Example Problems Based on Operation of Rational Numbers :
Here we are going to see some example problems on operations of rational numbers.
Question 1 :
Fill in the blanks
(i) The multiplicative inverse of 2 3/5 is _______
For any non-zero rational number b there exists a unique rational number 1/b such that b x (1/b) = 1 = (1/b) × b (Multiplicative Inverse property).
First let us convert the mixed fraction into improper fraction.
2 3/5 = (10 + 3)/5 = 13/5
The multiplicative inverse of 13/5 is 5/13.
Question 2 :
If −3 ⋅ (6/-11) = (6/-11) ⋅ x, then x is ________.
In order to get same answer for both left hand side and right hand side, we have to remember the commutative law.
a x b = b x a
Hence the value of x is -3.
Question 3 :
If distributive property is true for
then x, y, z are ________ , ________ and ________.
= (3/5) (y + z)
= (3/5) ⋅ y + (3/5) ⋅ z ------(1)
(3/5) ⋅ (-4/9) + (x ⋅ (15/17)) ------(2)
(1) = (2)
(3/5) ⋅ (-4/9) + (x ⋅ (15/17)) = (3/5) ⋅ y + (3/5) ⋅ z
x = 3/5, y = -4/9 and z = 15/17
(iv) If x ⋅ (-55/63) = (-55/63) ⋅ x = 1, then x is called the _________________ of 55/63 .
Since the product of x and -55/63 is 1, we say that x is the multiplicative inverse of -55/63.
Hence the value of x is -63/55.
(v) The multiplicative inverse of -1 is ________.
The multiplicative inverse of -1 is -1.
Question 2 :
Say True or False:
(i) (−7/8) × (−23/27) = (−23/27) × (−7/8) illustrates the closure property of rational numbers.
The given statement exactly matches with the general form
a x b = b x a
It means commutative property not closure.
Hence the answer is False.
(ii) Associative property is not true for subtraction of rational numbers.
(a - b) - c = a - (b - c)
If associative property is true, then it satisfies the above statement.
Let a = 1/2, b = 1/3 and c = 5/6
(a - b) - c = [(1/2) - (1/3)] - 5/6
= (1/6) - (5/6)
= -2/3 -----(1)
a - (b - c) = (1/2) - [(1/3)- 5/6]
= (1/2) - (-3/6)
= (3 + 3)/6
= 1 -----(2)
Hence the answer is True.
(iii) The additive inverse of −11/(-17) is 11/17.
The answer is false.
By simplifying 11/17 and 11/17, we will not get 0.
(iv) The product of two negative rational numbers is a positive rational number
The answer is True. Because negative times negative is positive.
(v) The multiplicative inverse exists for all rational numbers.
For the rational number 0 there is no multiplicative inverse. Hence the answer is false.
After having gone through the stuff given above, we hope that the students would have understood, "Example Problems Based on Operation of Rational Numbers"
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