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Unit 1:Negative Numbers
UNIT 1
NEGATIVE NUMBERS
B a s i c E s s e n t i a l
A d d i t i o n a l M a t h e m a t i c s S k i l l s
Curriculum Development Division
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TABLE OF CONTENTS
Module Overview 1
Part A: Addition and Subtraction of Integers Using Number Lines 2
1.0 Representing Integers on a Number Line 3
2.0 Addition and Subtraction of Positive Integers 3
3.0 Addition and Subtraction of Negative Integers 8
Part B: Addition and Subtraction of Integers Using the Sign Model 15
Part C: Further Practice on Addition and Subtraction of Integers 19
Part D: Addition and Subtraction of Integers Including the Use of Brackets 25
Part E: Multiplication of Integers 33
Part F: Multiplication of Integers Using the Accept-Reject Model 37
Part G: Division of Integers 40
Part H: Division of Integers Using the Accept-Reject Model 44
Part I: Combined Operations Involving Integers 49
Answers 52
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MODULE OVERVIEW
1. Negative Numbers is the very basic topic which must be mastered by everypupil.
2. The concept of negative numbers is widely used in many AdditionalMathematics topics, for example:
(a) Functions (b) Quadratic Equations
(c) Quadratic Functions (d) Coordinate Geometry
(e) Differentiation (f) Trigonometry
Thus, pupils must master negative numbers in order to cope with topics inAdditional Mathematics.
3. The aim of this module is to reinforce pupils understanding on the concept ofnegative numbers.
4. This module is designed to enhance the pupils skills in using the concept of number line; using the arithmetic operations involving negative numbers; solving problems involving addition, subtraction, multiplication and
division of negative numbers; and applying the order of operations to solve problems.
5. It is hoped that this module will enhance pupils understanding on negativenumbers using the Sign Model and the Accept-Reject Model.
6. This module consists of nine parts and each part consists of learning objectiveswhich can be taught separately. Teachers may use any parts of the module as
and when it is required.
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TEACHING AND LEARNING STRATEGIES
The concept of negative numbers can be confusing and difficult for pupils to
grasp. Pupils face difficulty when dealing with operations involving positive and
negative integers.
Strategy:
Teacher should ensure that pupils understand the concept of positive and negative
integers using number lines. Pupils are also expected to be able to performcomputations involving addition and subtraction of integers with the use of the
number line.
PART A:
ADDITION AND SUBTRACTION
OF INTEGERS USING
NUMBER LINES
LEARNING OBJECTIVE
Upon completion of Part A, pupils will be able to perform computationsinvolving combined operations of addition and subtraction of integers using a
number lines.
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PART A:
ADDITION AND SUBTRACTION OF INTEGERS
USING NUMBER LINES
1.0 Representing Integers on a Number Line
Positive whole numbers, negative numbers and zero are all integers. Integers can be represented on a number line.
Note: i) 3 is the opposite of +3
ii) (2) becomes the opposite of negative 2, that is, positive 2.
2.0 Addition and Subtraction of Positive Integers
3 2 1 0 1 2 3 4
LESSON NOTES
Rules for Adding and Subtracting Positive Integers
When adding a positive integer, you move to the right on anumber line.
When subtracting a positive integer, you move to the lefton a number line.
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
Positive integers
may have a plus sign
in front of them,
like +3, or no sign in
front, like 3.
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(i) 2 + 3
Alternative Method:
EXAMPLES
Adding a positive integer:
Start by drawing an arrow from 0 to 2, and then,
draw an arrow of 3 units to the right:
2 + 3 = 5
5 4 3 2 1 0 1 2 3 4 5 6
Start
with 2
Add a
positive 3
Adding a positive integer:
Start at 2 and move 3 units to the right:
2 + 3 = 5
Make sure you start from
the position of the first
integer.
5 4 3 2 1 0 1 2 3 4 5 6
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(ii) 2 + 5
Alternative Method:
Adding a positive integer:
Start by drawing an arrow from 0 to2, and then,draw an arrow of 5 units to the right:
2 + 5 = 3
5 4 3 2 1 0 1 2 3 4 5 6
Add a
positive 5
Make sure you start from
the position of the firstinteger.
5 4 3 2 1 0 1 2 3 4 5 6
Adding a positive integer:
Start at2 and move 5 units to the right:
2 + 5 = 3
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(iii) 25 =3
Alternative Method:
5 4 3 2 1 0 1 2 3 4 5 6
Subtracting a positive integer:
Start by drawing an arrow from 0 to 2, and then,
draw an arrow of 5 units to the left:
25 =3
Subtract a
positive 5
Subtracting a positive integer:
Start at 2 and move 5 units to the left:
25 =3
5 4 3 2 1 0 1 2 3 4 5 6
Make sure you start from
the position of the first
integer.
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(iv) 32 =5
Alternative Method:
Subtracting a positive integer:
Start by drawing an arrow from 0 to3, and
then, draw an arrow of 2 units to the left:
32 =5
5 4 3 2 1 0 1 2 3 4 5 6
Subtract a
positive 2
5 4 3 2 1 0 1 2 3 4 5 6
Subtracting a positive integer:
Start at3 and move 2 units to the left:
32 =5
Make sure you start from
the position of the firstinteger.
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3.0 Addition and Subtraction of Negative Integers
Consider the following operations:
41 = 3
42 = 2
43 = 1
44 = 0
45 =1
46 =2
Note that subtracting an integer gives the same result as adding its opposite. Adding orsubtracting a negative integer goes in the opposite direction to adding or subtracting a positive
integer.
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
4 + (5) =1
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 44 + (6) =2
4 + (1) = 3
4 + (2) = 2
4 + (3) = 1
4 + (4) = 0
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Rules for Adding and Subtracting Negative Integers
When adding a negative integer, you move to the left on anumber line.
When subtracting a negative integer, you move to the righton a number line.
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
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(i) 2 + (1) =3
Alternative Method:
5 4 3 2 1 0 1 2 3 4 5 6
Adding a negative integer:
Start at2 and move 1 unit to the left:
2 + (1) =3
EXAMPLES
5 4 3 2 1 0 1 2 3 4 5 6
Adding a negative integer:
Start by drawing an arrow from 0 to2, and
then, draw an arrow of 1 unit to the left:
2 + (1) =3
Add a
negative 1
Make sure you start from
the position of the first
integer.
This operation of
2 + (1) =3
is the same as
21 =3.
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(ii) 1 + (3) =2
Alternative Method:
5 4 3 2 1 0 1 2 3 4 5 6
Adding a negative integer:
Start at 1 and move 3 units to the left:
1 + (3) =2
Add a
negative 3
5 4 3 2 1 0 1 2 3 4 5 6
Adding a negative integer:
Start by drawing an arrow from 0 to 1, then, draw an arrow of
3 units to the left:
1 + (3) =2
Make sure you start from
the position of the first
integer.
This operation of
1 + (3) =2
is the same as
13 =2
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(iii) 3(3) = 6
Alternative Method:
5 4 3 2 1 0 1 2 3 4 5 6
Subtracting a negative integer:
Start at 3 and move 3 units to the right:
3(3) = 6
5 4 3 2 1 0 1 2 3 4 5 6
Subtracting a negative integer:
Start by drawing an arrow from 0 to 3, and
then, draw an arrow of 3 units to the right:
3(3) = 6
Subtract a
negative 3
This operation of
3(3) = 6
is the same as
3 + 3 = 6
Make sure you start from
the position of the first
integer.
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(iv) 5(8) = 3
Alternative Method:
5 4 3 2 1 0 1 2 3 4 5 6
Subtracting a negative integer:
Start at5 and move 8 units to the right:
5(8) = 3
5 4 3 2 1 0 1 2 3 4 5 6
Subtract a
negative 8
This operation of
5(8) = 3
is the same as
5 + 8 = 3
Subtracting a negative integer:
Start by drawing an arrow from 0 to5, and
then, draw an arrow of 8 units to the right:
5(8) = 3
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Solve the following.
1. 2 + 4
2. 3 + (6)
3. 2(4)
4. 35 + (2)
5. 5 + 8 + (5)
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
TEST YOURSELF A
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TEACHING AND LEARNING STRATEGIES
This part emphasises the first alternative method which include activities and
mathematical games that can help pupils understand further and master the
operations of positive and negative integers.
Strategy:
Teacher should ensure that pupils are able to perform computations involving
addition and subtraction of integers using the Sign Model.
PART B:
ADDITION AND SUBTRACTION
OF INTEGERS USING
THE SIGN MODEL
LEARNING OBJECTIVE
Upon completion of Part B, pupils will be able to perform computations
involving combined operations of addition and subtraction of integers usingthe Sign Model.
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PART B:
ADDITION AND SUBTRACTION OF INTEGERS
USING THE SIGN MODEL
In order to help pupils have a better understanding of positive and negative integers, we have
designed the Sign Model.
Example 1
What is the value of 35?
NUMBER SIGN
3 + + +
5
WORKINGS
i. Pair up the opposite signs.
ii. The number of the unpaired signs is
the answer.
Answer 2
+
+
+
LESSON NOTES
EXAMPLES
The Sign Model
This model uses the + and signs. A positive number is represented by + sign. A negative number is represented by sign.
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Example 2
What is the value of 53 ?
NUMBER SIGN
3 _ _ _
5
WORKINGS
There is no opposite sign to pair up, sojust count the number of signs.
_ _ _ _ _ _ _ _
Answer 8
Example 3
What is the value of 53 ?
NUMBER SIGN
3
+5 + + + + +
WORKINGS
i. Pair up the opposite signs.
ii. The number ofunpaired signs is the
answer.
Answer 2
_
+ + +
_
+
_
+
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Solve the following.
1. 4 + 8 2. 84 3. 127
4. 55 5. 574 6. 7 + 43
7. 4 + 37 8. 62 + 8 9. 3 + 4 + 6
TEST YOURSELF B
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PART C:
FURTHER PRACTICE ON
ADDITION AND SUBTRACTION
OF INTEGERS
TEACHING AND LEARNING STRATEGIES
This part emphasises addition and subtraction of large positive and negative integers.
Strategy:
Teacher should ensure the pupils are able to perform computation involving addition
and subtraction of large integers.
LEARNING OBJECTIVE
Upon completion of Part C, pupils will be able to perform computationsinvolving addition and subtraction of large integers.
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PART C:
FURTHER PRACTICE ON ADDITION AND SUBTRACTION OF INTEGERS
In Part A and Part B, the method of counting off the answer on a number line and the Sign
Model were used to perform computations involving addition and subtraction ofsmallintegers.
However, these methods are not suitable if we are dealing with large integers. We can use the
following Table Model in order to perform computations involving addition and subtraction
of large integers.
LESSON NOTES
Steps for Adding and Subtracting
Integers
1. Draw a table that has a column for + and a columnfor.
2. Write down all the numbers accordingly in thecolumn.
3. If the operation involves numbers with the samesigns, simply add the numbers and then put the
respective sign in the answer. (Note that we
normally do not put positive sign in front of a
positive number)
4. If the operation involves numbers with differentsigns, always subtract the smaller number from
the larger number and then put the sign of the
larger number in the answer.
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Examples:
i) 34 + 37 =+
34
37
+71
ii) 6520 =+
65 20
+45
iii)
73 + 22 =
+
22 73
51
iv) 228338 =+
228 338
110
Subtract the smaller number from
the larger number and put the sign
of the larger number in the
answer.
We can just write the answer as
45 instead of +45.
Subtract the smaller number from
the larger number and put the sign
of the larger number in the
answer.
Subtract the smaller number from
the larger number and put the sign
of the larger number in the
answer.
Add the numbers and then put the
positive sign in the answer.
We can just write the answer as
71 instead of +71.
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v) 428316 =+
428316
744
vi) 863 127 + 225 =+
225 863
127
225 990
765
vii) 234 675 567 =+
234 675
567
234 1242
1008
Add the numbers and then put the
negative sign in the answer.
Add the two numbers in the
column and bring down the number
in the + column.
Subtract the smaller number from
the larger number in the third row
and put the sign of the larger
number in the answer.
Add the two numbers in the
column and bring down the number
in the + column.
Subtract the smaller number from
the larger number in the third row
and put the sign of the larger
number in the answer.
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viii) 482 + 236 718 =+
236 482
718
236 1200
964
ix) 765 984 + 432 =
+
432 765
984
432 1749
1317
x) 1782 + 436 + 652 =+
436
652
1782
10881782
694
Add the two numbers in the
column and bring down the number
in the + column.
Subtract the smaller number from
the larger number in the third row
and put the sign of the larger
number in the answer.
Add the two numbers in the
column and bring down the number
in the + column.
Subtract the smaller number from
the larger number in the third row
and put the sign of the larger
number in the answer.
Add the two numbers in the +
column and bring down the numberin the column.
Subtract the smaller number from
the larger number in the third row
and put the sign of the larger
number in the answer.
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Solve the following.
1. 4789 2. 5448 3. 33125
4. 352556 5. 345437456 6. 237 + 564318
7. 431 + 366778 8. 652517 + 887 9. 233 + 408689
TEST YOURSELF C
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TEACHING AND LEARNING STRATEGIES
This part emphasises the second alternative method which include activities to
enhance pupils understanding and mastery of the addition and subtraction of
integers, including the use of brackets.
Strategy:
Teacher should ensure that pupils understand the concept of addition and subtraction
of integers, including the use of brackets, using the Accept-Reject Model.
PART D:
ADDITION AND SUBTRACTION
OF INTEGERS INCLUDING THE
USE OF BRACKETS
LEARNING OBJECTIVE
Upon completion of Part D, pupils will be able to perform computations
involving combined operations of addition and subtraction of integers, includingthe use of brackets, using the Accept-Reject Model.
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PART D:
ADDITION AND SUBTRACTION OF INTEGERS
INCLUDING THE USE OF BRACKETS
To Accept or To Reject? Answer
+ ( 5 ) Accept +5 +5
( 2 ) Reject +2 2
+ (4) Accept 4 4
(8) Reject 8 +8
LESSON NOTES
The Accept - Reject Model
+ sign means to accept.
sign means to reject.
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i) 5 + (1) =
Number To Accept or To Reject? Answer
5+ (1)
Accept 5Accept 1
+51
+ + + + +
5 + (1) = 4
We can also solve this question by using the Table Model as follows:
5 + (1) = 51
+
5 1
+4
EXAMPLES
This operation of
5 + (1) = 4
is the same as
51 = 4
Subtract the smaller number fromthe larger number and put the sign
of the larger number in the
answer.
We can just write the answer as 4
instead of +4.
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ii) 6 + (3) =
Number To Accept or To Reject? Answer
6+ (3)
Reject 6Accept3
63
6 + (3) = 9
We can also solve this question by using the Table Model as follows:
6 + (3) =63 =
+
6
3
9
This operation of
6 + (3) =9
is the same as
63 =9
Add the numbers and then put the
negative sign in the answer.
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iii) 7(4) =
Number To Accept or To Reject? Answer
7(4)
Reject 7Reject4
7+4
+ + + +
7(4) = 3
We can also solve this question by using the Table Model as follows:
7(4) =7 + 4 =
+
4 7
3
This operation of
7(4) =3
is the same as
7 + 4 =3
Subtract the smaller number from
the larger number and put the sign
of the larger number in the
answer.
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iv)5(3) =
Number To Accept or To Reject? Answer
5
(3)
Reject 5
Reject 3
5
3
5(3) = 8
We can also solve this question by using the Table Model as follows:
5(3) =53 =
+
5
3
8
This operation of
5(3) =8
is the same as
53 =8
Add the numbers and then put the
negative sign in the answer.
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v) 35 + (57) =3557 =
Using the Table Model:
+
35
57
92
vi) 123(62) =123 + 62 =
Using the Table Model:
+
62 123
61
This operation of
35 + (57)
is the same as
3557
Add the numbers and then put the
negative sign in the answer.
Subtract the smaller number from
the larger number and put the sign
of the larger number in the answer.
This operation of
123(62)
is the same as
123 + 62
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Solve the following.
1. 4 + (8) 2. 8(4) 3. 12 + (7)
4. 5 + (5) 5. 5 (7) + (4) 6. 7 + (4)(3)
7. 4 + (3) (7) 8. 6(2) + (8) 9. 3 + (4) + (6)
10. 44 + (81) 11. 118(43) 12. 125 + (77)
13. 125 + (239) 14. 125 (347) + (234) 15. 237 + (465)(378)
16. 412 + (334) (712) 17. 612(245) + (876) 18. 319 + (412) + (606)
TEST YOURSELF D
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PART E:
MULTIPLICATION OF INTEGERS
Consider the following pattern:
3 3 = 9
623
313
003 The result is reduced by 3 in
3)1(3 every step.
6)2(3
9)3(3
93)3(
62)3(
31)3(
00)3( The result is increased by 3 in
3)1()3( every step.
6)2()3(
9)3()3(
Multiplication Rules of Integers
1. When multiplying two integers of the same signs, the answer is positive integer.
2. When multiplying two integers ofdifferent signs, the answer is negative integer.
3. When any integer is multiplied by zero, the answer is always zero.
positive positive = positive
(+) (+) = (+)
positive negative = negative
(+) () = ()
negative positive = negative
() (+) = ()
negative negative = positive
() () = (+)
LESSON NOTES
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1. When multiplying two integers of the same signs, the answer is positive integer.
(a) 4 3 = 12(b) 8 6 = 48
2. When multiplying two integers of the different signs, the answer is negative integer.
(a) 4 (3) =12
(b) 8 (6) =48
3. When any integer is multiplied by zero, the answer is always zero.
(a) (4) 0 = 0
(b) (8) 0 = 0
(c) 0 (5) = 0
(d) 0 (7) = 0
EXAMPLES
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Solve the following.
1. 4 (8) 2. 8 (4) 3. 12 (7)
4. 5 (5) 5. 5 (7) (4) 6. 7 (4) (3)
7. 4 (3) (7) 8. (6) (2) (8) 9. (3) (4) (6)
TEST YOURSELF E
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PART F:
MULTIPLICATION OF INTEGERS
USING
THE ACCEPT-REJECT MODEL
TEACHING AND LEARNING STRATEGIES
This part emphasises the second alternative method which include activities to
enhance the pupils understanding and mastery of the multiplication of integers.
Strategy:
Teacher should ensure that pupils understand the multiplication rules of integers
using the Accept-Reject Model. Pupils can then perform computations involving
multiplication of integers.
LEARNING OBJECTIVE
Upon completion of Part F, pupils will be able to perform computationsinvolving multiplication of integers using the Accept-Reject Model.
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PART F:
MULTIPLICATION OF INTEGERS
USING THE ACCEPT-REJECT MODEL
The Accept-Reject Model
In order to help pupils have a better understanding of multiplication of integers, we havedesigned the Accept-Reject Model.
Notes: (+) (+) : The first sign in the operation will determine whether to acceptor to reject the second sign.
Multiplication Rules:
To Accept or to Reject Answer
(2) (3) Accept + 6
(2) (3) Reject 6
(2) (3) Accept 6
(2) (3) Reject + 6
Sign To Accept or To Reject Answer
( + ) ( + ) Accept +
() () Reject
( + ) () Accept
() ( + ) Reject +
LESSON NOTES
EXAMPLES
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Solve the following.
1. 3 (5) = 2. 4 (8) = 3. 6 (5) =
4. 8 (6) = 5. (5) 7 = 6. (30) (4) =
7. 4 9 (6) = 8. (3) 5 (6) = 9. (2) (9) (6) =
10. 5 (3) (+4) = 11. 7 (2) (+3) = 12. 5 8 (2) =
TEST YOURSELF F
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TEACHING AND LEARNING STRATEGIES
This part emphasises the division rules of integers.
Strategy:
Teacher should ensure that pupils understand the division rules of integers to
perform computation involving division of integers.
PART G:
DIVISION OF INTEGERS
LEARNING OBJECTIVE
Upon completion of Part G, pupils will be able to perform computations
involving division of integers.
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PART G:
DIVISION OF INTEGERS
Consider the following pattern:
3 2 = 6, then 6 2 = 3 and 6 3 = 2
3 (2) =6, then (6) 3 =2 and (6) (2) = 3
(3) 2 =6, then (6) 2 =3 and (6) (3) = 2
(3) (2) = 6, then 6 (3) =2 and 6 (2) =3
Rules of Division
1. Division of two integers of the same signs results in a positive integer.
i.e. positive positive = positive
(+) (+) = (+)
negative negative = positive() () = (+)
2. Division of two integers ofdifferent signs results in a negative integer.i.e. positive negative = negative
(+) () = ()
negative positive = negative
() (+) = ()
3. Division of any number by zero is undefined.
LESSON NOTES
Undefined means thisoperation does not have a
meaningand is thus not
assigned aninterpretation!
Source:
http://www.sn0wb0ard.com
http://www.sn0wb0ard.com/out/meaning/dictionary.htmhttp://www.sn0wb0ard.com/out/meaning/dictionary.htmhttp://www.sn0wb0ard.com/out/interpretation/dictionary.htmhttp://www.sn0wb0ard.com/out/interpretation/dictionary.htmhttp://www.sn0wb0ard.com/out/interpretation/dictionary.htmhttp://www.sn0wb0ard.com/out/interpretation/dictionary.htmhttp://www.sn0wb0ard.com/out/meaning/dictionary.htm8/9/2019 BEAMS_Unit 1 Negative Numbers
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1. Division of two integers of the same signs results in a positive integer.
(a) (12) (3) = 4
(b) (8) (2) = 4
2. Division of two integers ofdifferent signs results in a negative integer.(a) (12) (3) =4
(b) (+8) (2) =4
3. Division ofzero by any number will always give zero as an answer.(a) 0 (5) = 0
(b) 0 (7) = 0
EXAMPLES
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Solve the following.
1. (24) (8) 2. 8 (4) 3. (21) (7)
4. (5) (5) 5. 60 (5) (4) 6. 36 (4) (3)
7. 42 (3) (7) 8. (16) (2) (8) 9. (48) (4) (6)
TEST YOURSELF G
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PART H:
DIVISION OF INTEGERS
USING
THE ACCEPT-REJECT MODEL
TEACHING AND LEARNING STRATEGIES
This part emphasises the alternative method that include activities to help pupils
further understand and master division of integers.
Strategy:
Teacher should make sure that pupils understand the division rules of integers using
the Accept-Reject Model. Pupils can then perform division of integers, includingthe use of brackets.
LEARNING OBJECTIVE
Upon completion of Part H, pupils will be able to perform computations
involving division of integers using the Accept-Reject Model.
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PART H:
DIVISION OF INTEGERS USING THE ACCEPT-REJECT MODEL
In order to help pupils have a better understanding of division of integers, we have designedthe Accept-RejectModel.
Notes: (+) (+) : The first sign in the operation will determine whether to acceptor to reject the second sign.
: The sign of the numerator will determine whether to accept or
to reject the sign of the denominator.
Division Rules:
Sign To Accept or To Reject Answer
( + ) ( + ) Accept + +
( ) ( ) Reject +
( + ) () Accept
( ) ( + ) Reject +
)(
)(
LESSON NOTES
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To Accept or To Reject Answer
(6) (3) Accept + 2
(6) (3) Reject 2
(+6) (3) Accept 2
(6) (3) Reject + 2
Division [Fraction Form]:
Sign To Accept or To Reject Answer
)(
)(
Accept + +
)(
)(
Reject +
)(
)(
Accept
)()(
Reject +
EXAMPLES
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To Accept or To Reject Answer
)2(
)8(
Accept + 4
)2(
)8(
Reject 4
)2(
)8(
Accept 4
)2(
)8(
Reject + 4
EXAMPLES
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Solve the following.
1. 18 (6)2.
2
12
3.8
24
4.5
25
5.
3
6
6. (35) 7
7. (32) (4) 8. (45) 9 (5)9. )6(
)30(
10.)5(
80
11. 12 (3) (2) 12. (6) (3)
TEST YOURSELF H
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TEACHING AND LEARNING STRATEGIES
This part emphasises the order of operations when solving combined operations
involving integers.
Strategy:
Teacher should make sure that pupils are able to understand the order of operations
or also known as the BODMAS rule. Pupils can then perform combined operations
involving integers.
PART I:
COMBINED OPERATIONS
INVOLVING INTEGERS
LEARNING OBJECTIVES
Upon completion ofPart I, pupils will be able to:
1. perform computations involving combined operations of addition,subtraction, multiplication and division of integers to solve problems; and
2. apply the order of operations to solve the given problems.
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PART I:
COMBINED OPERATIONS INVOLVING INTEGERS
1. 10(4) 3=10(12)
= 10 + 12
= 22
2. (4) (83 )= (4) (11 )= 44
3. (6) + (3 + 8 ) 5= (6 )+ (5) 5= (6 )+ 1
= 5
LESSON NOTES
EXAMPLES
A standard order of operations for calculations involving +, , , andbrackets:
Step 1: First, perform all calculations inside the brackets.
Step 2: Next, perform all multiplications and divisions,working from left to right.
Step 3: Lastly, perform all additions and subtractions, working
from left to right.
The above order of operations is also known as theBODMAS Ruleand can be summarized as:
Brackets
power of
DivisionMultiplication
Addition
Subtraction
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Solve the following.
1. 12 + (8 2) 2. (35) 2 3. 4 (16 2) 2
4. (4) 2 + 6 3 5. (25) (35 7) 6. (20)(3 + 4) 2
7. (12) + (4 6) 3 8. 16 4 + (2) 9. (18 2) + 5(4)
TEST YOURSELF I
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TEST YOURSELF A:
1. 2
2. 3
3. 6
4. 4
5. 2
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
ANSWERS
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TEST YOURSELF B:
1) 4 2) 12 3) 54) 10 5) 6 6) 67) 0 8) 12 9) 7
TEST YOURSELF C:
1) 42 2) 102 3) 924) 908 5) 548 6) 97) 843 8) 282 9) 514
TEST YOURSELF D:
1) 12 2) 12 3) 194) 10 5) 8 6) 07) 8 8) 0 9) 110) 125 11) 161 12) 20213) 364 14) 238 15) 60616) 790 17) 19 18) 125
TEST YOURSELF E:
1) 32 2) 32 3) 844) 25 5) 140 6) 847) 84 8) 96 9) 72
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TEST YOURSELF F:
1) 15 2) 32 3) 304) 48 5) 35 6) 1207) 216 8) 90 9) 10810) 60 11) 42 12) 80
TEST YOURSELF G:
1) 3 2) 2 3) 3
4) 1 5) 3 6) 37) 2 8) 1 9) 2
TEST YOURSELF H:
1. 3 2. 6 3. 3
4. 5 5. 2 6. 5
7. 8 8. 1 9. 5
10. 16 11. 2 12. 2
TEST YOURSELF I:
1. 16 2. 16 3. 12
4 10 5 5 6 34