Page 39 - 'Blast_Into_Math

Blast into Math! ets of nummers: mathematical plaagrounds

An equivalent way to define the absolute value of a number is:

The absolute value of x is the distance between x and 0 on the number line.

For two numbers x and y ,

|x − y| is thedistancebetween x and y on thenumber line.

Thinking about math using pictures, even a picture as simple as this, can be helpful!

{3 {2 {1 0 1 2 3

Every game has rules. You probably know the following rules already, but just to be sure we all play fairly,
we’ll review the rules of the games of addition, subtraction, and multiplication within the playground
of the integers.

1. Let x and y be natural numbers. Then

x − y

is equal to the sum of x and the additive inverse of y . That is

x − y = x +(−y).

2. The additive inverse of −x is x , and therefore

−− x = x,

and

x − (−y)= x −−y = x + y.

3. The product of x and −y is equal to the additive inverse of xy . That is

x ∗ (−y)= −xy.

4. The product of −x and −y is equal to the product of xy . That is

(−x) ∗ (−y)= xy.

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