Integers

The Number Line

The number line is a line labeled with the integers in increasing order from left to right, that extends in both directions:

For any two different places on the number line, the integer on the right is greater than the integer on the left.

All integers on the right side of zero are positive and all integers to the left of zero are negative.

Uses of integers

Credits are represented by positive numbers and debts are represented by negative numbers.  This is used when you want to count on both sides of a fixed point of reference.

The graph below shows the difference between exports and imports from 1960 to 2010. 

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Addition

rules:

1. negative plus negative equals negative
2. positive plus positive equals positive if a>b            a+ -b=a-b
3. positive plus negative equals negative if a<b          a+ -b= -(b-a)

examples:

1. -3+-7=-10
2. 13+-5=8
3. 6+-11=-5

Subtraction

for any two integers a and b, a-b is the sum of a plus the opposite of b     a-b=a+-b

example: 15-7= 15+-7=8 (the opposite of 7 is -7)

Multiplication

rules:

1. positive times negative equals negative         ax-b=-(axb)
2. negative times positive equals negative         -axb=-(axb)
3. negative time negative equals positive          -ax-b=axb

examples:

1. 5x-2=-10
2. -7x3=-21
3. -4x-5=20

Division

for any integers a and b, with b not equal to 0

a/b=k if and only if a=bxk

for some integer k in this case b and k are factors of a

rules:

1. positive divided by negative equals negative            a/-b=-(a/b)
2. negative divided by positive equals negative           -a/b=-(a/b)
3. negative divided by negative equals positive           -a/-b=a/b

examples:

1. 24/-6=-4
2. -14/2=-7
3. -30/-6=5