CBSE Class 7 Mathematics Rational Numbers Assignment Set 03

Question. \( \frac{-3}{5} - \left( -\frac{2}{15} \right) \) is
(a) \( \frac{1}{15} \)
(b) \( \frac{15}{7} \)
(c) \( -\frac{15}{7} \)
(d) \( \frac{-7}{15} \)
Answer: (d) \( \frac{-7}{15} \)

Question. The negative of \( \frac{4}{-15} \) is
(a) \( \frac{-4}{-15} \)
(b) \( \frac{-15}{4} \)
(c) \( \frac{-4}{15} \)
(d) \( \frac{4}{15} \)
Answer: (d) \( \frac{4}{15} \)

Question. \( \frac{-15}{39} \div \frac{5}{13} \) is
(a) \( 1 \)
(b) \( -1 \)
(c) \( 2 \)
(d) \( -2 \)
Answer: (b) \( -1 \)

Question. \( -2\frac{1}{13} \div 2\frac{11}{13} \) is
(a) \( -\frac{27}{37} \)
(b) \( \frac{27}{37} \)
(c) \( \frac{37}{27} \)
(d) \( -\frac{37}{27} \)
Answer: (a) \( -\frac{27}{37} \)

Question. \( \frac{-3}{7} \times \frac{-2}{3} \div \frac{16}{-21} \) is
(a) \( \frac{3}{8} \)
(b) \( \frac{-3}{8} \)
(c) \( \frac{-32}{147} \)
(d) \( \frac{-8}{49} \)
Answer: (b) \( \frac{-3}{8} \)

Question. The product of two numbers is \( \frac{3}{4} \). If one of them is \( \frac{5}{6} \), the other no. is
(a) \( \frac{10}{9} \)
(b) \( \frac{9}{10} \)
(c) \( \frac{7}{9} \)
(d) \( \frac{9}{7} \)
Answer: (b) \( \frac{9}{10} \)

Question. \( \frac{3}{4} - \frac{1}{2} + \frac{5}{6} \) is
(a) \( \frac{11}{12} \)
(b) \( \frac{13}{12} \)
(c) \( \frac{-11}{12} \)
(d) \( \frac{-13}{12} \)
Answer: (b) \( \frac{13}{12} \)

Question. The reciprocal of \( -1 \) is
(a) \( 1 \)
(b) \( -1 \)
(c) \( \frac{1}{-1} \)
(d) None of the options
Answer: (b) \( -1 \)

Question. The multiplicative inverse of \( -\frac{3}{4} \) is
(a) \( \frac{3}{4} \)
(b) \( -\frac{3}{4} \)
(c) \( \frac{4}{-3} \)
(d) \( \frac{4}{3} \)
Answer: (c) \( \frac{4}{-3} \)

Question. If a number is multiplied by \( \left(-\frac{5}{6}\right) \), the result is \( 1 \), the number is
(a) \( \frac{6}{-5} \)
(b) \( \frac{-6}{-5} \)
(c) \( \frac{5}{6} \)
(d) \( -\frac{5}{6} \)
Answer: (a) \( \frac{6}{-5} \)

Question. The sign of \( '0' \) is
(a) Positive
(b) Negative
(c) neither positive nor negative
(d) None of the options
Answer: (c) neither positive nor negative

Question. Arun walks \( \frac{1}{3}\text{ km} \) from a place A towards East and then from there \( 1\frac{2}{3}\text{ km} \) towards west. Where will he be now from A.
(a) \( \frac{4}{3}\text{ km} \)
(b) \( -2\text{ km} \)
(c) \( -\frac{4}{3}\text{ km} \)
(d) \( \frac{4}{3}\text{ km} \)
Answer: (c) \( -\frac{4}{3}\text{ km} \)

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.