Exercise 1.1 (Rational Number)
Question 1:
Using appropriate properties find:
Answer:
(i)
[Using associative property]
[Using associative property]
(II)
[Using associative property]
[Using distributive property]
Question 2:
Write the additive inverse of each of the following:
(i) 2/8
(ii) 5/9
(iii) 6/5
(iv) 2/9
(v) 19/6
Answer 2:
We know that additive inverse of a rational number
(i) Additive inverse of 2/8 is 2/8
(ii) Additive inverse of 5/9 is 5/9
(iii) Additive inverse of 6/5 is 6/5
(iv) Additive inverse of 2/9 is 2/9
(v) Additive inverse of19/6 is 19/6
Question 3:
Verify that (x)= x for:
(i)x= 11/15
(ii)x= 13/17
Answer 3:
(i) Putting x= 11/15 in (x) =x
Hence, verified.
(ii)
Hence, verified.
Question 4:
Find the multiplicative inverse of the following:
Answer 4:
We know that multiplicative inverse of a rational number
(i) Multiplicative inverse of  13 is 1/13
(ii) Multiplicative inverse of 13/19 is 19/13
(iii) Multiplicative inverse of 1/5 is 5
(iv) Multiplicative inverse of
(v) Multiplicative inverse of
(vi) Multiplicative inverse of 1 is 1/1
Question 5:
Name the property under multiplication used in each of the following:
Answer 5:
(i) 1 is the multiplicative identity.
(ii) Commutative property.
(iii) Multiplicative Inverse property.
Question 6:
Multiply 6/13 by the reciprocal of 7/16
Answer 6:
The reciprocal of 7/16 is 16/7
According to the question,
Question 7:
Tell what property allows you to compute
Answer 7:
By using associative property of multiplication, a x (b x c) = (a x b) x c.
Question 8:
Is 8/9 the multiplicative inverse of Why or why not?
Answer 8:
Since multiplicative inverse of a rational number a is
Therefore,
But its product must be positive 1.
Therefore, 8/9 is not the multiplicative inverse of
Question 9:
Is 0.3 the multiplicative inverse of Why or why not?
Answer 9:
Since multiplicative inverse of a rational number a is
Therefore,
Therefore, Yes 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 10:
(i) 0
(ii) 1 and 1
(iii) 0
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