N4 Numbers : Addition and Subtraction

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Addition

~ bringing two or more numbers (parts) together to make a new total (whole).

              

          1 apple ADD TO 2 apples is equal to 3 apples    

                          1           +                2               =        3

                PART       +            PART           = WHOLE

       

                        2 + 1 is the same as 1 + 2 equals 3

Doing Addition Word Problems

Example

Judy has 3 books. Annie has 5 books. How many books do the girls have altogether?

  Judy part: 3

Annie Part: 5

Altogether -> total, the whole -> ADD

-> Add the parts to find the whole

3 + 5 = 8

The girls have 8 books altogether.

Method

Step1:        [Know the story, and underline] Who and what?

Step2:        [Plan the solution and double underline] What is needed? altogether 

Step3:        [Do] How to?

Example

Judy has 3 books. Annie has 5 books. How many books do the girls have altogether?

Step1: Know what is needed and Underline

              Judy part: 3

            Annie Part: 5

Step2: Plan needed: how many books altogether [double underline]

Altogether -> total, the whole -> ADD

Step3: Do

-> Add the parts to find the whole

            3 + 5 = 8

The girls have 8 books altogether.

Example

There are 4 pears and 2 oranges in a basket. Kenny puts 5 apples into the basket. How many fruits are there in the basket altogether?

Step1: [needed(keywords) and underline] Who and what? 

        Pears and oranges are fruits, In the basket

               pear : 4

            orange: 2

       Apple is also fruit. Put 5 apples in basket

Step2: [Plan]. What is Needed and underline : fruits altogether (double underline)

       Altogether -> total, the whole -> ADD

Step3: [Do]

      -> Add the parts to find the whole

            4 + 2 + 5 = 11

There are 11 fruits in the basket.

Subtraction

~ an operation to remove objects from a collection.

~ take away(something) from something else to decrease the number or amount

        

            To find one part, we subtract the other part from the whole

                        3 - 1 is the same as 2. 3 minus 1 equals 2

Example

Jana has 12 cookies. She ate 5 cookies . How many cookies does Jana have?

Method

Step1: [Keywords and underline] Who and what? 

            Jana : has 12 

                        ate    5

Step2: [Plan]. What is Required : left (double underline)

        left ->  subtract

Step3: [Do]

        -> 12 - 5

            12 – 5 = 7

There are 7 cookies left.

Example (add / subtract)

There were 15 passengers in the MRT cabin at first. At the next stop, 7 passengers entered the cabin and 9 passengers left. How many passengers are in the MRT cabin now?

Method

Step1: [Keywords and underline] Who and what? 

            passenger:   15  

                                     7 enter -> (more passengers)

                                      9 left -> (less passengers)

Step2: [Plan]. What is Required: in cabin now (double underline)

            enter -> add

            left ->  subtract

Step3: [Do]

             15 + 7 = 22

              22 – 9 = 13

There are 13 passengers in cabin.

Example (add/subtract)

Annie, Jen and Linda each has 8 balloons. Jen and Linda’s balloon burst and Jen has 4 balloons less than Linda. Annie has 2 balloons more than Linda. How many balloons do Jen and Linda have?

Method

Step1: [Keywords and underline] Who and what? 

   Annie   : 8 

    Jen     : 8 -

    Linda  : 8 - 

   Jen, Linda burst -> lesser. Annie has the most.

     Annie 2 balloons more than Linda  

Step2: [Plan]. What is Required: Jen and Linda ballons (double underline)

     Annie 2 balloons more than Linda , Annie has 8 balloons

             ->  Annie – Linda 

            Jen has 4 balloons less than Linda 

            -> Linda - Jen

Step3: [Do]

             Linda : 8 – 2 = 6

            Jen : 6 – 4 = 2

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N5. Whole Numbers - Factors and Multiples

FACTOR AND MULTIPLES

FACTORS

Factors are numbers that divide exactly into another number.

The factors of 12, for example, are 1, 2, 3, 4, 6 and 12.

=> 12 / 2 = 6 with no remainder, then 12 /6 = 2.

Thus, factors are in pairs and the pairs multiply to be the factors of the number

The factors of 12 are:

1 x 12 = 12    => 1 and 12 are factors of 12.

2 x 6 = 12      => 2 and 6 are factors for 12

3 x 4 = 12      => 3 and 4 are factors for 12.

The factors of 12 are 1, 2, 3, 4, 6 and 12.

All numbers greater than 1 has at least 2 factors :- 1 and the number itself

                        2 = 1 x 2.  1 and 2 are factors of 2

                        3 = 1 x 3.  1 and 3 are factors of 3

                        4 = 1 x 4 and 2 x 2. 1, 2 and 4 are factors of 4.

Example:

Find all the factors of 20.

Method

Step 1: List out the 2 factors of 1 and the number itself

            20 = 1 x 20

Step2:  Multiply from 2 until numbers

            2 x 10 = 20,

            3 – no

            4 x 5 = 20

            6,7,8,9 – no.

            10 found in 2 x 10. – can stop trying.

Step3: Answer

The factors of 20 are 1, 2, 4, 5, 10 and 20

Example:

Find all the factors of 36.

Method

Step 1: List out the 2 factors of 1 and the number itself

            36 = 1 x 36

Step2:  Multiply from 2 until ‘repeated’ factor

            2 x 18 = 36,

            3 x 12 = 36

            4 x 9 – 36

            5 – no

            6 x 6 = 36

            7,8 – no.

            9 found in 4 x 9 (repeated) can stop trying.

Step3: Answer

            The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Common Factors

            Factors of 6 :                                     Factors of 9 :

            1 x 6                                                               1 x 9

            2 x 3                                                               3 x 3

    1 and 3 are common factors of 6 and 9.

Example:

Find the common factors of 24 and 36.

Method

Step1: List out the factors of both numbers

                  24 = 1 x 24                      36 = 1 x 36

                        = 2 x 12                           = 2 x 18

                        = 3 x 8                             = 3 x 12

                        = 4 x 6                             = 4 x 9

                                                                 = 6 x 6

Step2: Circle/Underline the common factors

                  24 = 1 x 24                      36 = 1 x 36

                        = 2 x 12                           = 2 x 18

                        = 3 x 8                             = 3 x 12

                        = 4 x 6                             = 4 x 9

                                                                 = 6 x 6

Step3: Solve

            The common factors are 1, 2, 3, 4, 6 and 12

MULTIPLES

Multiples are extended times tables

The multiples of 2 are all the numbers in the 2 times table:
2, 4, 6, 8, 10, ...
Multiples of 2 always end with a 2, 4, 6, 8 or 0.

Example:

            2478 is a multiple of 2 because it ends with 8.

The multiples of 5 are all the numbers in the 5 times table:
5, 10, 15, 20, 25, ...
Multiples of 5 always end with a 5 or 0.

Example:

            395 is a multiple of 5 because it ends with a 5.

The multiples of 10 are all the numbers in the 10 times table:
10, 20, 30, 40, 50, …
Multiples of 10 always end with a 0.

Example:  

9910 is a multiple of 10 because it ends with a 0.

Common Multiple

First 5 multiples of 4: 4,8,12,16,20

First 5 multiples of 5: 5,10, 15, 20, 25

20 is a multiple of both 4 and 5.

=> 20 is a common multiple of 4 and 5.

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