Mastering Integer Multiplication: Rules and Examples

Mulplying Integers

Example: ‐ Temperatures below freezing are indicated by negave integers; temperatures above freezing by posive integers. In general, numbers such as 1,2,3, …are called positive integers; and numbers such as ‐1, ‐2,‐3,… are called negative integers. The negave integers, zero, and posive integers make up the set of integers, denoted by I.
So, I=…,-3,-2,-1,0,1,2,3,…
Integers such as ‐2 and 2 are called apposite integers.

Integers can be represented on a number line.

Note that any integer on the number line is greater than all the integers to its le and less than all the integers to its right.

Note that -5 is greater than -6.
Rules of Multiplication
–=+
-+=-
+-=-
++=+

Rules of Division
–=+
-+=-
+-=-
++=+
Note that the product/quoent of two integers with the same signs is posive, otherwise negave. Ex 1: Simplify.
a) (‐2)(+6)=-12
b) (‐7)(‐5)=+35
c) (+9)(‐6)=-54
d) (‐3)(‐4)(‐5)(‐1)=[(-3)(-4)][(-5)(-1)]=(12)(5)=60
e) (‐6)(‐4)(‐2)=[(-6)(-4)](-2)=(24)(-2)=-48
How can you determine the sign of the answer when you are mulplying more than two terms?
If you are multiplying an even number of negative or positive signs then the answer has a positive sign.

(See example 1 d)
If you are multiplying an odd number of negative signs then the answer has a negative sign
(See example 1 e)

Ex 2: Simplify.
a) +63÷ -9
=-7
b) (-42)÷ (-7)
=+6
c) -2-3-4-1-5
=-310

Note that posive integers are usually wrien without the positive sign.
Question: Can you divide any number by zero?
Dividing by zero has no me meaning.

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In other words any number divided by zero is undefined.
Ex.: 20=undefined
There is no number when multiplied by zero that equals 2 (0 × any number=0)