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**Tamauri****Member**- Registered: 2010-11-09
- Posts: 1

Dear all,

I am just a mother who is trying to help her 6th grader with math homework.

I would like to find a simple and easy way for her to know the value of a fraction.

For example, which of these fractions is closer to 1? 3/4 or 9/11

At the moment what I told her is to divide the numerator by denominator and see which decimal would be closer to the number 1.

So,

3/4= 0.75

9/11=0.81

So, 9/11 would be closer to 1.

But we have been using the calculator for the division and I think there must be a better way (more simple) for a 6th grader. Especially when comparing with improper fractions. Like: Which fraction would be closer to the number 1 ( 3/4 or 11/9)

Please help me

Thank you.

Elisa

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi Elisa;

I do not think there is any way that is easier than a calculator. The thing does it for you. For your second problem you could go

4 / 4 - 3 / 4 = 1 / 4

11 / 9 - 9 / 9 = 2 / 9

You could now subtract these 2 fractions 1 / 4 - 2 / 9. If the answer is positive than the 11 / 9 is closer.

If it is negative then the 3 / 4 is closer.

This requires that your child understands positive and negative numbers and how to subtract 2 fractions.

I do not think that is easier than a calculator but your child will learn important concepts. I am curious what method is the teacher recommending?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,393

Hi Elisa,

My own prefered way to explain fractions to students at any level I call my chocolate diagram method. I haven't yet found a fractions problem that couldn't be done this way. In the ideal mathematical world bars of chocolate would be sold in slabs of different length and width so you could actually make the fractions. At the end of the lesson you eat the chocolate!:)

Have a look at my picture below. You were asking to compare quarters and ninths so I did 4 x 9 = 36 and made my one bar of chocolate that size ( 4 x 9).

[For a new problem you have to decide afresh what size of bar is needed for that problem.]

For your problem make two more the same (4 x 9).

Then split the first into quarters and shade 3. That shows 3/4

The second is all shaded to show 9/9.

The third is split into 9 parts and has 2 shaded to show another 2/9.

The second and third taken together show 9/9 plus 2/9 = 11/9.

To decide which fraction is closer to 1, just look at how many squares of chocolate are needed to make the fraction up to one or how many need to be taken off to get down to one.

3/4 is 9 squares too small.

11/9 is 2/9 over which is 8 squares.

So 11/9 is closer by one square which is 1/36 as a fraction.

This method also lets you make equivalent fractions

eg. 3/4 = 27/36

and to add fractions

eg. 3/4 + 2/9 = 27/36 + 8/36 = 35/36.

Hope that helps.

Bob

*Last edited by bob bundy (2010-11-09 08:53:43)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

Neat! (But strange looking chocolate)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,393

Hi MIF,

It's the default colour. But I can change it to a more chocolatey brown if you'd prefer.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,532

There is another very simple way (which I think is easiest)to do this (it's almost the same as bobbym's - but no integers).

Psuedo

```
1. Since we know that both fraction's numerator's are not greater then the denominator, we can tell that both fractions are not one whole yet.
2. So then simply subtract the fraction with the highest numerator by the other one. To do so:
1. Find a common denominator: 44. 11*4 and 4*11.
2. Multiply the numerators by the number you multipled the denominators by to get 44: 3*11=33 and 9*4=36.
End
3. Then take out the denominators and just check which numerator is great. In this case it's 36, so 9/11 is greater. So it's closes to one whole.
```

Otherwise, I suggest that the best way is using a calculator.

-Shivam

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