Numbers Properties – pg. 1/2
Number Properties: 1, 2
Contents:
pg.1…..Number Properties – Equality and Signed Numbers, Measuring 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; and ;
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.
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).
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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