1. PRESIDENCY SCHOOL
(Affiliated to the Council for the Indian School Certificate Examinations, New Delhi)
CA4, HMT Layout, RT Nagar, Bengaluru-560032
Phone: 080 – 42351159/60, 42052428
Email: presidency-rtn@presidency.edu.in
Instructions to students:
Index maintenance
Write name of the topic / chapter/ lesson neatly in the index and fill in page no
SL.No. Date Topic / Chapter
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No.
Teacher’s
Remarks
Teacher’s
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Note Making
1. Draw double margin for the heading and write the date and name of the lesson
as shown below.
2. Do not forget to number the page.
3. Draw lines after each answer and double line at the close of the Unit/lesson.
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Date :
Chapter- 3 Integers
Definition:-
Integers: - Integers are all the whole numbers and all of their opposites with
negative symbol e.g… -3, 2, 4, -1, etc
Opposite Numbers – numbers that are the same distance from zero in the
opposite direction
EXERCISE – 3 A
CLASSWORK – Q1, 2 some parts in textbook (class), Q3 (i) (ii) (iii) in notebook
2. HOMEWORK – Q1, 2 some in T.B(home) , Q3 (iv) (v) (vi)
Set of integers is denoted by I or Z.
I = {…., -4,-3,-2,-1,0,+1,+2,+3,+4 …}
Integers can be represented on a number line.
Absolute value of an integer:- The absolute value of an integer a is the numerical
value of a regardless of its sign . It is denoted by IaI , called the modulus of a .
For example ; I9I = 9 and I-9I = 9
I16I =16 I-16I = 16
COMPARISON OF INTEGERS:-
• If We represent two integers by points on a number line ,then the integer
occurring on the right is greater than that occurring on the left.
• So we observe that
• Every negative is < 0
• Every positive is > 0
• Every negative integer is < every positive integer.
Exercise – 2A –
Classwork- Q4, Q 5 in textbook , Q6 (iv) (v) (vi) , Q7 (i) (ii) , Q8 (i) (ii)(v) In notebook
Homework- Q6 (i) (ii) (iii) , Q 7 (iii) (iv), Q 8 (iii) (iv), in notebook, Q9 In Textbook.
Fundamental operations on integers.
1. Addition of integers;
Rule 1-Addition of two Positive integers. --
The sum of two positive integers is a positive integer
obtained by taking numerical values of the addends .For eg.
12 + 45 = 57
Rule 2- Addition of two Negative integers
The sum of two negative integers is a negative integer are obtained by taking the
sum of the numerical values of the addends .
For eg . (-4) + (-9) = -(4+9) = -13
(−16)+ ( − 17)= −(16 + 17)= − 33
Rule 3- Addition of a Positive and a Negative integer ---
3. For adding a positive and a negative integer, we find the difference between their
numerical values and result will be given the sign of the integer with the
greater numerical value.
For eg. (-23)+ 50 = 27
(-100 ) + 68 = -32
36 + ( -60 ) = -24
3. Successor of an Integer --- The successor of an integer is 1 more than the
integer, so the successor of a is (a + 1) eg... -3 + 1 = -2 and 3 + 1 =4
4. Predecessor of an Integer -- The predecessor of an integer is 1 less than the
integer, so the predecessor of a is (a-1) eg.... 4-1 = 3 and –7-1 = -8
EXERCISE- 3B
CLASSWORK – Q1(v) to (ix) ,Q2 In textbook, Q3(i) (ii) , Q4(i) (ii)
HOMEWORK – Q1(i) to (iv) , Q3(iii) (iv) (v) , Q4(iii) (iv) (v)
Additive inverse
For every integer a, there exist an integer (-a) , such that
a + (-a) = 0 = (-a) +a , Where (-a) and a are additive
Inverse of each other. Every integer has its additive inverse.
2. Subtraction of Integers –
For two integers a and b, a – b = a + (-b) where a + (additive inverse of b )
OR a - (-b) a + ( additive inverse of –b ) = (a + b) Hence a - (-b) = (a + b) .
For eg. 9 – 3 = 9 + (-3) = 6 ,10 - (-5) = 10 + 5 = 15
(-11) - (-6) = (-11) + 6 = - 5, (-12 ) -8 = -12 + (-8) = -20
EXERCISE- 3B
CLASSWORK – Q5(v) to (ix), Q6(i) (ii)(ii),
HOMEWORK – Q 5(i) to (iv), Q6(iv)(v) (vi), Q7 in textbook
