Absolute Value and Opposites in Mathematics

Absolute Value of a Number

• The absolute value of a number is the distance between that number and zero on the number line.
• The absolute value of a number is never negative.
• It is denoted by two vertical bars (| |).
• For example, |2| = 2, |-2| = 2, |0| = 0

Opposites (Additive Inverses)

• Opposites are numbers that are equidistant from zero on the number line but have opposite signs.
• For example, the opposite of 3 is -3, the opposite of -5 is 5.
• The opposite of a number is also called its additive inverse.

Examples of Opposites

• Opposites of numbers: 3 and -3; -10 and 10; 56 and -56; 49 and -49
• Opposites of words/concepts: cold and warm; down and up; north and south; rising and falling; decrease and increase; backward and forward; below and above

Number Line

• A number line visually represents numbers in order from smallest to largest.
• Positive numbers lie to the right of zero on the number line; negative numbers lie to the left.
• Opposites are found on opposite sides of zero, equally distant from it.

Absolute Value Examples

• |4| = 4
• |-4| = 4
• |2+3|-|4-3| =5-1 = 4
• |7-4|-|5-3| =3-2 = 1 (Solved example of absolute value operation)

Comparing Absolute Values

• Symbols like < (less than), > (greater than), and = (equal to) are used to compare the absolute values of different numbers.
• For example: |2| > |-2|; |10 - 2| = |6 + 2|; |-5-2| < |-1 + 1| ; |8 -3| = |6 - 1|

Explore the concepts of absolute value and opposites (additive inverses) in this quiz. Learn how to identify absolute values and understand the relationship between numbers and their opposites on the number line. Perfect for reinforcing basic math principles!