**Absolute value and opposite integers :**

**Absolute value :**

Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies.

The absolute value of a number is never negative. The absolute value of -5 is 5.

**Opposite integers :**

The number which are having same numerical value but opposite signs are know as opposite integers. For example opposite integer of -5 is +5. That is they have same value but different signs.

When we add a number with its opposite integer, we will get zero.

Let us see some example problems based on the above concept.

**Example 1 :**

Find the absolute value of |-4|

**Solution :**

When we look at the number line, -4 is 4 units from 0.

Since -4 is 4 units from 0, we say that the absolute value of "-4" is 4.

Hence the value of |-4| = 4.

**Example 2 :**

Find the absolute value of |8|

**Solution :**

When we look at the number line, 8 is 8 units from 0.

Since 8 is 8 units from 0, we say that the absolute value of "8" is 8.

Hence the value of |8| = 8.

**Example 3 :**

Find the absolute value of |-7|

**Solution :**

When we look at the number line, -7 is 7 units from 0.

Since -7 is 7 units from 0, we say that the absolute value of "-7" is 7.

Hence the value of |-7| = 7.

**Example 4 :**

Find the absolute value of |-1|

**Solution :**

When we look at the number line, -1 is 1 units from 0.

Since -1 is 1 unit from 0, we say that the absolute value of "-1" is 1.

Hence the value of |-1| = 1.

**Example 5 :**

Find the opposite integer of -46

**Solution :**

Opposite integer means, the numerical value must be same, but different in signs.

Hence the opposite integer of -46 is 46.

**Example 6 :**

Find the opposite integer of 6

**Solution :**

Opposite integer means, the numerical value will be same, but different in signs.

Hence the opposite integer of 6 is -6.

**Example 6 :**

Jane completes several example problems that ask her to the find the opposite of the opposite of a number, and for each example, the result is a positive number. Jane concludes that when she takes the opposite of the opposite of any number, the result will always be positive. Is Jane correct? Why or why not?

**Solution :**

She is not correct. The opposite of the opposite of a number is the number itself. So, if Jane starts with a negative
number, she will end with a negative number.

After having gone through the stuff given above, we hope that the students would have understood "Absolute value and opposite integers".

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