Lecture
On the coordinate line you can draw any number as a point.
Zero is represented by point 0. In order to depict a positive or negative number, it is necessary to discard the sign from it and set aside from the beginning of the coordinate straight line segment equal to the number itself, in the direction that corresponds to the sign of the number.
Positive numbers are set to the right of zero, and negative numbers are left of zero.
The number indicating the position of a point on the coordinate axis is called the coordinate of this point .
The fact that the number n is the coordinate of the point A is written as: A (n).
Example. Find the coordinates of points A, B, C.
Answer: A (1); B (-2); C (3);
We mark on the coordinate line two points A and B, which are located at the same distance from point 0 to the right and left, respectively.
In this case, the lengths of the segments OA and OB are the same.
This means that the coordinates of points A and B differ only in sign.
It is also said that points A and B are symmetric about the origin of coordinates.
The coordinate of point A is positive "+2", the coordinate of point B has a minus sign "-2".
A (+2), B (-2).Numbers that differ only in sign are called opposite numbers . The corresponding points of the numerical (coordinate) axis are symmetric relative to the origin.
Each number has a unique number opposite to it . Only the number 0 does not have the opposite, but it can be said that it is opposite to itself.
The entry “-a” means the opposite of “a”. Remember that a letter can hide both a positive number and a negative number.
Example:
-3 - the number of the opposite number 3.We write in the form of an expression:
-3 = - (+ 3)Example:
- (- 6) - the number opposite to the negative number -6. So - (- 6) is a positive number 6.We write in the form of an expression:
- (- 6) = 6
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Arithmetic
Terms: Arithmetic