Using appropriate properties find.
Write the additive inverse of each of the following:
Verify that – (-x) = x for:
Find the multiplicative inverse of the following:
Name the property under multiplication used in each of the following:
(i) Existence of multiplicative identity.
(ii) Commutative property of multiplication.
(iii) Existence of multiplicative inverse.
Multiply by the reciprocal of .
Tell what property allows you to compute.
Associative property of multiplication over rational numbers allows us to compute :
Is the multiplicative inverse of – 1 ? Why or why not?
No, is not the multiplicative inverse of -1 .
Is 0.3 the multiplicative inverse of 3? Why or why not?
Yes, 0.3 is multiplicative inverse of 3.
(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.
(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.
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 ………..
(ii) 1, -1,
(v) rational number,