Page 6 - SM inner class 7.cdr

= + (16 + 13 ) |+ 13 |=13 For Ex am ple:
-
= + 29 or 29 (i) (+ 5 ) (+ 4 )
(
(
4
(
(
4
5
4
(ii) (-16 ) + (-13 ) Q |-16 |=16 = + ) + - ) Q - + ) = + - )
5
4
4
= + (5 - ) Q | |= 5 ,| |= 4
+
-
= - (16 + 13 ) |-13 |=13
= + 1 or 1
= - 29
We can show the solution on number line also :
Rule 2 : In te gers with un like signs : +5
–4
Two integers with unlike signs are added in the
following three steps.
–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5
(a) Take absolute values of given integers.
-
(ii) (+ 5 ) (-4 )
(b) Subtract the smaller absolute value from the = + ) + + ) Q - - ) = + + )
(
4
(
4
(
(
4
5
larger.
+
= (5 + ) Q | |= 5 + 4
4
5
,| |= 4
(c) Give the sign of the integer with the larger = + 9 or 9
absolute value to the result.
5 +4
Ex am ple 4 : Add the fol low ing :
(i) (+ 9 ) + (-4 ) (ii) (-9 ) + (+ 4 ) –1 0 +1 –2 +3 +4 +5 +6 +7 +8 +9 +10
(iii) (-16 ) + (+ 13 )
Multiplication of Integers
So lu tion : We know that multiplication is an operation of
+
9
(i) (+ 9 ) + (-4 ) Q | |= 9 repeated addition or we can say that
-
4
4
= + (9 - ) | |= 4 multiplication is a short method of adding the
same numbers.
= + 5 or 5
For Ex am ple :
9
(ii) (-9 ) + (+4 ) Q | |= 9
+
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 8 ´ 2 16
=
4
= -(9 - ) | |= 4
+
4
The rules for multiplication of integers are
= -5
given below:
(iii) (-16 ) + (+ 13 ) Q |-16 |=16
Rule 1 : In te gers with like signs :
-
= -(16 13 ) |+13 |=13
The product of two integers having same signs is
= -3 always positive.
Ex am ple 5 : Sim plify the fol low ing : For ex am ple:
+
6
[(-4 ) + (+ 6 )] (-9 ) Q | |= 6 (i) (+ 2 ) ´ (+ 3 ) = + 6
+
So lu tion : First solve brack ets. | |-4 = 4 (ii) (-2 ) ´ (-3 ) = + 6
4
9
[
(
= + (6 - )] + - )
Rule 2 : In te gers with un like signs :
= + ) + - ) Q | |= 2
+
(
2
(
2
9
The product of two integers having opposite signs is
2
9
= -(9 - ) = -7 | |= 9
-
always negative.
which is the required answer.
For ex am ple:
Subtraction of Integers : (i) (+ 1 ) ´ (-2 ) = (-2 )
To subtract integers, we use the following (ii) (- ´ (+ 2 ) = (-2 )
1
)
rules.
Rule 1 : Change the sign of the integer which is
be ing sub tract. Ex am ple 6 : Find the prod uct of the fol low ing
pairs.
Rule 2 : Add them ac cord ing to the ad di tion rules of
in te gers (i) + 13, + 9 (ii) -11, + 11
(iii) -8, -7 (iv) + 25, -6
6
Mathematics In Focus - 7