Math Is Fun Forum

Khushboo

Member

Registered: 2007-10-16

Posts: 47

Fraction Reasoning

When we introduce fractions the first thing a learner needs to know is the fact that for a given problem to qualify as a fraction, the number of divisions needs to be equal or we need to divide the shape or the collection equally. Why is it so? Are there any activities that explains the need for equal division?

Regards
Khushboo

Last edited by Khushboo (2008-01-23 22:41:50)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,340

Re: Fraction Reasoning

This is simply because there exists a single denominator. Try explaining dividing the same shape into different number of parts, each time you'd end up with equal parts. This is because a fraction has the same denominator. Different fractions have different denominators, but in each single case, the number of equal parts would be the same as the denominator, hence we end up with equal parts always. There is no alternative method, to the best of what I know!

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Fraction Reasoning

Yes, if a group of people want the same number of oreo cookies, then
you try to be fair, so you deal them out like a deck of cards.
One for you, one for you, one for you, and repeat until everyone
has as much as you can get.  The left over cookies have to be
broken into pieces I guess.
Now say top / bottom.
Say bottom is a half.
And top is one.
1/ (1/2) is 2.
How could we make a sentence where
this works out??
"One-half of the answer will be the top number."
Does this always work; I hope so; try it!!

---

igloo myrtilles fourmis

Khushboo

Member

Registered: 2007-10-16

Posts: 47

Re: Fraction Reasoning

Let me share this activity with you to illustrate the "need for equal division".

I have 2 rectangular shape. Each of these shapes are divided in three parts vertically and one part of the two rectangular shapes are shaded. The first has been divided equally into 3 parts and hence the shaded part is 1/3 whereas in the second case the rectangle has been divided into three parts but the divisions are not equal. Now if the rectangular region is 48cm^2, 1/3 of the first rectangular shape will be 16cm^2. However in the second case since the divisions were unequal it is difficult to find the fraction piece and say how much is the shaded region of the entire rectangular shape.

Regards
Khushboo

Last edited by Khushboo (2008-01-25 00:53:25)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Fraction Reasoning

Yes, it is harder to find without a millimeter-etched ruler.
But if you have a long roll of paper, maybe you can go
larger, instead of measuring smaller.  Say one piece is
about 40% of the rectangle.  If you make the rectangle
twice as long, then you can draw 5 of the pieces in a
line and it would end at the 2nd rectangle on the long
roll of paper.  So then you have 5 pieces inside 2
rectangles.  Each piece is 2/5 of a rectangle.  How I
know this is that I was taught it, but maybe you
could work on it more.

---

igloo myrtilles fourmis