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
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Two signed numbers are equal when they have same absolute value and same sign.
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Two signed numbers are opposite or symmetric, when they have same absolute value but their signs are opposites. Example: +2 and -2;
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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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