Mathematics & Statistic Tutor Perth - SPSS Help   

Adding and subtracting negative numbers
 

I will just give simple examples using a vertical number line. 

Moving upwards is adding
Moving downwards is subtracting

Example One:     2  - 3   

 So start at 2 and move down 3

5                               
4                               
3
2                                 Start
1                                 One place
0                                 Two places
-1                               Three places  End          So the answer is -1
-2
-3
-4
-5

Example Two:     - 2  - 3 

 So start at - 2  and move down 3

5                               
4                               
3
2                              
1                                
0                        
-1                              
-2                                Start
-3                               One place                        
-4                               Two places
-5                               Three places  End       So the answer is -5

 

Example Three:   - 4  + 3 

 So start at - 4 and move up 3

5                               
4                               
3
2                              
1                                
0                        
-1                                Three places  End       So the answer is -1
-2                                Two places
-3                               One place            
-4                                 Start
-5                              

Back to quadratics Example Three

Notice when multiplying with negative numbers

Negative times Negative makes Positive      -  5     x    -  5        =   + 25
Positive times Positive makes Positive         + 5     x  + 5         =  +  25
Positive times Negative makes Negative      - 5     x   + 5         =  -  25

Back to quadratics Example One

Back to quadratics Example Three

 Factors

 A factor is a number which divides equally into another number. This then leads you to two numbers that multiply together to give you the original number.

How do you find the factors of a number? There are a few ways so we will work through an example:

Finding the factors of 48.

First divide by 2 until you do not get a whole number as answer,
Then divide by 3 until you do not get a whole number as answer,
Then divide by 5 until you do not get a whole number as answer,
Then divide by 7 until you do not get a whole number as answer,
Then divide by the next prime number etc until you get the answer one.

2 | 48
   2 |24
       2 |12
         2 |6
             3|3
                 1|1

So now we know that 2  x 2  x 2  x 2  x 3 x 1 = 48, now we just take the numbers in different groups

for example: 4    x  (2  x 2  x 3 x 1 ) = 2  x 2  x 2  x 2  x 3 x 1

1  x   (2  x 2  x 2  x 2  x 3)     2    x  (2  x 2  x 2  x 3 x 1)    

4    x  (2  x 2  x 3 x 1 )            8   x  (2  x 3 x 1)                    16   x  (3 x 1 )

So we get the list of numbers that multiply to get 48 are:

1  x   48,     2    x  24,    4    x  12,      8   x  6,     16   x  3,

Another way is starting with 1 then 2 then 3 and so on finding whole numbers that multiply to give the original number noting the whole number answers as a pair.  Stop when one of the numbers is already in a pair.

So using 48 again

1 times 48 is 48 so the first pair is       (1  x  48),
2 times 24 is 48 so the second pair is   (2  x  24),
3 times 16 is 48  so the third pair is     (3 x  16),
4 times 12 is 48  so the fourth pair is   (4  x  12),
5 times there is no whole number, therefore no pair
6 times 8 is 48  so the fifth pair is       (6  x  8)
7 times there is no whole number, therefore no pair
8 times 6 is 48  we have 6 again which was in our fifth pair so we can stop.

1  x   48,     2    x  24,    4    x  12,      8   x  6,     16   x  3,

Back to quadratics

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