Page 44 - SM inner class 7.cdr
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m Division is an inverse operation of multiplication. So, for any two rational numbers
p r p r p s ps
, ¸ = ´ =
q s q s q r qr
0 is called additive identity and 1 is called multiplicative identity.
q p
m is called the reciprocal of
p q
p r
m If , are two rational numbers, then according to the commutative property:
q s
p r r p p r r p
+ = + ´ = ´
q s s q q s s q
p r t
m If , and are three rational numbers, then according to the associative property
q s u
æ p r ö t p r æ t ö æ p r ö t p r æ t ö
ç + ÷ + = + ç + ÷ ç ´ ÷ ´ = ´ ç ´ ÷
è q sø u q s è u ø è q sø u q s è u ø
p r t
m Now again consider the three rational numbers , and then according to the distributive property,
q s u
p r é t ù é p rù é p t ù
(i) ´ + = ê ´ ú + ê ´ ú
q ê s ë uû ú ë q s û ë q u û
p r é t ù é p rù é p t ù
(ii) ´ - = ê ´ ú - ê ´ ú
q ê s ë uû ú ë q s û ë q u û
m We can compare and arrange the rational numbers in ascending and descending order.
m We can find count less rational numbers between any two rational numbers.
Review Exercise
1. An swer the fol low ing ques tions.
(a) Define a rational number.
(b) Write the additive inverse of the rational numbers “a”.
p
q
(c) What is the reciprocal of the rational number ( ¹0 )?
q
p r
(d) Write the sum of two rational numbers and ( ,q r ¹0 )?
q s
(e) What is the rule to find the product of two rational numbers?
(f) What are the inverse operations of addition and multiplication?
2. Fill in the blanks.
(a) The________ consists of fractions as well as integers.
p -p
(b) The rational numbers and are called____ inverse of each other.
q q
p
(c) A number that can be expressed in the form of where p and q are integers and q 0 is called
q
the________ number.
(d) 0 is called additive identity whereas 1 is called ________ identity.
(e) The rational number 0 has no ________ .
(f) The ________ inverse of a rational number is its reciprocal.
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Mathematics In Focus - 7