes into 48 eight times so the 1 becomes an 8 for 8/48 (the same as 1/6)

8 goes into 48 six times so the 1 becomes a 6 for 6/48 (the same as 1/8).

Add these together: 8/48 + 6/48= 14/48 (the denominator does not change).

Cancel down: 7/24.

And there is your answer.

So the answer, depending on how you view the question, is either 1/6 and 1/8 or 7/24.

But you could say that you've got 8 slices left from one cake of 48 slices, and 6 slices left from the other cake of 48 slices.

So that is 14 slices left out of a total of 96 slices.

Cancel down and the answer is 7/48

[jeremyc]

And this, boys and girls, graphically illustrates the differences between Applied Maths and Pure Maths.

The key to Applied Maths is understanding how to use the computation to answer the (admittedly badly worded) real world problem.

Pure Maths simply asks what is 1/6 + 1/8.

[4x4Tyke]

It is Maths problem not an English grammar question so it should be worded as 'What fraction of the cakes are left?'

What does the book say?

Have you checked the publishers website for an errata?

AFAIC the correct answer is 7/24.

[Sparkov]

The question is badly written, but taken literally it asks for a single answer to be provided as a fraction, and for the unit of that answer to be given in "the cakes". Not 1 cake, not 3 cakes, the (i.e. 2) cakes. Define the units of your answer to remove ambiguity.

7/48 of the two cakes remain.

[ikarl]

the way the question is asked, as advised by the OP, the answer is 7/48

[dr_gn]

FredClogs said:

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

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

[Alias218]

boyse7en said:

Alias218 said:

1/6 remains of one cake, 1/8 of the other.

We need to find a common denominator: 6*8=48.

Now the numerators need to be adjusted to match the new denominators: 6 goes into 48 eight times so the 1 becomes an 8 for 8/48 (the same as 1/6)

8 goes into 48 six times so the 1 becomes a 6 for 6/48 (the same as 1/8).

Add these together: 8/48 + 6/48= 14/48 (the denominator does not change).

Cancel down: 7/24.

And there is your answer.

So the answer, depending on how you view the question, is either 1/6 and 1/8 or 7/24.

But you could say that you've got 8 slices left from one cake of 48 slices, and 6 slices left from the other cake of 48 slices.

So that is 14 slices left out of a total of 96 slices.

Cancel down and the answer is 7/48

When you put it like that it's plain to see what all the kerfuffle is about!

However, it is also mathematically wrong.

Lets turn the fractions into decimals, for ease of visualisation. So:

3/24 = 0.125
4/24 = 0.167

0.125 + 0.167 = 0.291, we can all agree on that.

Incidentally, 7/24 = 0.291.

What you are doing is taking a whole (24) and turning it into two wholes (48). Makes sense, there are two 24 piece cakes therefore 48 pieces.

However, if we take 0.125 of 1 cake and 0.167 of 1 cake we see that when we add them using the two cake logic:

0.125/1 + 0.167/1 = 0.291/2 (as 3/24 + 4/24 = 7/48)

But then when we strip that right back: 0.125/1 = 0.125 and 0.167/1 = 0.167 and 0.291/2 = 0.145

The two cake logic states that 0.125 + 0.167 = 0.145, which it most certainly does not. It equals 0.291 or 7/24.

Incidentally, 0.145 = 7/48.

I had to scratch my head a little to get past the two cake image, which does lead you to conclude that 3/24 and 4/24 = 7/48. But mathematically, it doesn't. It can't. by adding the denominators, the amount of cake is being doubled, which then halves the amount of cake, as a fraction, that is left!

It's a very misleading question that can lead you down the garden path, but if you stick to mathematic principles you won't go wrong.