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
↓ ↓ ↓ ↓
(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
(b)
24.6 ÷ 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.
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