Rational Numbers
Question 1.
Using appropriate properties find.
Solution:
Question 2.
Write the additive inverse of each of the following:
Solution:
Question 3.
Verify that – (-x) = x for:
(i)
(ii) .
Solution:
Question 4.
Find the multiplicative inverse of the following:
Solution:
Question 5.
Name the property under multiplication used in each of the following:
Solution:
(i) Existence of multiplicative identity.
(ii) Commutative property of multiplication.
(iii) Existence of multiplicative inverse.
Question 6.
Multiply by the reciprocal of
.
Solution:
Question 7.
Tell what property allows you to compute.
Solution:
Associative property of multiplication over rational numbers allows us to compute :
Question 8.
Is the multiplicative inverse of – 1
? Why or why not?
Solution:
No, is not the multiplicative inverse of -1
.
Because .
Question 9.
Is 0.3 the multiplicative inverse of 3? Why or why not?
Solution:
Yes, 0.3 is multiplicative inverse of 3.
Because .
Question 10.
Write:
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Solution:
(i) We know that there is no rational number which when multiplied with 0, gives 1. Therefore, the rational number 0 has no reciprocal.
(ii) We know that the reciprocal of 1 is 1 and the reciprocal of -1 is -1. 1 and -1 are the only rational numbers which are their own reciprocals.
(iii) The rational number 0 is equal to its negative.
Question 11.
Fill in the blanks :
(i) Zero has ……………. reciprocal.
(ii) The numbers ……………. and ………. are their own reciprocals.
(iii) The reciprocal of – 5 is …………….
(iv) Reciprocal of , where ≠0 is ………
(v) The product of two rational numbers is always a ………….
(vi) The reciprocal of a positive rational number is ………..
Solution:
(i) No,
(ii) 1, -1,
(iii)
(iv) x,
(v) rational number,
(vi) positive.