### e3l1l2divisionwholenumbers

```Division of whole numbers
September 2012. Kindly contributed by Joaquin Llorente, Trafford College.
Search for Joaquin on www.skillsworkshop.org
Visit the download page for this resource to find detailed teaching notes,
N1/E3.6 Divide two-digit whole numbers by single-digit whole numbers and interpret remainders
N1/L1.3 Add, subtract, multiply and divide using efficient written and mental methods
N1/L2.2 Carry out calculations with numbers of any size using efficient written and mental methods
and for underpinning Functional Mathematics
Entry 3: Solve practical problems involving multiplication and division by 2, 3, 4, 5 and 10.
Level 1: Add, subtract, multiply and divide whole numbers using a range of strategies
when you see this symbol
Understanding Division
N1/E3.6
N1/L1.3
N1/L2.2
J. Llorente
Foundation Learning,
Trafford College
Division of whole numbers
• This presentation covers the basic
division of whole numbers
• A gradual series of steps of increased
complexity covers the process, from
simple divisions to divisions with
remainders
• The last few slides use 2 everyday
situations as an introduction to
interpreting the remainders
Example 1: 69 ÷ 3
•
•
•
•
•
•
69 divided by 3?
69 shared between 3?
How many lots of 3 in 69?
CALCULATOR
69 ÷ 3
= 69 / 3
3 69
PEN AND PAPER
69 ÷ 3 ... The set up
3
1
2
3
T
U
6
9
69 ÷ 3 ... Sharing the Tens
Each bucket has 2 Tens
3
T
2
6
U
9
There are 2 lots of 3 in 6
3 goes 2 times into 6
1
2
3
69 ÷ 3 ... Sharing the Units
Each bucket has 3 Units
3
T
2
6
U
3
9
There is nothing left over
69 ÷ 3 = 23
1
2
3
Example 2: 75 ÷ 3
•
•
•
•
•
•
75 divided by 3?
75 shared between 3?
How many lots of 3 in 75?
CALCULATOR
75 ÷ 3
PEN AND PAPER
3 75
=75 / 3
75 ÷ 3 ... The set up
3
1
2
3
T
U
7
5
75 ÷ 3 ... Sharing the Tens
Each bucket has 2 Tens
There is 1 Ten left over...
3
1
2
3
T
2
7
U
1
5
Break down the Ten
into Units
75 ÷ 3 ... Sharing the Units
Each bucket has 5 Units
3
T
2
7
1
U
5
5
There is nothing left over
75 ÷ 3 = 25
1
2
3
Example 3: 12 ÷ 4
•
•
•
•
•
•
12 divided by 4?
12 shared between 4?
How many lots of 4 in 12?
CALCULATOR
12 ÷ 4
PEN AND PAPER
4 12
=12 / 4
12 ÷ 4 ... The set up
4
1
2
3
4
T
U
1
2
12 ÷ 4 ... Sharing the Tens
So
Wethere
don’t are
have
0 enough
Tens in Tens
each bucket
T
to
put one
each
bucket...
There
is 1inTen
left
over...
4
1
2
3
4
0
1
U
1
2
Break down the left
over Ten into Units
12 ÷ 4 ... Sharing the Units
There are 3 Units in each
bucket
4
T
0
1
U
3
1
2
There is nothing
left over
12 ÷ 4 = 3
1
2
3
4
Example 4: 208 ÷ 2
•
•
•
•
•
•
208 divided by 2?
208 shared between 2?
How many lots of 2 in 208?
CALCULATOR
208 ÷ 2
PEN AND PAPER
2 208
=208 / 2
208 ÷ 2 ... The set up
2
1
2
H
T
U
2
0
8
208 ÷ 2 ... Sharing the
Hundreds
There is 1 Hundred
in each bucket
2
1
2
H
1
2
T
U
0
8
208 ÷ 2 ... Sharing the Tens
There are 0
noTens
Tensin
to share
each
bucket
...
2
H
1
2
T
0
0
U
8
We need to write in
the 0 to hold the
Tens’ place
1
2
208 ÷ 2 ... Sharing the Units
There are 4 Units
in each bucket
2
H
1
2
T
0
0
U
4
8
There is nothing
left over
208 ÷ 2 = 104
1
2
Checkpoint 1
Try the following divisions:
1.
2.
3.
4.
5.
6.
7.
24 ÷ 2
36 divided by 3
5 85
How many 4s in 48?
99 / 9
52 ÷ 4
510 divided by 5
Division with remainders
• All the divisions we have seen so far
have no units left over
• Sometimes after doing the division
there are some units left over
• These left over units are called the
remainder
• The process is the same but, at the end,
we write an “r” (for remainder) followed
by the number of units left over
Example 5: 67 ÷ 3
•
•
•
•
•
•
67 divided by 3?
67 shared between 3?
How many lots of 3 in 67?
CALCULATOR
67 ÷ 3
= 67 / 3
3 67
PEN AND PAPER
67 ÷ 3 ... The set up
3
1
2
3
T
U
6
7
67 ÷ 3 ... Sharing the Tens
Each bucket has 2 Tens
3
T
2
6
U
7
There are 2 lots of 3 in 6
3 goes 2 times into 6
1
2
3
67 ÷ 3 ... Sharing the Units
Each bucket has 2 Units
3
T
2
6
U
2
7
r1
There is one unit left over
(remainder 1)
67 ÷ 3 = 22 r1
1
2
3
Checkpoint 2
Try the following divisions:
1.
2.
3.
4.
5.
6.
7.
25 ÷ 2
34 divided by 3
5 87
How many 4s in 47?
91 / 9
54 ÷ 4
512 divided by 5
• The meaning and interpretation of the
remainder depends on the situation
• Sometimes you need to round up to the
next whole number to find the correct
• Other times, you need to ignore the
remainder to find the correct answer
• Whether you do one thing or the other
depends on the type of problem
Interpreting remainders
18 friends are going to a party
A taxi can take only 4 people
How many taxis do they need?
18
÷
4 = 4 r2 ANSWER: 5 taxis
4 full taxis
2 more people waiting…
They need another taxi!
1
2
3
4
5
Interpreting remainders
DVDs cost £7 each
You have £19
How many DVDs can you buy?
19
÷
7 = 2 r5 ANSWER: 2 DVDs
2 DVDs
£5 left over…
Not enough for another DVD!
Interpreting remainders
• In the first example, we rounded the
result to the next whole number to find