Cake fraction problem: "Vladimir wants to have some cake left over for himself

[patelsm]

Hi,

I have got the answer to this question and I cannot understand why it is the chosen one:

"Vladimir wants to have some cake left over for himself after he distributes a share to each of his 8 friends.
Which of these options, of what fraction of a cake to give each friend, will allow this?
1) 12%
2) one seventh
3) 0.14
4) two ninths
5) 3/20

the answer is supposedly 12% - because 12 fits in "8" times in 100 (one whole cake) + leaving .33 remainder (100 divided 12 - 8.33)
so Valdimir friends gets 8 cakes and he get .3
Is this the correct concept being explained to my kid - what I am struggling to understand and explain is the .33 - how about the remaining .63 as that would make the whole cake.
Who would get the .63 bit?

i some how got 2/9ths as the answer and now I just cannot back track on how I got this...

please help.

thanks,
saf

 

[Dr.Peterson]

"Vladimir wants to have some cake left over for himself after he distributes a share to each of his 8 friends.
Which of these options, of what fraction of a cake to give each friend, will allow this?
1) 12%
2) one seventh
3) 0.14
4) two ninths
5) 3/20

the answer is supposedly 12% - because 12 fits in "8" times in 100 (one whole cake) + leaving .33 remainder (100 divided 12 - 8.33)
so Valdimir friends gets 8 cakes and he get .3
Is this the correct concept being explained to my kid - what I am struggling to understand and explain is the .33 - how about the remaining .63 as that would make the whole cake.
Who would get the .63 bit?

i some how got 2/9ths as the answer and now I just cannot back track on how I got this...

You don't need to work out the .33 to answer the question, so I'll focus first on how to solve the problem as stated.

All you need is to find which of the given numbers is less than 1/8, so that 8 times (the amount given) it will be less than 1 and there will be some left. If he gave each friend 1/8, then they would use up the whole cake; anything less leaves some for Vladimir.

You could do this in many ways. You could actually compare each choice to 1/8, or multiply each choice by 8 and compare to 1, and so on.

If you thought (for whatever reason) that 2/9 is the answer, then you can check by multiplying by 8 to see if the amount the friends get is small enough. 8*2/9 = 16/9 > 1, so that isn't right.

Now, when you check 12%, or 0.12, you find that 8*0.12 = 0.96 < 1, so that works. But note that he gets the rest, which is 1.00 - 0.96 = 0.04, not 0.33.

I think you misread the solution. What they apparently did was to divide 1 (or 100%) by each answer to see how many friends could get that much. (This is perhaps the hardest way to do it, since division is harder than multiplication -- if the book said this, shame on them.)

100/12 = 8.33... (or 8 1/3); what this means is not that Vladimir gets 0.33 of a cake, but that 8 1/3 people could each get 12%. He will be the extra 1/3 of a person -- that is, he will get 1/3 of the 12% the others get, namely 4% of a cake. This, again, is not the easiest way to answer that question, how much he gets.

 

[Denis]

I'll bite: why not simply cut the cake in 9 equal portions?

If circular: lay a protractor on the top and notch every 40 degrees

If square, yer lucky!

 

[patelsm]

You don't need to work out the .33 to answer the question, so I'll focus first on how to solve the problem as stated.

All you need is to find which of the given numbers is less than 1/8, so that 8 times (the amount given) it will be less than 1 and there will be some left. If he gave each friend 1/8, then they would use up the whole cake; anything less leaves some for Vladimir.

You could do this in many ways. You could actually compare each choice to 1/8, or multiply each choice by 8 and compare to 1, and so on.

If you thought (for whatever reason) that 2/9 is the answer, then you can check by multiplying by 8 to see if the amount the friends get is small enough. 8*2/9 = 16/9 > 1, so that isn't right.

Now, when you check 12%, or 0.12, you find that 8*0.12 = 0.96 < 1, so that works. But note that he gets the rest, which is 1.00 - 0.96 = 0.04, not 0.33.

I think you misread the solution. What they apparently did was to divide 1 (or 100%) by each answer to see how many friends could get that much. (This is perhaps the hardest way to do it, since division is harder than multiplication -- if the book said this, shame on them.)

100/12 = 8.33... (or 8 1/3); what this means is not that Vladimir gets 0.33 of a cake, but that 8 1/3 people could each get 12%. He will be the extra 1/3 of a person -- that is, he will get 1/3 of the 12% the others get, namely 4% of a cake. This, again, is not the easiest way to answer that question, how much he gets.

Dr Peterson - sincere apologies for not responding sooner. I read your immediate response and am ever so grateful as the study weekend would have come to a stop by me being stuck on this.
My child understands your explanation about the fact that if we gave 1/8 to 8 friends - then there no cake left 8/8).
As suggested, there were two ways to check this - A) either compare that each choice is less than 1/8 (so that there is some left over) and the other is to multiply with 8 and check it is less than 1.
As her exam is timed, i think the multiplication is easier - but how is the same as checking each choice is less than 1?

thank you
Sarfaraz

 

[Dr.Peterson]

Dr Peterson - sincere apologies for not responding sooner. I read your immediate response and am ever so grateful as the study weekend would have come to a stop by me being stuck on this.
My child understands your explanation about the fact that if we gave 1/8 to 8 friends - then there no cake left 8/8).
As suggested, there were two ways to check this - A) either compare that each choice is less than 1/8 (so that there is some left over) and the other is to multiply with 8 and check it is less than 1.
As her exam is timed, i think the multiplication is easier - but how is the same as checking each choice is less than 1?

thank you
Sarfaraz

I agree that multiplication is easier.

In terms of algebra, the first check is x < 1/8, while the second is 8x < 1, which are equivalent. (Multiply each side of the first equation by 8 to get the second.) That is, if you multiply a fraction less than 1/8 by 8, you get a number less than 1.

In terms of cake, multiplying the amount one person gets by 8 gives the amount they all get, which has to be less than 1 (whole cake). And if you multiply an amount less than 1/8 of the cake by 8, you get an amount less than 1.

Does that answer your question?

 

[HallsofIvy]

Hi,

I have got the answer to this question and I cannot understand why it is the chosen one:

"Vladimir wants to have some cake left over for himself after he distributes a share to each of his 8 friends.
Which of these options, of what fraction of a cake to give each friend, will allow this?
1) 12%

If he gives each of 8 friends 12% of the cake, he will give them 8(12)= 96% of the cake having 4% left for himself.

All of the other options give away more cake than he has!

2) one seventh

One seventh for each of 8 friends is 8/7 of the cake! Impossible!

3) 0.14

0.14 for each of 8 friends is 8(0.14)= 1.12. Not enough cake to go around!

4) two ninths

Two ninths for each of 8 friends is 16/9= 1 and 7 ninths. Again, too much.

5) 3/20

3/20 for each of 8 friends is 24/20= 1 and 1/5. Yet again, too much.

the answer is supposedly 12% - because 12 fits in "8" times in 100 (one whole cake) + leaving .33 remainder (100 divided 12 - 8.33)
so Valdimir friends gets 8 cakes and he get .3

Be careful explaining what your fractions represent. Vladimir's 8 friends get 12% of the cake and he gets 4%, 1/3 as much as each friend.

Is this the correct concept being explained to my kid - what I am struggling to understand and explain is the .33 - how about the remaining .63 as that would make the whole cake.

You are rounding 1/3 to 0.33- don't do that! I am sure your child will understand 4%, which is 1/3 as much as the 12% each of his friends gets, better than "0.33". Are you using a calculator? Calculators, especially when they are set to round to only two decimal places, don't work well with fractions! Do this kind of problem "by hand".

But will your child understand the concept of giving friends more than you keep for yourself? Kind of a hard concept!

Who would get the .63 bit?

I have no idea where you got ".63"! 1- .33= .67. Is that what you meant? But that is irrelevant anyway.

i some how got 2/9ths as the answer and now I just cannot back track on how I got this...

The answer to what question? If he were to divide the cake so that each of his friends
and himself got the same amount, each would get 1/9 but no one would get 2/9.

please help.

thanks,
saf