Page 24 - Math_Genius_V1.0_C8_Flipbook
P. 24
E:\Working\Focus_Learning\Math_Genius-8\Open_Files\01_Chapter_1\Chapter_1
\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________
6. Verify that x – y ≠ y – x, for each of the following.
−4 2 2 −1
(a) x = , y = (b) x = , y =
5 5 9 5
7. Verify that x – (y – z) ≠ (x – y) – z, for each of the following.
−4 2 2 2 −1 8
(a) x = , y = , z = (b) x = , y = , z =
5 5 7 9 5 9
Multiplication of Rational Numbers
Multiplication of rational numbers is same as multiplication of fractions. For their sign convention,
we must recall the sign convention as used in the multiplication of integers.
To multiply two rational numbers, we multiply the numerators to get the new numerator and
multiply the denominators to get the new denominator.
In general,
p r p r pr
×
if and are two rational numbers, then × = .
q s q s qs
×
Example 17: Find the product of:
3 − 3 −2 5 Think and Answer
(a) × (b) ×
7 5 9 −12 The Ganga River flows through hills
2 1 and plains during its 2,525 km long journey. If the
(c) −3 × 1
3 4 river flows about 1 of the journey through the
3 − 3 3 ×− ( 3) − 9 10
Solution: (a) × = = Himalayan valley, find the length of the river in plains.
7 5 7 × 5 35
−2 5 ( −2) × 5 1 × 5 5
(b) × = = =
9 −12 9 ×− ( 12 ) 9 × 6 54
2 1 −11 5 ( −11) × 5
(c) −3 × 1 = × =
3 4 3 4 3 × 4
−55 7
= =− 4
12 12
Properties of Multiplication of Rational Numbers
Closure Property
Let us multiply a few pairs of rational numbers.
5 × 3 = 15 (a rational number), −3 × 3 = −9 (a rational number), −7 ×= 0 (a rational number).
0
7 4 28 7 4 28 6
From the above examples, we observe that multiplying two rational numbers always results
in another rational number. This illustrates the closure property of multiplication for rational
numbers. Hence, the rational numbers holds the closure property for the multiplication. In other
words, rational numbers are closed under multiplication.
In general,
×
p r pr
if and are two rational numbers, then is also a rational number.
q s qs
×
Mathematics-8 22
