Monday, 1 October 2018

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 REMOVEor 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
   
       = 1 2.3 ÷ 100 = 0.123
         


Doing Word Problems
Example
Mr Hong gave $54 equally to 6 boys. How much does each boy have?
Method
Step1: [Knowthe story 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: [Knowthe story 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: [Knowthe story 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: [Knowthe story 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 ~~~~~ :)