Question 1:
Using appropriate properties find:
(i)
(ii)
Answer:
(i)
(ii)
(By commutativity)
Question 2:
Write the additive inverse of each of the following:
(i) (ii) (iii) (iv) (v)
Answer:
(i)
Additive inverse =
(ii)
Additive inverse =
(iii)
Additive inverse =
(iv)
Additive inverse
(v)
Additive inverse
Question 3:
Verify that −(−x) = x for.
(i) (ii)
Answer:
(i)
The additive inverse of is as
This equality represents that the additive inverse of is or it can be said that i.e., −(−x) = x
(ii)
The additive inverse of is as
This equality represents that the additive inverse of is − i.e., −(−x) = x
Question 4:
Find the multiplicative inverse of the following.
(i) (ii) (iii)
(iv) (v) (vi) −1
Answer:
(i) −13
Multiplicative inverse = −
(ii)
Multiplicative inverse =
(iii)
Multiplicative inverse = 5
(iv)
Multiplicative inverse
(v)
Multiplicative inverse
(vi) −1
Multiplicative inverse = −1
Question 5:
Name the property under multiplication used in each of the following:
(i)
(ii)
(iii)
Answer:
(i)
1 is the multiplicative identity.
(ii) Commutativity
(iii) Multiplicative inverse
Question 6:
Multiply by the reciprocal of .
Answer:
Question 7:
Tell what property allows you to compute .
Answer:
Associativity
Question 8:
Is the multiplicative inverse of ? Why or why not?
Answer:
If it is the multiplicative inverse, then the product should be 1.
However, here, the product is not 1 as
Question 9:
Is 0.3 the multiplicative inverse of ? Why or why not?
Answer:
0.3 × = 0.3 ×
Here, the product is 1. Hence, 0.3 is the multiplicative inverse of .
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.
Answer:
(i) 0 is a rational number but its reciprocal is not defined.
(ii) 1 and −1 are the rational numbers that are equal to their reciprocals.
(iii) 0 is the rational number that 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 is __________.
(v) The product of two rational numbers is always a __________.
(vi) The reciprocal of a positive rational number is __________.
Answer:
(i) No
(ii) 1, −1
(iii)
(iv) x
(v) Rational number
(vi) Positive rational number