Opposite numbers

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

• $8$ and $-8$ are opposite numbers.
• $+100$ and $-100$ are opposite numbers.

As we have already said, when we add two opposite numbers, the result is $0$.
Examples:

• $(-5)+(+5)=0$
• $(+54)+(-54)=0$
• $23.5+(-23.5)=0$

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

1. Of the following numbers, which pairs are opposite numbers?

• $+7, -4$
• $9.4, -9.4$
• $+4.35, -4.35$
• $80, +80$
• $+313, -313$
• $0, 0$
• $-45, +54$

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

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

• $4$ $-3+$__
• $-8$ $20+$__
• $-33$ __$+(+10)$
• $60$ $-64+$__
• $0$ $18+$__

4. What is the opposite of the following numbers?

• $0.7$
• $5$
• $-0.25$
• $87$
• $-7$
• $-{8\over7}$

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

• $-|-81| , |92|$
• $|-3| , |3|$
• $|56| , |-5.6|$
• $-|-801| , |+801|$
• $∣-\frac{1}{3}∣,∣\frac{3}{1}∣$
• $∣−8∣,∣\frac{64}{8}∣$

Positive and negative numbers and zero

The real line

Absolute value

Elimination of parentheses in real numbers

Addition and subtraction of real numbers

Multiplication and division of real numbers

On the Tutorela blog you will find a variety of articles about mathematics.

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 $-4$ and $4$ these two numbers are symmetrical, since they have different signs and are at the same distance from zero.

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: $6$ and $-6$ or $-14$ and $14$.

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:

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