Math Is Fun Forum

Khushboo

Member

Registered: 2007-10-16

Posts: 47

In your opinion what is equivalent fraction of 16/48.

We have been struggling for quite sometime. We have gone on various websites to see how they treate equivalent fractions.

Lets assume 16/48 as one fraction. We need to find the equivalent fraction for 16/48

Now do you think 15/45 is the equivalent fraction of 16/48 because both of them when reduced in there simplest form gives 1/3 and hence logically should be equal. In my opinion 15/45 cannot be the equivalent for 16/48. When we simplify 16/48 we get 16/48=8/24=4/12=1/3. The 16 parts out of 48 parts can be grouped in 8 parts which is equivalent to 16 parts. However the 16 parts cannot be grouped in 15 parts and hence 15/45 cannot be the equivalent of 16/48. If 15/45 is true then in that case we can have "n" no. of possibilities.

What is the right explaination for it? Kindly help...

Regards

Khushboo

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: In your opinion what is equivalent fraction of 16/48.

This is how I think about it:

When you do X/Y, you end up with X amounts of 1/Y. So in your examples, you have:
16 pieces of size 1/48
and
15 pieces of size 1/45

The fact that you have less 'pieces' of one is made up for by the fact that 1/45 is bigger than 1/48 so you don't need quite so many to acheive the same size.

I think a more extreme example would be: 5 pieces of 1/5 and 2 pieces of 1/2; they are equivalent, right? You can reduce 5/5 and 2/2 to 1/1, but not by the same factors (just like with 15/45 and 16/48).

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: In your opinion what is equivalent fraction of 16/48.

I think the question is confusing. You can't have "the" equivalent fraction, because there are lots of them.

15/45 is an equivalent fraction of 16/48, as are 8/24, 4/12, 2/6, 1/3, 2624786349/7874359047, and any other that you would care to name.

If the question wants the simplest equivalent fraction then you'd have to say 1/3, but if it doesn't specify that then you can say whatever.

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Why did the vector cross the road?
It wanted to be normal.

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: In your opinion what is equivalent fraction of 16/48.

Perhaps clarification is needed.

I didn't read your post as you wanting the only equivalent, but as wanting any equivalent fraction, but were unsure why 15/45 and 16/48 were equivalent?

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.

Khushboo

Member

Registered: 2007-10-16

Posts: 47

Re: In your opinion what is equivalent fraction of 16/48.

I have mentioned about the simplification of the said fractions in its simplest form . 15/45 or 16/48 when reduced in their simplest form will yield 1/3.

However thankyou for the post as i have been able to resolve the conflict and get the correct explaination for the same.

In my opinion a fraction such as 1/3 can have "n" no. of equivalent fractions. The reason being that when 1/3 becomes 2/6 , the 1 part of 3 parts gets rearranged and produces 2/6.Thus it is like  dividing and then rearranging them to yield the equivalent fraction.

I hope i am clear.

Thanxs & Regards

Khushboo

Last edited by Khushboo (2007-12-02 16:49:24)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: In your opinion what is equivalent fraction of 16/48.

Imagine you can slice up a squash pie really well into equal parts.
Now for 15/45, cut the pie into 45 slices.
Now cut a pumpkin pie of the same size in 48 parts.
Remove 15 slices of the squash pie.
Also remove 16 slices of the pumpkin pie.
Put these slices back into the wrong pies.
Wow, they fit perfectly.
It is simply weird, but true.
I've never tried it, but I believe it.
1/3 = 2/6 = 3/9 = 4/12 =
5/15 = 6/18 = 7/21 = 8/24 =
9/27 = 10/30=11/33 = 12/36 =
13/39 = 14/42 = 15/45 = 16/48 =
17/51 = 18/54 = 19/57 = 20/60=
21/63=22/66  Sounds good to me, but
I've never tried it that much.

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igloo myrtilles fourmis

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: In your opinion what is equivalent fraction of 16/48.

Khushboo

Good Point!

Actually you are an fundamentalist as I am.

Your question involves whether we could assume arbitary divisibility to one unit.

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X'(y-Xβ)=0

Khushboo

Member

Registered: 2007-10-16

Posts: 47

Re: In your opinion what is equivalent fraction of 16/48.

Thanxs George

Equivalent fraction is an important concept and designing activities to explain equivalent fraction is a tedious task...you will have to restrict yourself beyond a point if you are trying to illustrate equivalent fractions visually but on paper it is just fine.

Regards
khushboo