Simple Maths Problem

Simple Maths Problem

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dr_gn

Original Poster:

16,140 posts

183 months

Tuesday 9th January 2018
quotequote all
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

9,539 posts

170 months

Tuesday 9th January 2018
quotequote all
Very rusty but the remainders of the cakes are 1/8 + 1/6 = 3/24 + 4/24 = 7/24


Am43

276 posts

82 months

Tuesday 9th January 2018
quotequote all
The question is what fraction of cakes is left ?

To me that would be 7/24 of cake left

motco

15,919 posts

245 months

Tuesday 9th January 2018
quotequote all
Each cake? Average remainder? Ambiguous!

dr_gn

Original Poster:

16,140 posts

183 months

Tuesday 9th January 2018
quotequote all
motco said:
Each cake? Average remainder? Ambiguous!
It says "cakes"...

daddy cool

3,996 posts

228 months

Tuesday 9th January 2018
quotequote all
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

227 posts

88 months

Tuesday 9th January 2018
quotequote all
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

2,872 posts

272 months

Tuesday 9th January 2018
quotequote all
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

19,575 posts

243 months

Tuesday 9th January 2018
quotequote all
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

Original Poster:

16,140 posts

183 months

Tuesday 9th January 2018
quotequote all
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

3,701 posts

161 months

Tuesday 9th January 2018
quotequote all
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

9,975 posts

283 months

Tuesday 9th January 2018
quotequote all
The cake is a lie.

dr_gn

Original Poster:

16,140 posts

183 months

Tuesday 9th January 2018
quotequote all
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

4,048 posts

123 months

Tuesday 9th January 2018
quotequote all
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

9,975 posts

283 months

Tuesday 9th January 2018
quotequote all
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

Original Poster:

16,140 posts

183 months

Tuesday 9th January 2018
quotequote all
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

Original Poster:

16,140 posts

183 months

Tuesday 9th January 2018
quotequote all
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

9,975 posts

283 months

Tuesday 9th January 2018
quotequote all
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

4,048 posts

123 months

Tuesday 9th January 2018
quotequote all
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

Original Poster:

16,140 posts

183 months

Tuesday 9th January 2018
quotequote all
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.