Opposite of number 1. Opposite numbers, definition, examples

In this article we will explore opposite numbers. Here we will answer the question of what numbers are called opposites, show how the opposite of a given number is designated, and give examples. We will also list the main results characteristic of opposite numbers.

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Determining opposite numbers

It will help us to get an idea of ​​opposite numbers.

Let us mark some point M on the coordinate line, different from the origin. We can get to point M by sequentially laying off a unit segment, as well as its tenth, hundredth, and so on, from the origin in the direction of point M. If we plot the same number of unit segments and its shares in the opposite direction, then we will get to another point, denoted by the letter N. Let's give an example to illustrate our actions (see figure below). To get to point M on the coordinate line, we laid off two unit segments and 4 segments, constituting a tenth of a unit, in the negative direction. Now let's put two unit segments and 4 segments, constituting a tenth of a unit, in the positive direction. This will give us point N.

We are almost ready to understand the definition of opposite numbers; all that remains is to discuss a couple of nuances.

We know that each point on the coordinate line corresponds to a single real number, therefore, both point M and point N correspond to some real numbers. So the numbers corresponding to points M and N are called opposite.

Separately, it is necessary to say about point O - the origin. Point O corresponds to the number 0. The number zero is considered to be the opposite of itself.

Now we can voice determining opposite numbers.

Definition.

Two numbers are called opposite if the points on the coordinate line corresponding to these numbers can be reached by laying off the same number of unit segments from the origin in opposite directions, as well as fractions of a unit segment, the number 0 is opposite to itself.

Notation of opposite numbers and examples

It's time to enter symbols of opposite numbers.

To indicate the opposite of a given number, use the minus sign, which is written in front of the given number. That is, the number opposite to the number a is written as −a. For example, the opposite number 0.24 is −0.24, and the opposite number −25 is −(−25).

Let's give examples of opposite numbers. The pair of numbers 17 and −17 (or −17 and 17) is an example of opposite integers. The numbers and are opposite rational numbers. Other examples of opposite rational numbers are the pairs of numbers 5.126 and −5.126. as well as 0,(1201) and −0,(1201) . It remains to give a few examples of the opposite

Opposite numbers definition

Opposite numbers definition:

Two numbers are called opposite if they differ only in signs.

Examples of opposite numbers

Examples of opposite numbers.

1 -1;
2 -2;
99 -99;
-12 12;
-45 45

From here it is clear how to find the opposite of a given number: just change the sign of the number.

The opposite number to 3 is the number minus three.

Example. Numbers are opposite to data.

Given: numbers 1; 5; 8; 9.

Find the opposite numbers of the data.

To solve this task, simply change the signs of the given numbers:

Let's make a table of opposite numbers:

The opposite of zero

The opposite of zero is the number zero itself.

So the opposite number to 0 is 0.

Opposite Integers

Opposite integers differ only in sign.

Examples of opposite integers.

10 -10
20 -20
125 -125

Pair of opposite numbers

When they talk about opposite numbers, they always mean a pair of opposite numbers.

A number is the opposite of another number. And every number has only one opposite number.

Numbers opposite to natural numbers

The opposite of natural numbers are negative integers.

Let's make a table of opposite numbers for the first five natural numbers:

Sum of opposite numbers

The sum of opposite numbers is zero. After all, opposite numbers differ only in sign.

An interesting concept from the school curriculum is opposite numbers, which can be considered both mathematically and geometrically. Understanding this topic simplifies the study of mathematics and allows you to quickly cope with some problems - so we will look at what numbers are called opposites, and what rules work for them.

What is the essence of the term?

To understand the meaning of opposite numbers, let's turn to geometry for a moment. Let's draw a coordinate line and mark the zero point on it, and then put two more marks on the line - for example, “2” on the right side and “-2” on the left side of zero. Of course, from both points the distance to the origin will be exactly the same - and this can be easily verified by measurements. “2” and “-2” are the same distance from zero, but in different directions - accordingly, they are completely opposite to each other.

That's the point. Numbers can be as large or small as desired, whole or fractional. However, each of them has a certain number that is its exact opposite. The definition can be given as follows - if on the coordinate line from two points placed on both sides of zero, an equal distance can be set aside to the origin - these points, or more precisely, the numbers corresponding to them, will be opposite.

What rules can be derived from the definition?

It is worth remembering a few absolute statements regarding the topic under consideration:

• The principle of opposites for two numbers works both ways. For example, the number 3 is opposite to the number -3 - and therefore only the number 3 is opposite to the number -3, and not any other.
• A number cannot have two opposites - there is always only one.
• Numbers with different signs can be opposite to each other. If a number is positive, then its opposite number will have a minus sign - for example, 5 and -5. The same thing works in the opposite direction - for a number with a minus sign, the opposite will always be the one with a plus sign - for example, -6 and 6.
• Two opposite numbers have the same absolute value, or modulus. In other words, if for the number 4