My Math Forum Divide a 7/3 bar into 3/4

 Algebra Pre-Algebra and Basic Algebra Math Forum

September 23rd, 2012, 06:28 AM   #1
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Divide a 7/3 bar into 3/4

Hi. I can't find the right place for these questions. I think there is not a "just right" forum on here.

Anyway, this question is for a "Teaching of Mathematics" course my friend is in. I don't get the questions. I mean, what are they asking? What do they want her to do?

1b. Suppose that the bar in following represents 7/3. Create a bar that is equivalent to 3/4. (Then there is a picture of a horizontal bar.)

3. This question has one bar which is divided into 7 equal parts and another bar which is divided into 5 equal parts. The bars are horizontal, left-aligned, and equal length. The question is: Use a bar model to determine which one is bigger, 4/7 or 3/5, and explain how much one is bigger than the other. You must not calculate to find the solution and your explanation must be thorough. (Emphasis is mine.)

I enclosed a couple of pictures to enhance my outstanding (cough, cough ) descriptions. Thanks for helpin'.
J.

[attachment=2:kfi8yrwz]CaptureA.PNG[/attachment:kfi8yrwz]
[attachment=1:kfi8yrwz]CaptureB.PNG[/attachment:kfi8yrwz]
[attachment=0:kfi8yrwz]Capture3.PNG[/attachment:kfi8yrwz]
Attached Images
 CaptureA.PNG (6.0 KB, 72 views) CaptureB.PNG (6.1 KB, 72 views) Capture3.PNG (13.5 KB, 72 views)

September 23rd, 2012, 07:16 AM   #2
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Math Focus: Calculus/ODEs
Re: Divide a 7/3 bar into 3/4

Here's how I would do the first one:

[attachment=0:jdao3t93]bar1.jpg[/attachment:jdao3t93]

First, divide the bar into 5 equal segments, each segment representing 1/4 unit.

Second, divide each segment into 5 equal sub-segments since the denominator of 3/5 is 5, each sub-segment representing 1/20 unit.

Since 3/5 = 12/20, remove 12 sub-segments for a bar 3/5 units in length.

This suggests $\frac{12}{25}\cdot\frac{5}{4}=\frac{3}{5}$.

For the second one, divide the bar into 7 equal segments, each segment representing 1/3 unit.

Since the denominator of 3/4 is 4, divide each segment into 4 sub-segments, each representing 1/12 unit.

Since 3/4 = 9/12, remove 9 sub-segments for a bar 3/4 unit in length.

For the third one:

In the top bar, divide each segment into 5 sub-segments, each sub-segment representing 1/35 unit.

In the bottom bar, divide each segment into 7 sub-segments, each sub-segment representing 1/35 unit.

Now, count how many sub-segments are between the bold lines in each bar. This number is n. Then we know 4/7 + n/35 = 3/5.
Attached Images
 bar1.jpg (33.5 KB, 67 views)

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