N4/L4 : Whole Number Practice - Multiplication and Division

WHOLE NUMBERS – L4 (N4)      (~60mins)                 Date/Time:               Tutor:            

(Part 1) Revise(15-20mins)

                                                Start Time:                 

1. Concept and Use of multiplication

2. Concept and Use of Division, Division with remainder

3. Word Problems using Models 

(Part2) Practice (45~65mins)

 Multiplication  (~5mins)               Start Time:                             End Time:

Complete the table

3x2=	4x2=	5x2=	6x2=	7x2=	8x2=	9x2=	12x2=
3x3=	4x3=	5x3=	6x3=	7x3=	8x3=	9x3=	12x3=
3x4=	4x4=	5x4=	6x4=	7x4=	8x4=	9x4=	12x4=
3x5=	4x5=	5x5=	6x5=	7x5=	8x5=	9x5=	12x5=
3x6=	4x6=	5x6=	6x6=	7x6=	8x6=	9x6=	12x6=
3x7=	4x7=	5x7=	6x7=	7x7=	8x7=	9x7=	12x7=
3x8	4x8	5x8	6x8	7x8	8x8	9x8	12x8
3x9=	4x9=	5x9=	6x9=	7x9=	8x9=	9x9=	12x9=

1a.  63 x 10 =                        b.  127 x 100 =                     c.  854 x 1000 =

2a.  630 x 10 =                     b.  1270 x 100 =                   c.  8540 x 1000 =

3a.  940 ÷10 =                     b.  4980 ÷10 =                      c.  756000 ÷1000 =

4a.  9450 ÷50 =                   b.  4980 ÷60 =                      c.  756000 ÷7000 =

                                                                                                Total Mark:                /12

5.         What are the missing numbers?                          

       (a) 56 ÷7 =     + 7 =

            (b) 81 ÷9 =       - 9 =           

            (c) 9 x 6 =     + 6 = 

6. Find the product of 8 and 153

7. Divide 492÷8 with long division

8. Find the quotient and remainder of 769 ÷6   

                                                                                                Total Mark:                /18

 (III) Word Problems/PSLE            (35-50 mins)                         Start Time:                 

PSLE 2018F

1.         Amy has 3 times as much savings as Billy. Charlie has $70 more savings than Billy. How much savings does Charlie have if their total savings is $815? (12/p2/f)

2.         There are 42 pieces of cookies in the jar for 6 children. How many pieces of cookies can each child have?

3.         A packet contained 60 sweets. A tin contained 5 times as many sweets as a packet. Kelly bought 3 tins of sweets. How many sweets did she buy altogether?

4.         The theatre has 12 seats in each row. A group 43 of tourists occupied 4 rows of seat. How many seats in the 4 rows were not occupied by the tourist.

5*.       Carly has some sweets. If she gives each of her friends 5 sweets, there is no remainder. Is she gives each of them 3 sweets instead, she will have 36 sweet left. How many sweets does Carly have?

PSLE 2018S (Standard)

6.         David had a total of 345 local and foreign stamps. He gave half of his local stamps away and bought 15 more foreign stamps. In the end,

the number of the foreign stamps he had was thrice as many as the number of local stamps. How many local stamps did he have at first? (1/p2)

7.         Mr William sold 4 times as many iPads as laptops and collected a total

of $8400. Each laptop costs $325 more than an iPad. The amount collected for all the iPads sold was $3480 more than the amount collected for all the laptops sold. How many laptops did Mr William sell? (17/p2/s)

End Date/Time:                                                        Tutor:                          

                                                                                                Total Mark:                /7   Overall Mark :      /25

Tutor Remark:        

Answer Key

I

1a.      630

1b.      12700

1c.       854000

2a.      6300

2b.      1270000

2c.       8540000

3a.      94

3b.      498

3c.       758

4a.      189

4b.      83

4c.       108

5a.      56 / 7 = 1+ 7 = 8

5b.      81 / 9 = 18 – 9 = 9

5c.       9 x 6 = 48 + 6 = 54

6.         1224

7.       61.5

8.         quotient = 153 , remainder = 4

PSLE/Word Problems

1.         $219

2.         7

3.         180

4.         5

5.         90

6.         144

7.         3
Method 1:

Step1: Keywords/Values and Draw/Working of TUV

  Keywords/Value:  [Unit: 4 times ipad as laptop

     $value: ipad sold more by $3480, total = $8400] 

  Draw/Working:

Step2: Link the numbers

$i + $l + 3480 = 8400

$i + $l = 8400 - 3480 

                = 4920

$i = $l

$l = 4920/2 = $2460

Step3: Solve by forming equation

 ipad sales = $3480 + $2460 = $5940

 laptop = $2460

 For u unit of ipad and laptop, the values are

ipad = 5940/4 = 1486

Value of u unit of laptop = 2460

Value of u unit of ipad = 1486

Since laptop is $325 more for each laptop, 

Laptop: 1486 + 325u = 2460

       325u = 2460 – 1485

                = 975

             u = 975 / 325

                = 3

3 laptops are sold.

N7 Numbers : Division, Quotient and Remainder

DIVIDE , DIVISION , /

(1) DIVISION is 

            (a) splitting into equal parts or

            (b) put into groups, or

            (c) "fair sharing".

Example :  12 ÷ 3

12 ÷ 3 = 4         →  4 groups of 3 can be split from 12

                         → 12 can be put into 4 groups of 3

                         → 12 can be share fairly by 4 groups of 3

(2)  Division is repeated subtraction

                             1     2   3    4            4 times that 3 can be minus from 12

                             ↓    ↓    ↓   ↓      

12 ÷ 3 = 12 – 3 – 3 – 3 – 3

(3) Divide Symbol

                                    /    ÷     √

                        a/b = a ÷ b = b √ a 

                        1/10 = 1 ÷ 10 = 10 √ 1

                        5/3 = 5 ÷ 3 = 3√5

Tip:

If the student is confused with converting from / or ÷ to √,

Write a/b = a ÷ b = b √ a , and then fill in the numbers

DIVIDING WHOLE NUMBERS BY TENS, HUNDREDS, AND THOUSANDS

When any whole number is DIVIDE by 10, 100, or 1000,

                                           ↙     ↘                             ↴

                       we ‘REMOVE’ or ‘CANCEL’ the corresponding 0s to the number.

Example

   

   (a)  2460 ÷ 10   < 10 is to cancel one 0 from the number >

=2460 ÷ 10 = 246   

   (b)  24600 ÷ 100      < 100 is to cancels two 0s >

= 24600 ÷ 100 = 246

   (c)  246000 ÷ 1000    < 1000 cancels three 0s >

= 246000 ÷   1000 = 246

 

DIVIDING WHOLE NUMBER BY MULTIPLES OF 10s

Method: Split the 10 multiples

Examples

   (a) 2460 ÷ 20      <Split 10 multiples to x (times), then divide>

= 2460 ÷ 2 ÷ 10

                      = 1230 ÷ 10 = 123 <show cancellation of 0/s when dividing >

   (b) 24600 ÷ 200 = 24600 ÷ 2 ÷ 100

= 12300 ÷ 100

= 123

Practice

 (1) 246000 ÷ 1000             (2) 2460 ÷    20                     (3) 4640 ÷ 200

DIVIDING DECIMAL NUMBERS BY 10s, 100s, 1000s

When a decimal number is divided by 10,

        the decimal value shifts LEFT by one place.

     ⇒Divide by 10 is equal to 1 LEFT shift decimal point;

                   ⇒   100 -> 2 LEFT shifts>

Example

      (a) 24.6 ÷ 10

            = 24.6 ÷ 10 

                ↻ 

            = 2.46     <move arrow to the left by 1: divide by 10>

            

           (b) 24.6 ÷ 100

             =02 4.6 ÷100

                ↻↻

             = 0.246  <100 move arrows to left by 2, put 0 for decimal notation >

              (( CANNOT LEAVE THE ANSWER AS .246 ))

Practice

     (1)  24.6 ÷ 1000                   (2) 24700 ÷ 10                     (3) 38.09 ÷ 1000    

DIVIDING DECIMAL NUMBER BY MULTIPLES of 10s

Method: Split the 10 multiples

Example

         (a)  24.6 ÷ 20

          = 24.6 ÷ 2 ÷ 10

         = 12.3 ÷ 10 = 1.23

              ↻

        (b) 24.6 ÷ 200

      =24.6 ÷ 2÷ 100

   

     = 2 4.3 ÷ 100 = 0.123

         ↻↻

Doing Word Problems

Example

Mr Hong gave $54 equally to 6 boys. How much does each boy have?

Method

Step1: [ Keywords and underline] Who and what? 

            gave : $54

            No. of boys : 6 

Step2: [Plan]. What is needed: each boy has (1 boy)

            share $ -> $ / no. of boys

Step3: [Do]

            54 / 6 = 7

Each boy has $7.

Example

Bobby has 6 times as many stamps as Calvin. They have 84 stamps altogether. How many stamps does Bobby have?

Method

Step1: [Keywords and underline] Who and what? 

            bobby : 6 times as many (6 parts)

            Calvin : 1  (1 part)

            Stamps : 84

Step2: [Plan]. What is needed: Bobby stamps

            Total 84 stamps, total parts = 6 + 1 = 7 , bobby’s 6 parts

Step3: [Do]

            84 / 7 = 12

            Bobby = 12 x 6 = 72

Bobby has 72 stamps.

Example

Mary has 3 times as many stickers as Tracy at first. Mary has 36 stickers. Tracy double her number of stickers. How many stamps does Tracy have?

Method

Step1: [Keywords and underline] Who and what? 

            Mary : 3 times , 36 stickers

            Tracy : 1

            Tracy : 1 x 2 = 2

Step2: [Plan]. What is needed: Tracy stickers

               Tracy : Mary 1 part x 2

Step3: [Do] <One-Unit Method>

         Draw a ‘grid’ to find 1-unit, and multiply needed

Tracy has 24 stickers.

Practice

     (a)       24.6 ÷ 2000              (b)       242 ÷ 20        (c) 936 ÷ 300

   QUOTIENT and REMAINDER

   There are special names for each number in a division.

                             12  ÷   4        =   3

                              ↓        ↓            ↓

dividend ÷  divisor = quotient

   What happens when we divide 13 ÷ 4

           

      13 ÷ 4 = 3 R 1. R stands for remainder.

    

     The remainder must be less than the divisor. 

       Remainder as a Fraction

       The fraction part:   Remainder

                                       Dividend

          ↠ 13 / 4 = 4 1/3

   MULTIPLICATION AND DIVISION (QUOTIENT AND REMAINDER)

Doing Word Problems

Example

The theatre has 12 seats in each row. A group 43 of tourists occupied 4 rows of seat. How many seats in the 4 rows were not occupied by the tourist.

Method

Step1: [Keywords and underline] Who and what? 

            1 row : 12 seats

            Tourist : 43 , 4 rows

Step2: [Plan]. What is needed: not occupied seats - remainder 

            Remainder of 43 / 12

Step3: [Do]

            43 /12 = 3 remainder 7

7 seats are not occupied.

     ~~~~ END ~~~~~ :)