The document discusses integers and their representation on a number line. It defines integers as the set of whole numbers and their negatives, ranging from negative infinity to positive infinity. It explains that on a number line, numbers increase as you move right and decrease as you move left. Predecessors are numbers one less, successors are numbers one more. Addition and subtraction of integers follows rules like keeping the sign of the number with the greater absolute value.

1. B.J.P.S Samiti’s
M.V.HERWADKAR ENGLISH MEDIUM HIGH SCHOOL
Integers
Program:
Semester:
Course: NAME OF THE COURSE
Sandhya S.Kulkarni 1

2. INTEGERS
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 2
Representation of integers on a number line
The sign that is used is the placement of a minus sign
attached to the number .This indicates that numbers with a
negative sign are less than zero. These are called negative
numbers

3. If a movement of only 1 is made to the left, we
get the predecessor of a number
Example: Predecessor of 0 is -1, Predecessor of +2 is +1,
Predecessor of +7 is +6, Predecessor of -7 is -8
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 3
-8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8
Predecessor

4. Successor
If a movement of only 1 is made to the right, we
get the Successor of a number
Example: Successor of 0 is +1, Successor of +1 is +2,
Successor of +6 is +7, Successor of -8 is -7
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 4
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8

5. INTEGERS
Since profit and loss are opposite situations
Profit is represented by ‘+’ sign,
Loss can be represented by ‘–’ sign
• Height 100 m below sea level is -100 m
• Temperature of 25°C above 0°C is +25°C
• Temperature of 15°C below 0°C is -15°C
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 5

6. INTEGERS
Whole numbers and the negative numbers
together, the new collection of numbers will look
like 0, 1, 2, 3, 4, 5,..., –1, – 2, – 3,–4, –5, ... and
this collection of numbers is known as Integers.
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 6

7. INTEGERS
Thus, we see that on a number line the number
increases as we move to the right and decreases
as we move to the left.
Therefore, – 3 < – 2, – 2 < – 1, – 1 < 0, 0 < 1, 1 < 2,
2 < 3 so on.
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 7

8. INTEGERS
Compare the following pairs of numbers
using > or <.
0 & -8, 5 & -5, 1 & 8, -1 & -15
Ans: 0 > -8, 5 > -5, 1< 8, -15 < -1
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 8

9. INTEGERS
Example 1 : By looking at the number line, answer the
following questions :
Which integers lie between – 8 and – 2? Which is the
largest integer and the smallest integer among them?
Solution : Integers between – 8 and – 2 are
– 7, – 6, – 5, – 4, – 3.
The integer – 3 is the largest and – 7 is the smallest.
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 9

10. INTEGERS
• Every positive integer is larger than every negative
integer.
• Zero is less than every positive integer.
• Zero is larger than every negative integer.
• Zero is neither a negative integer nor a positive
integer.
• Farther a number from zero on the right, larger is its
value.
• Farther a number from zero on the left, smaller is its
value.
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 10

11. INTEGERS
Example 1 : By referring the number line, answer the following
questions :Which integers lie between – 8 and – 2? Which is
the largest integer and the smallest integer among them?
Solution : Integers between – 8 and – 2 are – 7, – 6, – 5, – 4, – 3.
The integer
– 3 is the largest and – 7 is the smallest.
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 11

12. INTEGERS
Write the temperatures of these places in the form of
integers in the blank column. Select the Coolest place
Place Temperature
Siachin 10°C below 0°C - 10°C
Shimla 2°C below 0°C - 2°C
Ahmedabad 30°C above 0°C 30°C
Delhi 20°C above 0°C 20°C
Srinagar 5°C below 0°C - 5°C
The Coolest place is Siachin
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 12

13. INTEGERS
Write all the integers between the given pairs
(write them in the increasing order.)
(a) 0 and – 7
Ans: -7 -6 -5 -4 -3 -2 -1 0
(b) – 4 and 4
Ans: -4 -3 -2 -1 0 1 2 3 4
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 13

14. INTEGERS
Draw a number line and answer the following :
(a) Which number occurs if we move 4 numbers to the right of
-2. Ans: 2
(b) Which number will we reach if we move 5 numbers to the
left of 1. Ans: -3
(c) If we are at – 8 on the number line, in which direction
should we move to reach – 13 ? Ans: Left
(d) If we are at – 6 on the number line, in which direction
should we move to reach – 1 ? Ans: Right
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 14

15. INTEGERS
Additon of Integers
Add when there are two positive integers like (+3) + (+2) = +5
[= 3 + 2].
Add when there are two negative integers, but the answer
will take a minus (–) sign like (–2) + (–1) = – (2+1) = –3.
Numbers such as 3 and – 3, 2 and – 2, when added to each
other give the sum zero. They are called additive inverse of
each other.
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 15

16. INTEGERS
When one positive and one negative integer are added the
answer will take the sign of the bigger integer (Ignoring the
signs of the numbers decide which is bigger).
Example: Add the integers -8 and 5 i.e. -8 +5= -3
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 16

17. INTEGERS
Example : Find the sum of (– 9) + (+ 4) + (– 6) + (+ 3)
Solution : We can rearrange the numbers so that the positive
integers and the negative integers are grouped together. We
have
(– 9) + (+ 4) + (– 6) + (+ 3) = (– 9) + (– 6) + (+ 4) + (+ 3)
= (– 15) + (+ 7) = – 8
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 17

18. INTEGERS
Subtraction of integers
To subtract an integer from another integer it is enough to add
the additive inverse of the integer that is being subtracted,
to the other integer.
Example: Subtract 6 from 10.
10 – 6 = 10 + (-6) = 4 where -6 is the additive inverse of 6
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 18