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A Rational Number can be written in several equivalent forms. The Questions are framed by subject experts cover whether given rational numbers are equal or not, equality of rational numbers using the standard form, cross multiplication, common denominator, etc.
1. If each of the following pairs represents a pair of equivalent rational numbers, find the values of x.
(i) 3/5 and 6/x
(ii) -5/4 and x/3
(iii) 8/7 and x/-2
Solution:
(i) 3/5 and 6/x
Since they are equivalent rational numbers
3/5 = 6/x
Cross multiplying them to obtain the value of x we have
3x=30
x= 10
(ii) -5/4 and x/3
Since they are equivalent rational numbers
-5/4=x/3
Cross multiplying them to obtain the value of x we have
4x= -15
x = -15/4
(iii) 8/7 and x/-2
Since they are equivalent rational numbers
8/7 = x/-2
Cross multiplying them to obtain the value of x we have
7x= -16
x= -16/7
2. A Number which can be expressed in the form of p/q where p, q are integers and q is not equal to 0 is called …….
Solution:
Rational Number.
3. Two Rational are said to be equal if they have the same ……. Form
Solution:
Standard Form
4. Standard Form of -2 is ……..
Solution:
Standard Form is -2/1 and the Rational Number doesn’t have any common factors other than 1.
5. Which of the following Rational Numbers are Equal?
(i) -15/27 and 6/-18
(ii) -18/24 and 15/-20
(iii) -8/32 and 24/-96
(iv) -6/-18 and 11/19
Solution:
(iii) -8/24 and 24/-96
The Given Set of Rational Numbers are Equal as they have the same standard form
-8/32 = -1/4
24/-96 = 1/-4 = -1/4
6. Is the Statement True or False
Two Rational Numbers with Different Numerators cannot be Equal.
Solution:
False
7. Are the Rational Numbers -7/3 and -5/3 equal?
Solution:
No, the Rational Numbers -7/3 and -5/3 are not equal. They might have a common denominator but the numerators are not equal.
8. Determine whether the Rational Numbers 3/-9 and -15/45 are equal or not using a standard form?
Solution:
Standard Form of 3/-9 = 1/-3 = -1/3
Standard Form of -15/45 = -1/3
Since the Standard Forms of both the Rational Numbers 3/-9 and -15/45 are Equal the given Rational Numbers are Equal.