Download Student`s Worksheet - CBSE

STUDENT'S SECTION
MATHEMATICS
Integers
The CBSE-International is grateful for permission to reproduce
and/or translate copyright material used in this publication. The
acknowledgements have been included wherever appropriate and
sources from where the material may be taken are duly mentioned. In
case any thing has been missed out, the Board will be pleased to rectify
the error at the earliest possible opportunity.
All Rights of these documents are reserved. No part of this publication
may be reproduced, printed or transmitted in any form without the
prior permission of the CBSE-i. This material is meant for the use of
schools who are a part of the CBSE-International only.
The Curriculum initiated by Central Board of Secondary Education -International (CBSE-i) is a progressive step in making
the educational content and methodology more sensitive and responsive to the global needs. It signifies the emergence of a
fresh thought process in imparting a curriculum which would restore the independence of the learner to pursue the
learning process in harmony with the existing personal, social and cultural ethos.
The Central Board of Secondary Education has been providing support to the academic needs of the learners worldwide. It
has about 11500 schools affiliated to it and over 158 schools situated in more than 23 countries. The Board has always been
conscious of the varying needs of the learners in countries abroad and has been working towards contextualizing certain
elements of the learning process to the physical, geographical, social and cultural environment in which they are engaged.
The International Curriculum being designed by CBSE-i, has been visualized and developed with these requirements in
view.
The nucleus of the entire process of constructing the curricular structure is the learner. The objective of the curriculum is to
nurture the independence of the learner, given the fact that every learner is unique. The learner has to understand,
appreciate, protect and build on values, beliefs and traditional wisdom, make the necessary modifications, improvisations
and additions wherever and whenever necessary.
The recent scientific and technological advances have thrown open the gateways of knowledge at an astonishing pace. The
speed and methods of assimilating knowledge have put forth many challenges to the educators, forcing them to rethink
their approaches for knowledge processing by their learners. In this context, it has become imperative for them to
incorporate those skills which will enable the young learners to become 'life long learners'. The ability to stay current, to
upgrade skills with emerging technologies, to understand the nuances involved in change management and the relevant
life skills have to be a part of the learning domains of the global learners. The CBSE-i curriculum has taken cognizance of
these requirements.
The CBSE-i aims to carry forward the basic strength of the Indian system of education while promoting critical and
creative thinking skills, effective communication skills, interpersonal and collaborative skills along with information and
media skills. There is an inbuilt flexibility in the curriculum, as it provides a foundation and an extension curriculum, in all
subject areas to cater to the different pace of learners.
The CBSE has introduced the CBSE-i curriculum in schools affiliated to CBSE at the international level in 2010 and is now
introducing it to other affiliated schools who meet the requirements for introducing this curriculum. The focus of CBSE-i is
to ensure that the learner is stress-free and committed to active learning. The learner would be evaluated on a continuous
and comprehensive basis consequent to the mutual interactions between the teacher and the learner. There are some nonevaluative components in the curriculum which would be commented upon by the teachers and the school. The objective
of this part or the core of the curriculum is to scaffold the learning experiences and to relate tacit knowledge with formal
knowledge. This would involve trans-disciplinary linkages that would form the core of the learning process. Perspectives,
SEWA (Social Empowerment through Work and Action), Life Skills and Research would be the constituents of this 'Core'.
The Core skills are the most significant aspects of a learner's holistic growth and learning curve.
The International Curriculum has been designed keeping in view the foundations of the National Curricular Framework
(NCF 2005) NCERT and the experience gathered by the Board over the last seven decades in imparting effective learning to
millions of learners, many of whom are now global citizens.
The Board does not interpret this development as an alternative to other curricula existing at the international level, but as
an exercise in providing the much needed Indian leadership for global education at the school level. The International
Curriculum would evolve on its own, building on learning experiences inside the classroom over a period of time. The
Board while addressing the issues of empowerment with the help of the schools' administering this system strongly
recommends that practicing teachers become skillful learners on their own and also transfer their learning experiences to
their peers through the interactive platforms provided by the Board.
I profusely thank Shri G. Balasubramanian, former Director (Academics), CBSE, Ms. Abha Adams and her team and Dr.
Sadhana Parashar, Head (Innovations and Research) CBSE along with other Education Officers involved in the
development and implementation of this material.
The CBSE-i website has already started enabling all stakeholders to participate in this initiative through the discussion
forums provided on the portal. Any further suggestions are welcome.
Vineet Joshi
Chairman
Advisory
Conceptual Framework
Shri Vineet Joshi, Chairman, CBSE
Dr. Sadhana Parashar, Director (Training),
Shri G. Balasubramanian, Former Director (Acad), CBSE
Ms. Abha Adams, Consultant, Step
Dr. Sadhana Parashar, Director (Training),
Ideators VI-VIII
Ms Aditi Mishra
Ms Guneet Ohri
Ms. Sudha Ravi
Ms. Himani Asija
Ms. Neerada Suresh
Ms Preeti Hans
Ms Neelima Sharma
Ms. Gayatri Khanna
Ms. Urmila Guliani
Ms. Anuradha Joshi
Ms. Charu Maini
Dr. Usha Sharma
Prof. Chand Kiran Saluja
Dr. Meena Dhani
Ms. Vijay Laxmi Raman
Material Production Groups: Classes VI-VIII
English :
Physics :
Mathematics :
Ms Neha Sharma
Ms. Vidhu Narayanan
Ms. Deepa Gupta
Ms Dipinder Kaur
Ms. Meenambika Menon
Ms. Gayatri Chowhan
Ms Sarita Ahuja
Ms. Patarlekha Sarkar
Ms. N Vidya
Ms Gayatri Khanna
Ms. Neelam Malik
Ms. Mamta Goyal
Ms Preeti Hans
Ms. Chhavi Raheja
Biology:
Ms Rachna Pandit
Mr. Saroj Kumar
Ms Renu Anand
Hindi:
Ms. Rashmi Ramsinghaney
Ms Sheena Chhabra
Mr.
Akshay Kumar Dixit
Ms. Prerna Kapoor
Ms Veena Bhasin
Ms. Veena Sharma
Ms Trishya Mukherjee Ms. Seema Kapoor
Ms.
Nishi Dhanjal
Mr. Manish Panwar
Ms Neerada Suresh
Ms. Kiran Soni
Ms. Vikram Yadav
Ms Sudha Ravi
Ms. Monika Chopra
Ms Ratna Lal
Ms Ritu Badia Vashisth Ms. Jaspreet Kaur
CORE-SEWA
Ms Vijay Laxmi Raman Ms. Preeti Mittal
Ms. Vandna
Ms. Shipra Sarcar
Ms.Nishtha Bharati
Chemistry
Ms. Leela Raghavan
Ms.Seema Bhandari,
Ms. Poonam Kumar
Ms. Seema Chopra
Mendiratta
Ms. Madhuchhanda
Ms. Rashmi Sharma
MsReema Arora
Ms. Kavita Kapoor
Ms
Neha Sharma
Ms. Divya Arora
Ms. Sugandh Sharma, E O
Mr. Navin Maini, R O
(Tech)
Shri Al Hilal Ahmed, AEO
Ms. Anjali, AEO
Shri R. P. Sharma,
Consultant (Science)
Mr. Sanjay Sachdeva, S O
Coordinators:
Dr. Srijata Das, E O
Dr Rashmi Sethi, E O
(Co-ordinator, CBSE-i)
Ms. Madhu Chanda, R O (Inn)
Mr. R P Singh, AEO
Ms. Neelima Sharma, Consultant
(English)
Ms. Malini Sridhar
Ms. Leela Raghavan
Dr. Rashmi Sethi
Ms. Seema Rawat
Ms. Suman Nath Bhalla
Geography:
Ms Suparna Sharma
Ms Aditi Babbar
History :
Ms Leeza Dutta
Ms Kalpana Pant
Ms Ruchi Mahajan
Political Science:
Ms Kanu Chopra
Ms Shilpi Anand
Economics :
Ms. Leela Garewal
Ms Anita Yadav
CORE-Perspectives
Ms. Madhuchhanda,
RO(Innovation)
Ms. Varsha Seth, Consultant
Ms Neha Sharma
Ms.S. Radha Mahalakshmi,
EO
4.
Study Material
1
5.
Student's support material (Student's worksheets)
19
v
SW 1: Warm Up Activity W1
20
Recall Integers
v
SW 2: Warm Up Activity W2
22
Appreciate Your Knowledge
v
SW 3: Pre Content Worksheet P1
23
Addition of Integers
v
SW 4: Pre Content Worksheet P2
25
Addition and Subtraction of Integers 1
v
SW 5: Content Worksheet C1
27
Addition and Subtraction of Integers 2
v
SW 6: Content Worksheet C2
28
Multiplication of Integers
v
SW 7: Content Worksheet C3
30
Skill Drill
v
SW 8: Content Worksheet C4
31
Multiplication of more than two integers
v
SW 9: Content Worksheet C5
33
Properties of multiplication of Integers
v
SW 10: Content Worksheet C6
38
Distributive Property of Integers
v
SW 11: Content Worksheet C7
41
Properties of Integers
SW 12: Content Worksheet C8
v
Division of Integers
44
v
SW 13: Content Worksheet C9
46
Properties of division of Integers
v
SW 14: Content Worksheet C10
48
BODMAS- Simplification of brackets
v
SW 15: Content Worksheet C11
51
Independent Practice
v
SW 16: Content Worksheet C12
53
Word problems on Integers
v
SW 17: Post Content Worksheet PC1
57
Appreciate your knowledge
v
SW 18: Post Content Worksheet PC2
60
Evaluate your knowledge
6.
Acknowledgments
62
7.
Suggested videos/ links/ PPT's
63
STUDY
MATERIAL
1
Introduction
In Class VI, you studied about a special type of numbers called integers. You also learnt
how to compare integers and to arrange them in ascending or descending order.
Concepts of absolute value of an integer, operations of addition and subtraction on
integer were also discussed. In this unit, we shall first recall these concepts in brief and
learn more about integers regarding their multiplication and division. Finally, we shall
discuss properties of operations on integers and solve some word problems involving
integers. Simplification of expressions using BODMAS rules will also be explained.
1.
Basic Concepts: A recall
Integers
The numbers
….., –4, –3, –2, –1, 0,1, 2, 3, 4, ….. are called integers.
Numbers ….., –4, –3, –2, –1, are called negative integers and numbers 1, 2, 3, 4,
….. are called positive integers.
‘0’ is neither negative nor positive number.
Integers can be represented on a number line:
Negative integers
positive integers
Fig 1.
Ordering of Integers
An integer a lying to the left of another integer b on the number line is smaller
i.e, a < b or b > a.
(i)
Every positive integer is greater than every negative integer
i.e, 5 > –3, 2 > –100, 1 > –999 etc.
2
(ii)
Zero (0) is less than every positive integer and greater than every
negative integer.
For example,
0 < 1 < 2, 0 < 5 etc.
0 >–1, 0 >–5 etc
(iii)
For any two integers a and b, if a > b then –a < –b, and if a < b then
–a > –b.
For example,
4 > 3 and –4 < –3,
9 > 7 and –9 < –7
6 < 8 and –6 > –8
and so on.
Absolute value of an Integer
Absolute value of an integer is its numerical value regardless of its sign.
For example, absolute value of –4, denoted as |–4|, is 4. Absolute values of 3,
denoted as |3|, is 3. Similarly, |–99| = 99,
|2|
= 2
|–5| =
5
|18| = 18
Addition of integers
Rules
(i)
When two integers are of the same sign, i.e., both positive or both
negative, then we add their absolute values and assign the sign
common to both.
For example, (+ 19) + (71)
= + (|19| + |71|) + (|19| + |71|)
= + (19 + 71)
= + 90 or 90
3
(–35) + (–13) = – (|–35| + |–13|)
= – (35 + 13)
= – 48
(ii)
When two integers are of different signs, i.e., one integer is positive
and the other is negative, then to find their sum, we first ‘find’ absolute
values of the integers, subtract smaller absolute value from the greater
absolute value and assign the sign of the integer with greater absolute
value.
For example,
(–92) + 98
= + (|98| – |–92|)
= + (98 – 92)
= 6
Similarly,
(+91) + (–98)
= – (|–98| – |91|)
= – (98 – 91)
=–7
(iii)
When 0 is added to any integer, we get the integer itself.
For example,
(–3) + 0 = –3
0 + (4)
= 4
Additive inverse
If the sum of two integers is 0, then each integer is called the additive inverse
of the others.
For example,
as 4 + (–4) = 0,
so, –4 is the additive inverse of 4 and 4 is the additive inverse of –4.
Similarly, 481 is the additive inverse of – 481 and – 481 is the additive inverse
of 481 as 481 + (–481) = 0
Additive inverse of 0 is 0 as 0 + 0 = 0
4
Subtraction of Integers
Subtraction is considered as inverse operation of addition. Therefore, to
subtract an integer b from another integer a, we add additive inverse of b i.e.
(–b) to a.
For example,
3 – (–7) = 3 + (+ 7)
= 10
Similarly,
(Rule 1 of addition)
–53 – (42) = –53 + (–42)
= –95
(Rule 1 of addition)
–51 – (–10) = –51 + (+ 10)
= –41
2.
(Rule 2 of addition)
Multiplication of Integers
Recall that multiplication of whole numbers is repeated addition.
For example
3 x 7 = 7 + 7 + 7 = 21,
10 x 3 = 3 + 3+ 3 +3 +3 +3 +3 +3+3 +3 = 30
In the same way, we can find
3 x (–7) = (–7) + (–7) + (–7) = –21
10 x (–3) = (–3) + (–3) + (-3) + (–3) + (–3) + (–3) + (–3) + (–3) + (–3) + (–3)
= –30
6 x (–3) = (–3) + (–3) + (–3) + (–3) + (–3) + (–3) = –18
and so on.
From the above discussion, we can say that
If a and b are two positive integers then
a x b = ab [positive integers x positive integers = positive integer]
and
a x (–b) = – (ab) [Positive integers x negative integer = negative integer]
5
What about the product (–3) x 6?
To find this, observe the following pattern:
3 x 6 = 18
2 x 6 = 12
1x6=6
0x6=0
–1 x 6 = ?
–2 x 6 = ?
–3 x 6 = ?
Observe that in the above case, first number is decreasing by 1 at each step, and
the corresponding product is decreasing by 6 (= 2nd integer).
3 x 6 = 18
(3 –1)
2 x 6 = 12
(18 – 6)
(2 –1)
1x6=6
(12 – 6)
(1 –1)
0x6=0
(6 – 6)
(0 –1)
–1 x 6 = –6
(0 –6)
(–1 –1)
–2 x 6 = –12
(–6 –6)
(–2 –1)
–3 x 6 = –18
(–12 –6)
Thus, –3 x 6 = –18 = – (3 x 6)
What is the product –4 x 6?
It will be
–18–6 = –24
(see the above pattern)
We have
(–1) x 6 = –6 = – (1 x 6)
(–2) x 6 = –12 = – (2 x 6)
(–3) x 6 = –18 = – (3 x 6)
(–4) x 6 = –24 = – (4 x 6)
6
In general, we can say that for two positive integers a and b,
(–a) x b = – (ab)
Negative integer x positive integer = negative integer
What is the product (–3) x (–6)?
Observe the following:
(–3) x 6 = –18
5=6–1
(–3) x 5 = –15
(–18+3)
4=5–1
(–3) x 4 = –12
(–15+3)
3 = 4 –1
(-3) x 3 = – 9
(–12+3)
2=3–1
(–3) x 2 = –6
(–9+3)
1=2–1
(–3) x 1 = –3
(–6+3)
0 = 1 –1
(–3) x 0 = 0
(–3+3)
–1 = 0 –1
(–3) x (–1) = ?
–2 = –1 –1
(–3) x (–2) = ?
–3 = –2 –1
(–3) x (–3) =?
Do you see any pattern? Observe how do the products change.
You can see that 2nd number in each step is decreasing by 1 and product is
increasing by 3, From the pattern,
(–3) x (–1) = 0+3 = 3 = 3 x 1
(–3) x (–2) = 3+3 = 6 = 3 x 2
(–3) x (–3) = 6+3 = 9 = 3 x 3
and so on.
7
Thus,
(–3) x (–6) = 3 x 6 = 18
In general, for positive integers a and b
(–a) x (–b) = ab
Negative integer x negative integer = positive integer
We can now summarise the discussion on multiplication of two integers as
follows:
1. To find the product of two integers of like signs, find the product of their
absolute values and assign the ‘+’ sign to the product.
2. To find the product of two integers of unlike signs, find the product of their
absolute values and assign ‘–’sign to the product.
Let us consider some examples illustrating product of integers.
Example 1: Find the following products:
(i)
(–4) x 6
(ii)
3 x 11
(iii)
2 x (–19)
(iv)
(–11) x (–16)
(v)
(–5) x (–6) x (–3)
(vi)
(–5) x (–4) x (–3) x (–4)
Solution
(i)
(–4) x 6 = – (4 x 6) = –24
[ (–a) x b = – (ab)]
(ii)
3 x 11 = 33
(iii)
2 x (–19) = – (2 x 19) = –38 [a x (–b ) = –ab]
(iv)
(–11) x (–6) = +(11 x 6) = 66
(v)
(–5) x (–6) x (–3)
[(–a) x (–b) = ab]
= [(–5) x (–6)] x (–3)]
= [+ (5 x 6)] x (–3)
8
= 30 x (–3)
= – (30 x 3) = –90
(vi)
(–5) x (–4) x (–3) x (–4)
=
[(–5) x (–4)] x (–3) x (–4)
=
(20) x (–3) x (–4)
=
[20 x (–3)] x (–4)
=
(–60) x (–4)
=
240
From the above products, you can observe that
(i)
Product of integers involving even number of negative integer is positive.
(ii)
Product of integer involving odd number of negative integer is negative.
Example 2: Find the sign of the following products:
(i)
(–1) x (–1) x (–1) x (–1) x (–1)
(ii)
(–20) x (–31) x (–1001) x (43)
(iii)
(124) x (–108) x 99 x (–99) x (–1241) x (–100)
Solution:
(i)
There are five (odd) negative integers.
So, their product will be negative.
(ii)
Number of negative integer is 3 (odd)
So, the product will be negative
(iii)
Number of negative integer is 4 (even)
So, the product will be positive.
3.
Division of integers
You know that division is the inverse operation of multiplication. Recall that for
a multiplication fact in whole numbers, there are two corresponding division facts
(i)
5 x 8 = 40,
9
The division facts are:
40 ÷ 5 = 8
40 ÷ 8 = 5
Similarly, for 4 x 9 = 36, we have the following division facts.
36 ÷ 4 = 9
36 ÷ 9 = 4
We can extend it to integers as follows:
Multiplication fact
Division facts
(–2) x (–3) = 6
6 ÷ (–2) = –3
and
(–8) x (9) = –72
6 ÷ (–3) = –2
(–72) ÷ (–8) = 9
and
(10) x (–5) = –50
(–72) ÷ 9 = –8
(–50) ÷ 10 = –5
and
(–10) x (–5) = 50
(–50) ÷ (–5) = 10
50 ÷ (–10) = –5
and
3 x (–11) = –33
50 ÷ (–5) = –10
(–33) ÷ 3 = –11
and
– 4 x 5 = –20
(–33) ÷ (–11) = 3
(–20) ÷ (–4) = 5
and
(–20) ÷ 5 = –4
From the above division facts, observe that
(i)
If the dividend and divisor are integers of like signs, then the quotient is an
integer with a positive sign (+), provided the absolute value of the dividend is
divisible by the divisor.
For example,
40 ÷ 5 = 8
36 ÷ 4 = 9
10
(–72) ÷ (–8) = +
=9
(–50) ÷ (–5) = 10
(ii)
If the dividend and divisor are integers of unlike signs, then the quotient is an
integer with a negative sign (–), provided the absolute value of the dividend is
divisible by the divisor.
For example,
6 ÷ (–2)
=–
= –3
50 ÷ (–5) = –
= –10
(–50) ÷ 10 = –
= –5
(–72) ÷ 9 = –
= –8
Example 3: Find
(i)
18 ÷ (–3)
(ii)
(–54) ÷ 18
(iii) (–18) ÷ (–6)
(iv)
(–8) ÷ (–2)
(v) 16501 ÷ (–16501)
(vi)
(–729) ÷ (–81)
(vii) 190 ÷ (–1)
Solution:
(i)
18 ÷ (–3) = –
= –6
(ii)
(–54) ÷ 18 = –
(iii)
(–18) ÷ (–6) = +
(iv)
(–8) ÷ (–2) = + = 4
(v)
16501 ÷ (–16501) = –
(vi)
(–729) ÷ (–81) = +
= –3
=3
= –1
=9
11
(vii)
190 ÷ (–1) = –
= –190
Division of an Integer by 0
Recall that division is repeated subtraction as multiplication is repeated addition.
Let us try to find –23 ÷ 0, using repeated subtraction
We have
(–23)– 0 = –23
(–23) – 0 = –23
(–23) – 0 = –23
(–23) – 0 = –23
--------This process is never ending.
So, we say that division of an integer by 0 is meaningless.
What about division of 0 by a non zero integer? Like whole numbers, the
quotient is 0.
4.
Properties of Operations on Integer
Addition
(i) The sum of two integers is an integer
For example
5 + (–3) = 2 (integer) (–3) + (–5) = –8 (integer)
8+ (–8) = 0 (integer)
This property is called closer property for addition
(ii) For any two integers a and b,
a+b=b+a
For example,
5 + (–3) = 2, and (–3) – 5 = 2
5 + (–3) = (–3) + 5
12
Similarly, (–9) + (2) = 2 + (–9)
This property is called commutative property of addition.
(iii) For any three integers a, b and c
a + (b+c) = (a+b) + c
For example, 3 + [(–2) + (–5)] = 3 + (–7) = –4
and [3 + (–2)] + (5) = 1 + (–5) = –4
So,
3 + [(–2) + (–5)] = [3+ (–2)] + (–5)
This property is called associative property of addition
(iv) For any integer a,
a+0=0+a=a
0 is called the identity element (or additive identity)
Subtraction
(i) For any two integers a and b
a – b or b – a is an integer
For example, 3 – (–2) = 5 (integer)
This property is called closure property for subtraction
(ii) Subtraction is not commutative
For example, (–8) – (–7) = –1
(–7) – (–8) = 1
So,
(–8) – (–7) ≠ (–7) – (–8)
(iii) Subtraction is not associative
For example
(–5) – [(–2) + (–3)] ≠ [(–5) – (–2)] + (–3)
(iv) 0 is not an identity element for subtraction because
a – 0 = but 0 – a = -a
i.e. a – 0 ≠ 0 – a
Multiplication
(i)
For any two integers a and b, a x b or ab is an integer.
13
For example,
(–2) x (–1) = 2 (integer)
(–11) x 5 = –55 (integer)
This is called closure property for multiplication
(ii) For any two integers a and b,
axb=bxa
This is called commutative property of multiplication
(iii) For any three integers a, b and c
a x (b x c) = (a x b) x c
For example, (–3) x [(8 x 5)] = (–3) x 40 = –120
[(–3) x 8] x 5 = –24 x 5 = –120
i.e.
(–3) x [(8 x 5) = [(–3) x 8] x 5
This is called associative property of multiplication.
(iv) 1 is the multiplicative identity (or identity element) of any integer a
i.e. 1 x a = a x 1 = a
Property of zero (0)
For any integer a,
ax0=0xa=0
Distributive property of multiplication over addition
For any three integers a, b and c
a x (b + c) = a x b + a x c
(a + b) x c = a x c + b x c
You may verify it by taking any three different integers a, b and c.
Division
None of the above properties is true for division of integers.
14
You may satisfy yourself by taking different integers a, b, c etc.
Example 4:
Fill in the blanks:
(i)
2 + (–15) = -------- +2
(ii)
–3785 ÷ ---------- = 1
(iii)
------- ÷ 555 = –1
(iv)
-------- ÷ 578 = 0
(v)
– 6 + --------- = 0
(vi)
19 + -------- = 0
(vii)
15 + (–15) = ------
(viii) (–2) x [3 x (–5)] = [(―) x 3] x (–5)
(ix)
–578 x ----- = –578
(x)
(–5) x [(–2) + 3] = (–5) x (―) + (―) x 3
Solution:
(i) –15
(ii)
–3785
(vi) –19
(vii) 0
(iii) –555
(iv) 0
(v) 6
(viii) –2
(ix) 1
(x) –2 , –5
Example 5: Which of the following statements are true and which are false?
(i)
Addition of integers is commutative
(ii)
Integers are closed for division
(iii)
1 is the identity element for addition of integers
(iv)
Multiplication is association for integers
(v)
0 is the identity element for subtraction
(vi)
Quotient of two integers is an integer
(vii)
Addition is distributive over multiplication for integers
(viii) 1 is the identity element for multiplication
15
Solution :
5.
(i) True
(ii) False
(iii) False
(iv) True
(v) False
(vi) False
(vii) False
(viii) True
BODMAS Rule
In BODMAS, B stands for ‘brackets’, O for ‘of’, D for ‘Division’, M for
Multiplication’, A for ‘Addition’ and S for ‘Subtraction’. In simplifying expression,
we perform these operations in the order, they are listed above. We explain this
through some examples:
Example 6: Find the value of
(i)
30 – 5 x 2 of 3 + (19 – 3) ÷ 4
(ii)
81 of [59 – {7 x 8+ (17–2 of 5)}]
Solution: (i) 30 – 5 x 2 of 3 + (19 – 3) ÷ 4
= 30 – 5 x (2 of 3) + 16 ÷ 4 (Removing the brackets)
= 30 – 5 x 2 x 3 + 16 ‚ 4 (Performing ‘of’)
= 30 – 5 x 2 x 3 + 4
(Performing D)
= 30 – 30 + 4
(Performing M)
= 34 – 30
(Performing A)
=4
(Performing S)
(ii) 81 of [59 – {7 x 8+ (17–2 of 5)}]
= 81 of [59 – {7 x 8 + (17 – 2 x 5)}]
= 81 of [59 – {7 x 8 + (17 –10)}]
= 81 of [59 – {56 + 7}]
= 81 of [59 – 63]
= 81 of (–4) = 81 x (–4)
= –324
16
6.
Applications of Integers
We now explain the use of operations on integers in solving some daily life
problems.
Example 7: A question paper contains 15 questions. 4 marks are given for every correct
answer and –1 marks are given for every correct answer. Hamid attempts all the
questions. What is his total score, if only 10 of his answers are correct?
Solution:
Marks given for 1 correct answer
=
4
So, marks for 10 correct answers
=
4 x 10 = 40
Marks for 1 incorrect answer
=
–1
So, marks for (15–10) = 5 incorrect answers
=
–1 x 5 = –5
So, total score of Hamid
=
40 + (–5)
=
35
Example 8: A shopkeeper earns a profit of 80 per bag of wheat sold and a loss of 50
per bag of rice sold. The company sold 2500 bags of wheat and 3400 bags of rice in a
month. Calculate the profit of loss or the shopkeeper.
Solution:
Profit on 1 bag of wheat
=
80
So, profit on 2500 bags of a wheat =
80 x 2500
=
200000
Loss on 1 bag of rice
=
50
i.e., profit on 1 bag of rice
=–
50
So, profit on 3400 bags of rice
=–
50 x 3400
Total Profit
=
(–50 x 3400)
=
(–170000)
=
[200000 + (–170000)]
=
30000
17
Example 9: A certain freezing process requires that room temperature be lowered from
45ºC at the rate of 5ºC every hour. What will be the room temperature at the end of 12
hours?
Solution:
Decrease in temperature in 1 hour = 5ºC
Room temperature after 12 hours
= 45ºC + (–5ºC) x 12
= 45ºC + (–60 ºC)
= –15ºC
18
19
Student’s Worksheet – 1
Warm Up (W1)
Recall Integers
Name of the student ______________________
Date ____________
Activity - Numbers and more Numbers. . .
1. What are whole numbers? Can they be negative?
________________________________________________________________________
________________________________________________________________________
2. What are integers? Write 15 integers of your choice in the space given below.
_______________________________________________________________________
_______________________________________________________________________
OUT
20
Put these numbers in the appropriate boxes. One Number may be put in more than one
box.
Natural Numbers
Whole Numbers
Integers
Write True or False on the basis of your observations.
All whole numbers are natural.
__________
All whole numbers are integers.
__________
All natural numbers are whole numbers.
__________
21
Student’s Worksheet – 2
Warm Up (W2)
Appreciate Your Knowledge
Name of the student ______________________
Date ____________
Activity - Mirror Numbers on Number Line.
Recall that negative integers are the images of positive integers and vice-a-versa.
Integer ‘0’ is neither positive nor negative.
Fill up the given table. One example is done for you.
Integer Write image of
(A)
integer (B)
5
-5
Give an integer >
Image
Give an integer <
Image
Find (A) + (B)
-2
-8
5 + (-5) = 0
(-2 > -5 )
( -8 < -5 )
-3
7
0
-4
-2
9
-15
23
-16
-3
-41
Write your observation. Is a + (-a) =0 ?(where a is any integer)
______________________________________________________________________________
______________________________________________________________________________
22
Student’s Worksheet – 3
Precontent (P1)
Addition of Integers
Name of the student ______________________
Date ____________
Activity - Integer Grid
Find 3 integers in a row, column or a diagonal, where the third number is the sum of
the first and the second number. One is already done for you.
Here, (-7) + 2 = -5.
Find at least 5 more such relations and record them here.
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
23
Activity -Addition of Integer on Number line
Add on number line
1. ( – 5 ) + 7 = _______
2. 5 + ( – 4 ) = _______
3. – 7 – 2 = ________
4. – 8 + 6 – 3 = _______
5. 5 + 3 – 8 = ________
24
Student’s Worksheet – 4
Precontent (P2)
Addition and Subtraction of Integers 1
Name of the student ______________________
Date ____________
Activity - The Number SPIDER
Start with an integer of your choice and encircle it to form the body of a SPIDER .
Draw eight ‘legs’ rediating from the body and write another way of writing the
selected integer , using addition and subtraction of integers.
An example is provided here. Go ahead and complete it .
Make SIX NUMBER SPIDERS of your choice.
25
Make your own CRAWLY SPIDERS.
26
Student’s Worksheet – 5
Content Worksheet (C1)
Addition and Subtraction of Integers - 2
Name of the student ______________________
Date ____________
Task 1: Find the hidden number.
Solve the expression in each box.Colour it red if answer is -3 and blue if answer is - 4.
Identify the hidden number.
7-11
3-6
10-13
-2-2
5-9
6-10
-3-1
4-7
16-20
0-4
13-17
-1-2
31-35
-42+36
59-63
27-30
11-14
76-79
-11+7
-5+1
-9+5
3-7
12-16
21-25
-8+4
The hidden number is………………..
Task 2:Add or subtract the integers.
Help the rat to perform the operation correctly and move forward and eat the cheese.
27
Student’s Worksheet – 6
Content Worksheet (C2)
Multiplication of Integers
Name of the student ______________________
Date ____________
Task 1: Complete the multiplication table.
Multiply each integer in the row with corresponding integer in the column:
X
-3
-2
-3
0
3
-2
4
-1
2
0
0
1
-1
-3
-2
2
0
1
2
3
4
5
-3
-6
-9
-12
-15
-2
-4
-3
-4
-5
0
0
0
0
-1
1
2
2
3
-9
3
4
-8
5
-10
6
-18
0
-6
0
5
10
6
12
28
3
5
6
8
9
12
12
16
15
6
12
25
Task 2: Solve and then join the dots in ascending order. Colour the figure obtained.
Task 3: Write the integer that makes the following statement true.
1.
4 x
2.
3.
4.
5.
= 44
x ( 5) = 45
2x
6 x ( 5)
9x
=8
=
= 63
29
Student’s Worksheet – 7
Content Worksheet (C3)
Skill Drill
Name of the student ______________________
Date ____________
Activity - Integer Grid with multipication
Find 3 integers in a row, column or a diagonal, where the third number is the product of
the first and the second number. One is already done for you.
Here, (–2) x (–1) = 2
Find at least 5 more such relations and record them here.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
_______________________________________________________________________
30
Student’s Worksheet – 8
Content Worksheet (C4)
Multiplication of Three or More Integers
Name of the student ______________________
Date ____________
Task 1: Multiply the following integers:
3 × ( -5) × 9
=_____________
(-9) × (-2) × 8
=_____________
(-7 ) × 3 × 3
=_____________
7 × (-6) × (-8) =_____________
(-8) × 5 × 0
=_____________
(-5) × (-5) × 7 =_____________
7 × (-6) × 8 =_____________
(-2)×(-10)×(-8) =_____________
(-2) × 2 × (-9) =_____________
8 × (-1) × 4
Task 2: If ∆ = - 5 ,
a)
b)
c)
=_____________
= -2 ,evaluate the following:
=
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
_______________________________________________________________
31
Task 2: Solve and place the integers in order starting with the least or smallest.(the
first one is done for you.)
-2 X 3 X3
-4 X 2 X 4
2X5X3
(-6) X (-2) X 3 3 X (-4)X 2 4 X 4 X -3
-5 X 0 X 2
5 X (-1) X 3
-2 X 2X1
-2 X -3 X -7
5 X 2 (-3)
2 X -3 X -1
6 X -3 X 2
-4 X -2 X 3
-3 X -7 X 0
32
Student’s Worksheet – 9
Content Worksheet (C5)
Properties of Multiplication of Integers
Activity 1: Choose the correct property of multiplication from the cloud and write in
the blank.
Commutative
Distributive
Associative
Closure
Multiplicative identity
i)
6 X 13 = 13 X 6
………………….................................
ii)
2X1=2
………………….................................
iii)
-6 X 3 = -18
………………….................................
iv)
(9 X 12) X 3 = 9 X (12 X 3)
……………………..............................
v)
7 X (3 + 10) = 7 X 3 + 7 X 10
…………………………......................
vi)
1X9=9
vii)
13 X (-9) = (-9) X 13
viii)
-13 X (8 + 10) = -13 X 8 + (-13) X 10…………...........................................
ix)
-4 X (-3) = -3 X (-4)
x)
-2 X (45 +33) = (-2) X 45 + (-2) X 33...........................................................
……………………..............................
……………………..............................
……………….....................................
33
Activity 2: In numbers 1-9, select the property that is being illustrated and encircle it.
1)
-3 + 6 = 6 + -3
Associative Property of Addition
Commutative Property of Addition
Distributive Property
Property of Additive Inverse
2)
3)
3 + (5 + 7) = 3 + (7 + 5)
a)
Distributive Property
b)
Property of Additive Inverse
c)
Associative Property of Addition
d)
Commutative Property of Addition
7•3=3•7
a)
Property of Multiplicative Inverse
b)
Associative Property of Multiplication
c)
Commutative Property of Multiplication
d)
Distributive Property
34
4)
5)
6)
7)
8)
(7 • 5) • 2 = 7 • (5 • 2)
a)
Identity Property for Multiplication
b)
Associative Property of Multiplication
c)
Property of Multiplicative Inverse
d)
Commutative Property of Multiplication
2(7 + 3) = 2(7) + 2(3)
a)
Commutative Property of Addition
b)
Associative Property of Multiplication
c)
Property of multiplicative inverse
d)
Distributive Property
-2(x + 5) = -2x - 10
a)
Property of multiplicative inverse
b)
Associative Property of Multiplication
c)
Distributive Property
d)
Identity Property for Multiplication
-3(x - 3) = -3x + 9
a)
Identity Property for Multiplication
b)
Commutative Property of Multiplication
c)
Property of multiplicative inverse
d)
Distributive Property
x+0=x
a) Commutative Property of Addition
b) Associative Property of Addition
c) Property of Additive Inverse
d) Identity Property of Addition
35
9)
a=a•1
a)
Associative Property of Multiplication
b)
Identity Property of Multiplication
c)
Property of Multiplicative Inverse
d)
Commutative Property of Multiplication
Activity 3: In numbers 10-16, choose the best answer that answers the question and
encircle it.
10)
11)
12)
Which of the following is an illustration of the associative property?
A)
a(b + c) = ab + ac
B)
ab + 0 = ab
C)
a + (b + c) = (a + b) + c
D)
a+b=b+a
Which sentence is an example of the distributive property?
A)
a (b + c) = ab + ac
B)
a•1=a
C)
ab = ba
D)
a(bc) = (ab)c
What number is the additive identity element?
A) 1
13)
B) 0
D) 2
Which statement best illustrates the additive identity property?
A) 6 + 2 = 2 + 6
14)
C) -1
B) 6 + 0 = 6
C) 6 + (-6) = 0
What number is the multiplicative identity element?
A) ½
B) 0
C) -1
D) 1
36
D) 6(2) = 2(6)
15)
16)
Which statement best illustrates the inverse property of addition?
A)
3 + 3= 6
B)
-3 + 3= 0
C)
3+0=3
D)
3(1) = 3
Which statement best illustrates the inverse property of multiplication?
A)
2 • (-½) = -1
B)
2•1=2
C)
2•0=0
D)
2•½=
37
Student’s Worksheet – 10
Content Worksheet (C6)
Distributive Property of Integers
1. Draw tens-sticks and ones-dots to illustrate the numbers. Then use the distributive
property to multiply. One is done for you. Illustrate the next three sums on its basis.
5 × 23
5 × 20 =
5×3=
5 × 23 = 100 + 15 = 115
2 × 65
38
3× 58
4 × 27
39
2. Break the second number (factor) into tens and ones. Multiply in parts (tens and
ones separately), and add.
5 × 17 = 5 × (10 + 7).
8 × 41 = 8 × (__ + _).
5 × 10 =
5×7=
8 × 40 =
8×1=
+
5 × 17 = 5 × (__ + _).
5×
5×
+
6 × 73 = 6 × (__ + _).
+
3. Now break the second number (factor) into hundreds, tens and ones. Multiply in
parts (hundreds, tens, and ones separately), and add.
a. 5 × 123
5 × 100 =
5 × 20 =
5×3=
b. 8 × 115
8 × 100 =
8 × 10 =
8×5=
+
g. 5 × 149
+
h. 7 × 106
+
+
40
Student’s Worksheet – 11
Content Worksheet (C7)
Independent Practice
Task 1: Match the following
Additive inverse of 9
1 +0
Multiplicative identity
-2 x 1
10
Additive inverse of -6
0 x 10
Multiplicative inverse of -5
-3 + 9
Additive inverse of 0
3 x (-3)
Task 2 :Solve and arrange in ascending orderAdditive inverse of -2, additive inverse of 3, multiplicative identity of 19, additive
identity of -5 and multiplicative inverse of -1.
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
_______________________________________________________________
________________________________________________________________
41
Task 3 : Sunny and Bunny are two rabbits. They want to pick pairs of two apples such
that number on one apple is additive inverse of the number on the other apple. Colour
such pairs of apples with same shade and help them.
How many such pairs are their
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
42
Task 5: Answer the following questions. Also write 5 more examples of your own.
Question
Answer
1. (50/3)
2.
3.
4.
5.
6.
7.
=
8. 1
43
Student’s Worksheet – 12
Content Worksheet (C8)
Division of Integers
Name of the student ______________________
Date ____________
Activity -Integer Grid does Division Trickkkk….
Find 3 integers in a row, column or a diagonal, such that when you divide the second
number with the first one then you get the third number. One is already done.
Here, (–90)
(–30) = 3
Find at least 5 more such relations and record them here.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
44
Recall that absolute value of a
Task: Absolute Star
number n is |n|.
The absolute value of a number is
always a positive number (or zero).
Solve the following absolute values:
a)
b)
c)
d)
e)
f)
g)
h)
-|-6|
|-12|-|-5|
|-12|+ |-2|
|-21| + |5-12|
|0| ÷|-6|
|11-5| ×|1-5|
|-21| +|21|
|-1-6| -|-17|
i)
Write your observation about absolute value:
The absolute value of an integer is always ______________________than the integer.
The absolute value of an integer is never _______________________ than the
number.
Integers having absolute value 5 are ______________________.
45
Student’s Worksheet – 13
Content Worksheet (C9)
Properties of Division of Integers
Name of the student ______________________
Date ____________
Activity - Make Me Happy
Apply your knowledge of properties of division of integers and find which statements
are true.
I am Happy : Write the serial number of true statements in the happy face.
I am Sad : Write the serial number of false statements in the sad face.
Make Me Happy : Correct the false statements and write them in the Big Happy
Face and thus make them happy again.
1. The collection of integers is commutative under division.
2. Division is closed in integers.
3. Division is associative in integers.
4. There is no division identity for integers.
5. The distributive prorety of division over addition holds good in integers.
6. (−a) ÷ b = −(a ÷ b).
7. (−4) ÷ 0 = 0.
8. a ÷ (−a) = −1 = (−a) ÷ a
9.
Division is distributive over subtraction in integers.
10. 0 ÷ (−a) = 0.
11. 1 is the division identity element.
12. Commutative Property of division does not hold good in integers.
13. {(−8) ÷ (−4)} ÷(−2) ≠ (−8) ÷ {(−4) ÷(−2)}.
46
14. 1 ÷ 0 is not defined.
Dear friends, now Make Me Happy again by correcting the false statements. Recall all
PROPERTIES OF INTEGERS.
47
Student’s Worksheet – 14
Content Worksheet (C10)
Bodmas – Simplification of Brackets
Name of the student ______________________
Date ____________
Activity - Find the Mystry Number
(A) You get me if 24 is added to, 15 divided by 3. Find me.
Now observe that,
Mystry Number = (15 ÷ 3) + 24
= 5 + 24
= 29
(B) Based on the above illustration find the BODMAS expression for the following
statements and solve them using BODMAS rules.
1. The difference of eight, and four multiplied by twenty.
2. Twenty eight is divided by, four subtracted fromnegative three.
3. The sum of five ,and two divided by negative two.
4. Negative five multipied by negative six, is subtractedfrom quotient of forty
fivedivided by negative nine.
5. Four divided by, the difference between ten and six.
6. The additive inverse of fifteen is multiplied by the sum of twelve and additive
inverse of forty two.
7. Negative four multiplied by negative ten is subtracted from eight multiplied by
negative one.
8. Four divided by, the difference between ten and six.
48
Bodmas expression
Working / Solution
49
(C) Solve using the order of operations.
Inner
most
brackets
÷
x
+
−
1) 3 + 6 − (7 − 8)
2) {(12 − 7) x (2 x 4)} ÷ 8
3) 56 − 24 ‚ (11 − 3) x 8 + 4
4) −7 x 6 − 18 ‚ 3 + 11 (36 ‚ 9 − 6) − 5
5) (15) x (−4) ÷ {(−5) x (−3) x (−2)}
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
50
Student’s Worksheet – 15
Content Worksheet (C11)
Independent Practice
Name of the student ______________________
Date ____________
Task 1 Solve the following expressions:1. 10 – [ 9 – { 16 ÷ 2 –( 6 – 9)}]
2. 18 – 8 ÷ 4 x 3
3. 7 (14 – 3 – 4) + (–2)
4. (–4) x (–16) ÷ (–4) + (–3)
5. 9 + { 6 + 5 x 3 – ( 7 ÷ (–7))}
6. – 3 –[(–7) x {( –4) + 7 – (–1)}]
7. – 8 – [7 – {2 + 5 – (6 – 7 – 3)}]
8. 9 ÷ (15 – 7 – 5) + 6
9. 25 – 12 ÷ 6 – 3 x 8
10. 8 + [6 – 3 –{ 5 + 2 + 8 ÷ (–2)}]
11. 15 x 4 + 12 ÷ 6 - 9 x 4
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
51
Task 2 :Place parenthesis in the following problem to make the solution correct.
I think …I know who
should be treated first.
1. 8 x 0 −7 + 7 −5 = −19
________________________________
2. 9 – 4 + 7 – 6 x 2 = 3
________________________________
3. 3 – 4 – 18 ÷ – 6 + 12 = 2
________________________________
4. –13 + 52 ÷ – 4 – 9 = – 3
________________________________
5. – 6 x – 2
________________________________
–3x–4=1
Task 3:
Make bodmas expressions on your own using { } , ( ) , at least five
integers having answers:
5
–4
–13
17
52
Student’s Worksheet – 16
Content Worksheet (C12)
Word Problems on Integers
Name of the student ______________________
Date ____________
Activity - Reality Report
1. In a class test containing 15 questions, 5 marks are given for every correct answer
and (–3) marks given for every incorrect answer and 0 marks for question not
attempted. Find Martin’s scores if,
Gosh!....I will get –3 for every
incorrect answer…. It will bring
my score down…
a) he gets 9 correct and 6 incorrect answers.
b) he gets 6 correct and 5 incorrect answers.
2. A shopkeeper earns a profit of Re 1 by selling one pen and incurs a loss of 40p per
pencil of her old stock.
a) In a particular month she incurs a loss of Rs 5. In this period, she sold 45 pens.
How many pencils did she sell in this period.
b) In the next month she neither earned profit nor loss. If she sold 70 pens, how
many pencils did she sell?
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
53
_______________________________________________________________________
_______________________________________________________________________
3. If a toy company earns a profit of Rs 20 on sale of a Barbie doll but suffers a loss of
Rs 12 on sale of a Drum.
a) If company sold 20 dolls and 25 drums in a month then find the profit or loss as
the case may be.
b) If company sold 15 dolls in a month then find the number of drums it must sell
so as to have neither profit no loss.
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
4. A submarine was situated 800 feet below sea level. If it descends 250 feet per hour,
what is its new position after 6 hours?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
5. The temperature was 14°F at 4P.M. If the temperature dropped by 2°F per hour,
what will be the temperature at midnight?
__________________________________________________________________________
__________________________________________________________________________
54
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
6. An earthworm is 30 feet deep in the well. Every day he climbs 3 feet up the walls of
the well but slips down 2 feet at night, as the walls becomes damp. How many days
will it take him to climb out of the well?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
7. A submarine left the surface of the water at the rate of 5 m per second. How long
will it take the submarine to reach 535m below the sea level?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
8. In a game of ‘Table Polo’, marbles have to be shot into a hole. All players decided
that each marble in the hole will be awarded 5 points where as each marble missed
will have a penalty of 2 points. Kevin shoots 5 in the hole out of his 12 chances. Find
his final score.
__________________________________________________________________________
__________________________________________________________________________
55
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
9. A water tanker contains 750 liters of water but due to a small hole, water is leaking
at the rate of 7 liters per hour. What will be the quantity of water left in the tanker
after 15 hours?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
10. An elevator descends into a mine shaft at the rate of 14m/minute. If the descent
starts from 15 m above the ground level, how long will it take to reach 265m below
the ground level?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
56
Student’s Worksheet – 17
Post Content Worksheet (PC1)
Appreciate Your Knowledge
Name of the student ______________________
Activity - Speed Drill
1. (-7) x (-5) =
2. (-8) x (10) =
3. (+2) x (-15) =
4. (0) x (-9) =
5. (-13) x (+3) =
6. (-9) x (+2 – 6) =
7. (-12) x (+7) =
8. (+30)
(-6) =
9. (-24)
(+6) =
57
Date ____________
10. (-7)
(-7) =
11. (+30) x (-2) x (-4) =
12. (+7) x (-9) x (+2) x (-2) =
13. (-24)
(-8) =
14. (+8)
(+2) =
15. (+15) x (+3) =
16. (+9 – 4 + 2) x (+1) =
17. (1 – 4 +7) x (–5 +8) =
18. (-6) x (-7 + 1) =
19. (-5) x (0) x (+2) x (+8) =
20. {(-6) x (-2)}
{(-3) x (-4)} =
58
Activity - Multi Magic
(A)
Complete the MAGIC SQUARE so that the product of the numbers in each
row,column or diagonal is –1728.
(B)
Complete this multiplication table by using positive and negative numbers.
(C) 1. Simplify and name the property used.
( – 756)
( – 131) + 756
2. Verify that a
(b+c)=(a
( – 31).
b ) + (a
where a = – 3, b = –2 and c = 5 .
Name the property verified.
59
c)
Student’s Worksheet – 18
Post Content Worksheet (PC2)
Evaluate Your Knowledge
Name of the student ______________________
Task 1: Complete the crossword.
60
Date ____________
Task 2: Match the following:_____
5x(3+8)=(5x3)+(5x8)
1) Associative Property of Multiplication
_____
0/5=0
2) Associative Property of Addition
_____
4x5=5x4
3) Commutative Property of Addition
_____
(3x5)x7=3x(5x7)
4) Identity Property of 0
_____
(6+8)+(4+6)=(4+6)+(6+8)
5) Multiplication and Division Property of 0
_____
(2+5)+5=2+(5+5)
6) Commutative Property of Addition
_____
24/1=24
7) Multiplication and Division Property of 0
_____
2x9=9x2
8) Associative Property of Multiplication
_____
0+5=5
9) Distributive Property
_____
(6x35)x4=6x(35x4)
10) Multiplication and Division Property of 0
_____
3x0=3
11) Distributive Property
_____
(8x5)-(6x5)=5x(8-6)
12) Associative Property of Multiplication
_____
48x1=48
13) Associative Property of Multiplication
_____
15-15=0
14) Identity Property of 1
_____
19+12=12+19
15) Identity Property of 0
_____
(4x10)x10=4x(10x10)
16) Commutative Property of Multiplication
_____
3x(2+7)=(3x2)+(3x7)
17) Distributive Property
_____
(5+12)+18=5+(12+18)
18) Identity Property of 1
_____
28x0=0
19) Associative Property of Addition
_____
(16x10)x10=16x(10x10)
20) Commutative Property of Multiplication
61
Acknowledgments
Websites Referred to:
1. http://www.helpingwithmath.com/resources/math_facts.htm
2. http://www.math-drills.com/integers.shtml
3. http://www.ixl.com/math/grade/seventh/
4. http://www.softschools.com/quizzes/math/multiply_integers/quiz3215.html
5. http://www.col.org/stamp/JSMath3.pdf
6. http://www.softschools.com/grades/6th_and_7th.jsp
7. http://www.homeschoolmath.net/teaching/md/distributive.php
8. http://www.discoveryeducation.com/free-worksheets/properties-of-numbermatching.fun
9. http://www.kwiznet.com
Reference Books:
1. NCERT Mathematics for class 7
62
Suggested Video Links
Name
Title/Link
Area and perimeter in real contexts.
Video Clip 1
http://www.youtube.com/watch?v=1cuN8e-y-fI
2+1 math rocks introduction to perimeter and area
Video Clip 2
http://www.youtube.com/watch?v=D5jTP-q9TgI
definition of perimeter and finding perimeter
Video Clip 3
http://www.youtube.com/watch?v=Ceqc-Q-tqkc&feature=related
Defining perimeter and calculating for irregular shapes
http://www.youtube.com/watch?v=XgDC1qb48ps&feature=channel
Introducing & Teaching Perimeter & Area Using Graph Paper
Video Clip 4
http://www.youtube.com/watch?v=K4I27chrYHc
Area of rectangle
Video Clip 5
http://www.youtube.com/watch?v=ZTQWVsJ2cxw&feature=related
Area and perimeter part 1
http://www.youtube.com/watch?v=YMdRhsdOeZI
Video introducing a Perimeter, Area and Volume Unit
Video Clip 6
http://www.youtube.com/watch?v=iBtVLnTmEYU
Area and perimeter of composite shapes
Video Clip 7
http://www.youtube.com/watch?v=97gIIl0NPBY&feature=related
http://matti.usu.edu/nlvm/nav/category_g_2_t_4.html
Weblink1
http://www6.funbrain.com/poly/index.html
Weblink 2
http://www.aaamath.com/geo78-perimeter-rectangle.html - section2
Weblink 3
63
CENTRAL BOARD OF SECONDARY EDUCATION
Shiksha Kendra, 2, Community Centre, Preet Vihar,
Delhi-110 092 India