Name: _____________________________________________________
Date: ______________
8.3 Exploring Integer Division
Working Example 1: Divide Using Integer Chips
Find each quotient using integer chips.
a) (+12) ÷ (+3)
Quotient is the answer
when you divide.
Solution
Draw 12 positive integer chips in groups of 3.
The number of groups equals the quotient.
+ + + +
+ + + +
+ + + +
+ + + +
+ + + +
+ + + +
There are 4 groups, so the quotient is +
How many groups of +3
can be made from +12?
.
Division statement: (+12) ÷ (+3) = +
b) (–12) ÷ (–3)
Solution
Draw 12 negative integer chips in groups of 3.
- - - - - - - - - -
- - - - - - - - - -
There are 4 groups, so the quotient is +
Division statement: (–12) ÷ (–3) =
Separate the 12 white
chips into groups of 3.
Circle the groups of 3.
.
You cannot model this division
by separating the 12 white
chips into –3 groups.
c) (–12) ÷ (+4)
Solution
If you divide (–12) into 4 groups, how many will there be in each group?
Draw 12 negative integer chips in groups of 4.
- - - - - - - - - -
- - - - - - - - - -
Separate the 12 white
chips into 4 equal groups.
Count the number of negative chips in each group.
There are
negative chips in each group, so the quotient is
Division statement: (–12) ÷ (+4) =
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MHR ● Chapter 8: Integers
.
Name: _____________________________________________________
Date: ______________
Draw integer chips to solve each statement.
a) (+14) ÷ (+7)
Draw 14 positive integer chips. Separate the chips into groups of 7.
Circle the groups.
There are
groups of 7 positive chips, so the quotient is
.
(+14) ÷ (+7) =
b) (–9) ÷ (–3)
Draw
Circle the groups.
negative integer chips. Separate the chips into groups of 3.
How many groups of (–3) are there?
So, the quotient is
.
(–9) ÷ (–3) =
c) (–16) ÷ (+2)
Draw
Circle the groups.
There are
(
)÷(
integer chips. Separate the chips into groups of
.
chips in each group, so the quotient is
.
)=
8.3 Exploring Integer Division ● MHR 431
Name: _____________________________________________________
1. a) Allison modelled (+12) ÷ (+6)
using integer chips.
+ +
+
+
+ +
+
+
+ +
+
+
Date: ______________
Tyler also modelled (+12) ÷ (+6)
using integer chips.
+
+
+
+
+
+
+
+
+
+
+
+
Explain how they each found the correct quotient (answer).
__________________________________________________________________________
__________________________________________________________________________
b) Model (+12) ÷ (+2) in 2 different ways.
Use Allison’s and Tyler’s methods.
2. Use the diagram to complete each division statement.
a) (+10) ÷ (+2) =
b) (–16) ÷ (–4) =
+ + + + +
+ + + + +
--------
---- ----
+ + + + +
+ + + + +
--------
---- ----
c) (–14) ÷ (+2) =
d) (–15) ÷ (+3) =
- - - - - - -
- - - - - - -
- - - - - - -
- - - - - - -
- - - - - - - - - - - - -
- - - - - - - - - - - - -
8.3 Exploring Integer Division ● MHR 433
Name: _____________________________________________________
Date: ______________
3. Use the diagram to complete both division statements.
a) (+14) ÷ (+2) =
b) (–10) ÷ (–2) =
(+14) ÷ (+7) =
(–10) ÷ (+5) =
+++++++
+++++++
+ + + + + + +
+ + + + + + +
- - - - - - - - -
- - - - - - - - -
4. Draw integer chips to solve each division statement.
Have a partner check your drawing.
b) (–7) ÷ (+7) =
a) (+16) ÷ (+4) =
Draw 16
integer chips.
Separate the chips into groups of
. Circle the groups.
There are
groups,
so the quotient is
.
d) (–10) ÷ (+2) =
c) (–12) ÷ (–6) =
5. A submarine was diving at 3 m/min. How long did it take to dive 21 m?
Diving 3 m = (
Diving 21 m = (
)
)
Sentence: ___________________________________________________________________
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MHR ● Chapter 8: Integers