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Learning Math Home
Number and Operations Session 2. Part C: Examining Zero
 
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Session 2, Part C:
Examining Zero

In This Part: The Behavior of Zero | Positional Number Systems
Exploring Zero and Infinity on a Graph

We can further explore the number line and its elements through a graphic representation of an equation. For example, on such a graph we can visually locate an irrational number or demonstrate what happens when we try to divide with 0.

Let's explore the graph of the equation x • y = 12.

Use the Interactive Activity to explore this graph. Answer Problems C3-C8 and corroborate your answers on the graph.

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version of this activity, examine the graph below and answer Problems C3-C8.


 
 

Here is the graph of the equation x • y = 12 in the first quadrant:


 

Problem C3

Solution  

a. 

Would the point (2,6) be on the graph? How do you know?

b. 

What about the point (24,0.5)?

c. 

What about the point (-3,4)?

d. 

Experiment with putting different numbers from the number line into the equation. What happens?


 

Problem C4

Solution  

What y value would be paired with x = 4? How do you know?


 

Problem C5

Solution  

a. 

What is the significance of the point of intersection of this graph and the line y = x?

b. 

Estimate the coordinates of this point.


 

Problem C6

Solution  

Will the graph ever touch either the x- or y-axis? Explain.


 

Problem C7

Solution  

What happens on the graph when x = 0 or y = 0? How does this demonstrate why you cannot divide a number by 0?



video thumbnail
 

Video Segment
In this video segment, Andrea and L.J. explore whether the curve will ever touch one of the two axes. Professor Findell helps them resolve their dilemma. Watch this video segment after you've completed Problem C7.

Think about whether the graph will behave in the same way for all four quadrants.

If you are using a VCR, you can find this segment on the session video approximately 21 minutes and 1 seconds after the Annenberg Media logo.

 

 

Problem C8

Solution  

Using the Interactive Activity, switch to the four-quadrant version of the graph. Now try plotting points for x = -0.5, x = -1, and x = -4. Does this view change your answer to Problem C5?

For a non-interactive version of this problem, look at the graph of x • y = 12 above. This graph shows only the first quadrant. Would there be points in any other quadrant? Does this change your answer to Problem C5? Explain.


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