Page 13 - SM inner class 8.cdr

For example: 2 æ4 3 ö 2 4 2 3
LHS = ´ ç + ÷ RHS = ´ + ´
3 1 ø 3 9 3 5
For three rational numbers , 5 and , we have 3 è 9 5
4 2
3 æ 1ö æ 3 ö 1 = 2 æ20 + 27 ö = 8 + 2
¸ ç 5 ¸ ÷ ¹ ç ¸ 5÷ ¸ ´ ç ÷ ø 27 5
è
4 è 2ø è 4 ø 2 3 45
3 æ 1 ö æ3 ö 1
LHS = ¸ ç5 ¸ ÷ RHS = ç ¸ ÷ ¸ = 2 ´ 47 = 94 = 40 + 54 = 94
5
4 è 2 ø è4 ø 2 3 45 135 135 135
3 æ5 2 ö æ3 1 ö 1
= ¸ ç ´ ÷ = ç ´ ÷ ¸
4 è1 1 ø è4 5 ø 2 \ LHS = RHS
3 3 1 \ Multiplication is distributive over addition.
= ¸10 = ¸
4 20 2
3 1 3 2 2. Distributive property of multiplica-
= ´ = ´ tion over subtraction
4 10 20 1
3 3 Multiplication of rational numbers is
= =
40 10 distributive over subtraction.
\ LHS ¹ RHS a c e
If , and are any three rational numbers,
\ Associative property is not true for division. b d f
a æ c eö a c a e
Property of 1 then ´ ç - ÷ = ´ - ´ .
b è d f ø b d b f
For every rational number a/b we have: 3 4 1
For three rational numbers , and , we
(a/b ÷ 1) = a/b 7 5 2
have
For example:
3 æ 4 1ö 3 4 3 1
5 5 ´ ç - ÷ = ´ - ´
(i) ¸ 1 = 7 è 5 2ø 7 5 7 2
8 8
3 æ4 1 ö 3 4 3 1
-4 -4 LHS = ´ ç - ÷ RHS = ´ - ´
(ii) ¸ = 7 è 5 2 ø 7 5 7 2
1
9 9
5
3 æ8 - ö 12 3
5 5 = ´ ç ÷ = -
(iii) ¸ 1 = 7 è 10 ø 35 14
- 2 - 2
3 3 9 24 -15 9
= ´ = = =
Distributive Property 7 10 70 70 70
\ LHS = RHS
1. Distributive property of multiplica-
\ Multiplication is distributive over subtraction.
tion over addition
Multiplication of rational numbers is Absolute Value of a Rational Number
distributive over addition. Recall the absolute value of - = -4 | 4| = 4
a c e Absolute value of 4 =| |4 = 4
If , and are any three rational numbers,
b d f Absolute value of 0 =| |0 = 0
a æ c eö a c a e The absolute value of a rational number is
then ´ ç + ÷ = ´ + ´ .
b è d f ø b d b f also given by the same rule.

2 4 3 For example:
For three rational numbers , and , we -3 -3 3
3 9 5 Absolute value of = =
have 4 4 4
2 æ 4 3ö 2 4 2 3 2 2 2
´ ç + ÷ = ´ + ´ Absolute value of = =
3 è 9 5ø 3 9 3 5 3 3 3

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Mathematics In Focus - 8