Division of whole numbers
September 2012. Kindly contributed by Joaquin Llorente, Trafford College.
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Curriculum links
Adult Numeracy
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
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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
SPREADSHEET
= 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
SPREADSHEET
=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
SPREADSHEET
=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
SPREADSHEET
=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
SPREADSHEET
= 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
About the remainders
• 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
answer to a division problem
• 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
the answer (5 taxis)
• In the second example we ignored the
remainder to find the answer (2 DVDs)
• To find a few more problems on
interpreting remainders try the
worksheet “Division – Interpreting
Remainders”