Opposite numbers

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In the previous articles we studied about the number line and integers. In this article we will explain what opposite numbers are, and how to identify them.

What are opposite numbers, and how to identify them?

Opposite numbers are numbers that when added together result in the number 0 0 .

The opposite of a number has the same absolute value, but with opposite sign.

Examples:

  • +3 +3 and βˆ’3 -3 are opposite numbers.
  • +9.4 +9.4 and βˆ’9.4 -9.4 are opposite numbers.
  • +14 +\frac{1}{4} and βˆ’14 -\frac{1}{4} are opposite numbers (fractions).
What are opposite numbers, and how to identify them

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What is the opposite number of \( 5 \)

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As we have already studied in previous articles, in positive numbers, the plus sign can be omitted.
So it is that:

  • 8 8 and βˆ’8 -8 are opposite numbers.
  • +100 +100 and βˆ’100 -100 are opposite numbers.

As we have already said, when we add two opposite numbers, the result is 00.
Examples:

  • (βˆ’5)+(+5)=0(-5)+(+5)=0
  • (+54)+(βˆ’54)=0(+54)+(-54)=0
  • 23.5+(βˆ’23.5)=023.5+(-23.5)=0

Also when we add 0+00 + 0the result is zero. Therefore, the number opposite zero is zero itself. This is a special case.


Do the following exercises, applying what we have studied in this article:

  1. Of the following numbers, which pairs are opposite numbers?
  • +7,βˆ’4+7, -4
  • 9.4,βˆ’9.49.4, -9.4
  • +4.35,βˆ’4.35+4.35, -4.35
  • 80,+8080, +80
  • +313,βˆ’313+313, -313
  • 0,00, 0
  • βˆ’45,+54-45, +54

2. Create 8 8 addition operations, in which the result of each one of these will give us 0 0 .


3. Fill in the blanks, to get the number opposite the number shown.

  • 44 βˆ’3+-3+__
  • βˆ’8-8 20+20+__
  • βˆ’33-33 __+(+10)+(+10)
  • 6060 βˆ’64+-64+__
  • 00 18+18+__

4. What is the opposite of the following numbers?

  • 0.70.7
  • 55
  • βˆ’0.25-0.25
  • 8787
  • βˆ’7-7
  • βˆ’87-{8\over7}

5. Based on what you have learned about the topic absolute value Determine if the following pairs of numbers are opposites:

  • βˆ’βˆ£βˆ’81∣,∣92∣-|-81| , |92|
  • βˆ£βˆ’3∣,∣3∣|-3| , |3|
  • ∣56∣,βˆ£βˆ’5.6∣|56| , |-5.6|
  • βˆ’βˆ£βˆ’801∣,∣+801∣-|-801| , |+801|
  • βˆ£βˆ’13∣,∣31∣ ∣-\frac{1}{3}∣,∣\frac{3}{1}∣
  • βˆ£βˆ’8∣,∣648∣ βˆ£βˆ’8∣,∣\frac{64}{8}∣

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Review questions

What are the opposite or symmetrical numbers?

The opposite numbers or also called symmetric numbers are those that have the same number, but with opposite sign, we can also define them as those numbers that are at the same distance from zero on the number line. For example, in the following line we have βˆ’4 -4 and 4 4 these two numbers are symmetrical, since they have different signs and are at the same distance from zero.

1 - Different sign and they are at the same distance from zero


Do you know what the answer is?

What do the opposite numbers mean?

They mean that they are at the same distance from zero, opposite numbers mean that they have the same quantity but with different signs, for example: 6 6 and βˆ’6 -6 or βˆ’14 -14 and 1414 .


How to make the opposite numbers?

In order to find the opposite or symmetric numbers we just write the same number but with the opposite sign, for example we are going to write the opposites of the following numbers:

  • βˆ’9 -9 we write again the same number but in this case as it is negative then its symmetric will be positive. 9 9
  • 3.5 3.5 its symmetric number will be the same number but with opposite sign, that is, βˆ’3.5 -3.5
  • 35 \frac{3}{5} we write the same number but with opposite sign βˆ’35 -\frac{3}{5} .

Ejemplos y ejercicios con soluciones de nΓΊmeros opuestos

Exercise #1

What is the opposite number of 5 5

Video Solution

Answer

βˆ’5 -5

Exercise #2

What is the opposite number of 87 87

Video Solution

Answer

βˆ’87 -87

Exercise #3

What is the opposite number of 0.7 0.7

Video Solution

Answer

βˆ’0.7 -0.7

Exercise #4

What is the opposite number of βˆ’7 -7

Video Solution

Answer

7 7

Exercise #5

What is the opposite number of βˆ’0.25 -0.25

Video Solution

Answer

0.25 0.25

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