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.

[selym]

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

[Am43]

The question is what fraction of cakes is left ?

To me that would be 7/24 of cake left

[motco]

Each cake? Average remainder? Ambiguous!

[dr_gn]

motco said:

Each cake? Average remainder? Ambiguous!

It says "cakes"...

[daddy cool]

Heres how it should be worded:

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.
1) What fraction of cake is left?
2) Which person is most likely to become Type 2 diabetic?

[dionbee93]

I've worked it out like... altogether there's 14 'pieces' of cake (6+8) and out of the 14, 12 have been taken (5+7) therefore;

I'd say 12/14 have gone therefore 2/14 left over or simplified to 1/7 left over

Dion.

[tight fart]

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?

[Einion Yrth]

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.

[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.

[brrapp]

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.

[Alex]

The cake is a lie.

[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.

[Shaoxter]

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.

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

Not sure if serious.....

[Alex]

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?

[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

[Alex]

To simplify the problem for a second, let's say you took 7/8 from each cake. What fraction of the cakes would be left?

1/8 + 1/8 = 2/8 = 1/4?

Is the intuitive mathematical answer, but is now clearly wrong. Imagine the cakes on top of each other (one tall cake) and removing 7/8. You would be left with 1/8 of the total, not 2/8.

So the formula should be:

1/16 + 1/16 = 2/16 = 1/8

This leads me to accept 7/48 as the correct answer to the original problem.

[Shaoxter]

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...

[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.