Page 5 - SM inner class 7.cdr

+ 4 % 1 ¼ 3 ÷ ¾
×
Chapter1 6 ½ –

Integers

Introduction [ Q 0 lies to the left of 1 on a number line]
(ii) -10 > -15
We have learnt about some basics of integers
in previous class. We know that integers form [Q-10 lies to the right of -15 on the number line]
a bigger collection of numbers which contains (iii) -100 10, , -100 10
<
whole numbers and negative numbers. Let us [ Q -100 lies to the left of 10 on the number line]
revise and learn more about integers.
In te gers are like whole numbers, but Absolute or Numerical Value of
they also in clude neg a tive num bers ... but still an Integer
no frac tions al lowed! Numerical or absolute value of a directed
So, integers can be negative {-1, -2, -3, -4, number is a distance from zero to that
-5,K }, positive {1, 2, 3, 4, 5, …}, or zero {0} number on the number line.
We can put that all together like this : We can say that the numerical or absolute
Integers = {…, -5, -4, -3, -2, -1, 0,1, 2, 3, 4, 5, value of 3 and –3 is the same because the
…} distance from 0 to 3 and 0 to -3 is same i e. .
For Ex am ple, these are all in te gers : absolute value gives us only distance but not
direction.
,
-16, -3 0 1 198
,
,
We can write it as :
(But numbers like 1/2, 1.1 and 3.5 are not
in te gers) Absolute value of | |+ =3 3
Integers are also known as di rected Absolute value of | |- =3 3
num bers because these numbers represent Ex am ple 2 : Find the nu mer i cal val ues of the
both the direction, as well as the fol low ing in te gers.
mea sure ment. (i) -4 (ii) 22 (iii) -9
Ordering of Integers So lu tion :

(i) | |-4 = - (-4 ) = 4 Numerical value of -4 is 4.
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 (ii) | |22 = 22 Numerical value of 22 is 22
We can observe that on the number line, the (iii) | |- 9 = - (-9 ) = 9 Numerical value of -9 is 9.
integer that lies to the left of another integer is
always smaller and the integer lies to the right Addition of Integers
of the same integer is always greater.
Rule 1 : In te gers with like signs :
For ex am ple, Zero lies to the left of all
Two integers with like signs are added in the
pos i tive in te gers on the num ber line. So, 0 <1 , following three steps.
2 , 3 ........ and the in te ger 0 lies to the right of
all neg a tive in te gers. So, 0 > –1, –2, –3, …… or (a) Take absolute values of given integers.
we can write the above state ments as: ……, (b) Add the absolute values.
3
- < - < - < 0 < + < + 2 < + 3, ……¥ (c) Give the common sign to the result.
1
1
2
Ex am ple 1 : Put the ap pro pri ate sign > or <
be tween the given pairs. Ex am ple 3. Solve the fol low ing :.
(i) (+ 16 ) + (+ 13 ) (ii) (-16 ) + (-13 )
(i) 0, 1 (ii) -10, -15 (iii) -100 10,
So lu tion :
So lu tion :
(i) (+ 16 ) + (+ 13 ) Q |+ 16 |=16
(i) 0 < 1
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Mathematics In Focus - 7