CBSE Class 7 Mathematics Rational Numbers Assignment Set C

CBSE Assignment on Rational Numbers. Prepared by HOD Mathematics of one of the CBSE best schools in Delhi. Based on CBSE and CCE guidelines. The students should practice these assignments to gain perfection which will help him to get more marks in CBSE examination.

RATIONAL NUMBER (STANDARD FORM)

Question. Write each of the following rational numbers in the standard form:
(i) (2/10)
(ii) (-8/36)
(iii) (4/-16)
(iv) (-15/-35)
Solution:
(i) Given (2/10)
We know that HCF of 2 and 10 is 2
Now dividing the numerator and denominator by HCF i.e. 2, we get:
(2/10) ÷ (2/2) = (1/5)
Therefore (1/5) is the standard form of given number

(ii) Given (-8/36)
We know that HCF of 8 and 36 is 4
Now dividing the numerator and denominator by HCF i.e. 4, we get:
(-8/36) ÷ (4/4) = (-2/9)
Therefore (-2/9) is the standard form of given number

(iii) Given (4/-16)
Here denominator is negative so we have multiply both numerator and denominator by -1
(4/-16) × (-1/-1) = (-4/16)
We know that HCF of 4 and 16 is 4
Now dividing the numerator and denominator by HCF i.e. 4, we get:
(-4/16) ÷ (4/4) = (-1/4)
Therefore (-1/4) is the standard form of given number

(iv) Given (-15/-35)
Here denominator is negative so we have multiply both numerator and denominator by -1
(-15/-35) × (-1/-1) = (15/35)
We know that HCF of 15 and 35 is 4
Now dividing the numerator and denominator by HCF i.e. 5, we get:
(15/35) ÷ (5/5) = (3/7)
Therefore (3/7) is the standard form of given number

Question. Which of the following rational numbers are equal?
(i) (-9/12) and (8/-12)
(ii) (-16/20) and (20/-25)
Solution:
(i) Given (-9/12) and (8/-12)
The standard form of (-9/12) is (-3/4) [on diving the numerator and denominator of given number by their HCF i.e. by 3]
The standard form of (8/-12) = (-2/3) [on diving the numerator and denominator of given number by their HCF i.e. by 4]
Since, the standard forms of two rational numbers are not same. Hence, they are not equal.

(ii) Given (-16/20) and (20/-25)
Multiplying numerator and denominator of (-16/20) by the denominator of (20/-25)
i.e. -25.
(-16/20) × (-25/-25) = (400/-500)
Now multiply the numerator and denominator of (20/-25) by the denominator of
(-16/20) i.e. 20
(20/-25) × (20/20) = (400/-500)
Clearly, the numerators of the above obtained rational numbers are equal.
Hence, the given rational numbers are equal

Question. In each of the following pairs represent a pair of equivalent rational numbers, find the values of x.
(i) (2/3) and (5/x)
(ii) (-3/7) and (x/4)
Solution:
(i) Given (2/3) and (5/x)
Also given that they are equivalent rational number so (2/3) = (5/x)
x = (5 × 3)/2
x = (15/2)
(ii) Given (-3/7) and (x/4)
Also given that they are equivalent rational number so (-3/7) = (x/4)
x = (-3 × 4)/7
x = (-12/7)

Question. In each of the following, fill in the blanks so as to make the statement true:
(i) A number which can be expressed in the form p/q, where p and q are integers and q is not equal to zero, is called a ………..
(ii) If the integers p and q have no common divisor other than 1 and q is positive, then the rational number (p/q) is said to be in the ….
(iii) Two rational numbers are said to be equal, if they have the same …. form
(iv) If m is a common divisor of a and b, then (a/b) = (a ÷ m)/…..
(v) If p and q are positive Integers, then p/q is a ….. rational number and (p/-q) is a …… rational number.
(vi) The standard form of -1 is …
(vii) If (p/q) is a rational number, then q cannot be ….
(viii) Two rational numbers with different numerators are equal, if their numerators are in the same …. as their denominators.
Solution:
(i) Rational number
(ii) Standard form
(iii) Standard
(iv) b ÷ m
(v) Positive, negative
(vi) (-1/1)
(vii) Zero
(viii) Ratio

Question. In each of the following state if the statement is true (T) or false (F):
(i) The quotient of two integers is always an integer.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.
(iv) Every traction is a rational number.
(v) Every rational number is a fraction.
Solution:
(i) False
Explanation:
The quotient of two integers is not necessary to be an integer

(ii) True
Explanation:
Every integer can be expressed in the form of p/q, where q is not zero.

(iii) False
Explanation:
Every rational number is not necessary to be an integer

(iv) True
Explanation:
According to definition of rational number i.e. every integer can be expressed in the form of p/q, where q is not zero.

(v) False
Explanation:
It is not necessary that every rational number is a fraction.