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Numbers Properties – pg. 1/2

Posted in Math Theory by Lia on 06/03/2014

Number Properties: 1, 2

Contents:

pg.1…..Number Properties  – Equality and Signed NumbersMeasuring numbers

pg.2…..Number Properties – Signs used in algebra

 

1.   Equality and Signed Numbers

  • Two signed numbers are equal when they have  same absolute value and same sign.

  • Two signed numbers are opposite or symmetric, when they have same absolute value but their signs are opposites.                                                                                                 Example: +2 and -2; {+ {7/8}} and {- {7/8}}{...}

2.   Measuring numbers

Let’s consider the horizontal line segment “ab” where we place the numbers in ascending order, as shown in Fig.1. Starting from  0  to the right, are positive numbers and to the left are negative numbers.

Numbers properties dwg 1

This line segment is named Number Line.

In order to consider a sign for the direction of a segment, we need to consider the direction in which we count (Fig. 2).

Numbers properties dwg 2

 

Examples: 

The segments OB = + 4 and OF = – 4 are symmetric.

The segment OB starts in O  and goes in the positive direction towards B.

The segment OF starts in O and goes in the negative direction towards F.

The segment “EA” goes from E towards A in the positive direction therefore, its value will have the sign “+”. If we count the number of units for EA on the Number Line ab“, there are 3 units, therefore EA = + 3.

Now let’s consider the reverse, the segment “AE” that goes from A towards E therefore it goes in the negative direction. The number of units is 3 as well but the sign in front of the number is ““. That’s means that “AE” = – 3.

We can say that “AE” and  “EA” have same absolute value but different signs. 

Any segment that starts in O  has its value the number of units from O  to the other end of the segment and, its sign is function of its direction. For instance point A is 2 (equivalent with the number of units from O to A (“OA“) and its direction is positive); point C is 7 (equivalent with the number of units from O to C (“OC“) and its direction is positive); point F is – 4 (equivalent with the number of units from O to F (“OF“) and its direction is negative), point H is – 9 (equivalent with the numbers of units from O to H (“OH“) and its direction is negative).

A number on the Number Line is larger than the numbers on its left and it’s smaller than the numbers on its right.

 

 Number Properties: 1, 2

 

 

 

 

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