Integers

Integers are whole numbers, which can be positive or negative.

Polarity

The polarity of a number says whether it is positive or negative:-
Numbers bigger than zero are positive, those less than zero are negative.
Zero itself is neutral.

A negative number is written with  a minus sign in front of it.
It is good practice to put negative numbers into brackets e.g. (-6)

 

Examples

If you have an account at the bank and you have arranged an overdraft facility then:

If you are £6 overdrawn on your account, you owe the bank £6 and therefore have less money available than if you had £12 in your account.

If you are £125 overdrawn on your account, you owe the bank more money than if you were £5 overdrawn.

If you have £5 in your account, you have more money available than you would if you were £50,000 overdrawn on your account.

 

Addition / Subtraction

• Start at the first number
• Face the polarity of the second number
• The operator in-between numbers is important

   + means go forwards         -   means go backwards.

•  Move the number of steps given as the second number
• Finish

 

Example

3 + 4 = 7

• Start at 3
• Face towards the positive
   (the 4 is positive since it does not have brackets and a minus sign in front of it)
• go  4 steps forwards, since the operator is +
• finish at 7

Example

3 - 4 = -1

• Start at 3
• Face towards the positive
   (the 4 is positive since it does not have brackets and a minus sign in front of it)
• go  4 steps backwards
• finish at -1

Example

-6 + 2 = -4

 

Example

-1 - 4 =( -5)

 

• Start at -1
• Face towards the positive
   (the 4 is positive since it does not have brackets and a minus sign in front of it)
• go  4 steps backwards
• finish at -5

 

Adding a negative number is the same as subtracting its positive counterpart.
(Using the Bank examples above, this could be likened to making a purchase with a debit card)

Examples

-5 + (-3) =  -5 -3 = -8

 

 

• Start at -5
• Face towards the negative  since (-3)  is a negative number
• go  3 steps forwards
• finish at  - 8

 

Subtracting a negative number is the same as adding its positive counterpart.
(Using the Bank examples above, this could be likened to making a purchase with a debit card , then taking the goods back for a refund on the same account.)

Examples

-5 - (-8) = -5 +8 = 3

 

• Start at -5
• Face towards the negative  since (-8)  is a negative number
• go  8 steps backwards
• finish at  3

Multiplying Integers

 

Like signs produce a positive answer.

Mixed signs produce a negative answer.

 

Examples

5 x  8 =  40
(-5) x  (-8) = 40

(-5) x  8 = (- 40)
5 x ( - 8) = (- 40)
      

Dividing Integers

 

Like signs produce a positive answer.

Mixed signs produce a negative answer.

Example

40 ÷  8 =  5
(- 40) ÷ (- 8) =  5

(- 40) ÷ 8 =  (- 5)
40 ÷ (- 8) =  (- 5)