11.
What will be the sign of the product a x b if
i) a is the product of 5 positive integers and b is the product of 9
negative integers.
ii) a is the product of 6 positive integers and b is the product of 8
negative integers.
iii) a is positive and be is the product of 50 negative integers.
Answers
Step-by-step explanation:
Given:-
i) a is the product of 5 positive integers and b is the product of 9 negative integers.
ii) a is the product of 6 positive integers and b is the product of 8 negative integers.
iii) a is positive and be is the product of 50 negative integers.
To find:-
What will be the sign of the product a x b ?
Solution:-
i) Given that
a = the product of 5 positive integers
a = positive integer
(since (+) quantity×(+) quantity= (+) quantity)
b = the product of 9 negative integers.
b = negative integer
(since if the number of negative numbers is odd then the product will be negative)
Now ,
a×b = positive integer× negative integer
a×b = negative integer.
ii) Given that
a = the product of 6 positive integers
a = positive integer
(since (+) quantity×(+) quantity= (+) quantity)
b = the product of 8 negative integers.
b = positive integer
(since if the number of negative numbers is even then the product will be positive)
Now ,
a×b = positive integer× positive integer
a×b = positive integer
iii) Given that
a = positive integer
b= the product of 50 negative integers.
b = positive integer
(since if the number of negative numbers is even then the product will be positive)
Now ,
a×b = positive integer× positive integer
a×b = positive integer
Answer:-
i)a×b is a negative integer.
ii)a×b is a positive integer
iii)a×b is a positive integer
Used formulae:-
- (+) quantity×(+) quantity= (+) quantity
- (+) quantity×(-) quantity= (-) quantity
- (-) quantity×(+) quantity= (-) quantity
- (-) quantity×(-) quantity= (+) quantity
- the number of negative numbers is even then the product will be positive.
- if the number of negative numbers is even then the product will be positive.