Rd Sharma (2014) Solutions for Class 7 Math Chapter 4 Rational Numbers are provided here with simple step-by-step explanations. These solutions for Rational Numbers are extremely popular among Class 7 students for Math Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma (2014) Book of Class 7 Math Chapter 4 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma (2014) Solutions. All Rd Sharma (2014) Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

#### Question 1:

Determine whether the following rational numbers are in the lowest form or not:

(i) $\frac{65}{84}$
(ii) $\frac{-15}{32}$
(iii) $\frac{24}{128}$
(iv) $\frac{-56}{-32}$

(i) We observe that 65 and 84 have no common factor i..e., their HCF is 1.

Thus, $\frac{65}{84}$ is in its lowest form.

(ii) We observe that $-$15 and 32 have no common factor i..e., their HCF is 1.

Thus, $\frac{-15}{32}$is  in  its lowest form.

(iii) HCF of 24 and 128 is not 1.

Thus, given rational number is not in its simplest form.

(iv) HCF of 56 and 32 is 8.

Thus, given rational number is not in its simplest form.

#### Question 2:

Express each of the following rational numbers to the lowest form:
(i) $\frac{4}{22}$
(ii) $\frac{-36}{180}$
(iii) $\frac{132}{-428}$
(iv) $\frac{-32}{-56}$

Lowest form of:

#### Question 3:

Fill in the blanks:
(i) $\frac{-5}{7}=\frac{\dots }{35}=\frac{\dots }{49}$
(ii)
(iii)
(iv)

#### Question 1:

Write each of the following rational numbers in the standard form:
(i) $\frac{2}{10}$
(ii) $\frac{-8}{36}$
(iii) $\frac{4}{-16}$
(iv) $\frac{-15}{-35}$
(v) $\frac{299}{-161}$
(vi) $\frac{-63}{-210}$
(vii) $\frac{68}{-119}$
(viii) $\frac{-195}{275}$

(i) The denominator is positive and HCF of 2 and 10 is 2.

$\therefore$ Dividing the numerator and denominator by 2, we get:

(ii) The denominator is positive and HCF of 8 and 36 is 4.

$\therefore$ Dividing the numerator and denominator by 4, we get:

(iii)

The denominator is negative.

HCF of 4 and 16 is 4.

$\therefore$ Dividing the numerator and denominator by 4, we get:

(iv) The denominator is negative.

HCF of 15 and 35 is 5.

$\therefore$ Dividing the numerator and denominator by 5, we get:

(v) The denominator is negative.

HCF of 299 and 161 is 23.

$\therefore$ Dividing the numerator and denominator by 23, we get:

(vi) The denominator is negative.

HCF of 63 and 210 is 21.

$\therefore$ Dividing the numerator and denominator by 21, we get:

(vii) The denominator is negative.

HCF of 68 and 119 is 17.

$\therefore$ Dividing the numerator and denominator by 17, we get:

(viii) The denominator is positive and HCF of 195 and 275 is 5.

$\therefore$ Dividing divide the numerator and denominator by 5, we get:

#### Question 1:

Which of the following rational numbers are equal?
(i)
(ii)
(iii)
(iv)

(i)

(ii)

(iii)

(iv)

#### Question 2:

If each of the following pairs represents a pair of equivalent rational numbers, find the values of x:
(i)
(ii)
(iii)
(iv)

(i)
(ii)
(iii)
(iv)

#### Question 3:

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 $\frac{p}{q}$, 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 $\frac{p}{q}$ is said to be in the ....
(iii) Two rational numbers are said to be equal, if they have the same .... form.

$\frac{a}{b}=\frac{a÷m}{....}$
(v) If p and q are positive integers, then $\frac{p}{q}$ is a ..... rational number and $\frac{p}{-q}$ is a ..... rational number.

(vi) The standard form of −1 is ...

(vii) If $\frac{p}{q}$ 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.

(i) rational number
(ii) standard rational number
(iii) standard form
(iv) $\frac{a}{b}=\frac{a÷m}{b÷m}$
(v) positive rational number, negative rational number
(vi) $\frac{-1}{1}$
(vii) zero
(viii) ratio

#### Question 4:

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 fraction is a rational number.
(v) Every rational number is a fraction
(vi) If $\frac{a}{b}$ is a rational number and m any integer, then $\frac{a}{b}=\frac{a×m}{b×m}$
(vii) Two rational numbers with different numerators cannot be equal.
(viii) 8 can be written as a rational number with any integer as denominator.
(ix) 8 can be written as a rational number with any integer as numerator.
(x)

(i) False; not necessary
(ii) True; every integer can be expressed in the form of p/q, where q is not zero.
(iii) False; not necessary
(iv) True; every fraction can be expressed in the form of p/q, where q is not zero.
(v) False; not necessary
(vi) True
(vii) False; they can be equal, when simplified further.
(viii) False
(ix) False
(x) True; in the standard form, they are equal.

#### Question 1:

Draw the number line and represent the following rational numbers on it:
(i) $\frac{2}{3}$
(ii) $\frac{3}{4}$
(iii) $\frac{3}{8}$
(vi) $\frac{-5}{8}$
(v) $\frac{-3}{16}$
(vi) $\frac{-7}{3}$
(vii) $\frac{22}{-7}$
(viii) $\frac{-31}{3}$

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

#### Question 2:

Which of the two rational numbers in each of the following pairs of rational numbers is greater?
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)

(i) We know that every positive rational number is greater than zero and every negative rational number is smaller than zero. Thus,

$\frac{-3}{8}>0$
(ii) $\frac{5}{2}>0.$ Because every positive rational number is greater than zero and every negative rational number is smaller than zero.
(iii) $\frac{-4}{8}<\frac{3}{11}.$ Because every positive rational number is greater than zero and every negative rational number is smaller than zero.
(iv)

(v)

(vi)

(vii)

(viii)

#### Question 3:

Which of the two rational numbers in each of the following pairs of rational numbers is smaller?
(i)
(ii)
(iii)
(iv)

(i) $\frac{-6}{-13}=\frac{6}{13}<\frac{7}{13}$
(ii) $\frac{16}{-5}<3$
(iii)

(iv)

#### Question 4:

Fill in the blanks by the correct symbol out of >, =, or <:
(i) $\frac{-6}{7}.....\frac{7}{13}$
(ii) $\frac{-3}{5}.....\frac{-5}{6}$
(iii) $\frac{-2}{3}.....\frac{5}{-8}$
(iv)

#### Question 5:

Arrange the following rational numbers in ascending order:
(i)
(ii)

(i) Ascending order:

(ii)

#### Question 6:

Arrange the following rational numbers in descending order:
(i)
(ii)

We have to arrange them in descending order.

(i)

(ii)

#### Question 7:

Which of the following statements are true:
(i) The rational number $\frac{29}{23}$ lies to the left of zero on the number line.
(ii) The rational number $\frac{-12}{-17}$ lies to the left of zero on the number line.
(iii) The rational number $\frac{3}{4}$ lies to the right of zero on the number line.
(iv) The rational numbers are on the opposite side of zero on the number line.
(v) The rational numbers are on the opposite side of zero on the number line.
(vi) The rational number $\frac{-3}{-5}$ is one the right of $\frac{-4}{7}$ on the number line.

(i) False; it lies to the right of zero because it is a positive number.
(ii) False; it lies to the right of zero because it is a positive number.
(iii) True
(iv) True; they are of opposite signs.
(v) False; they both are of same signs.
(v) True; they both are of opposite signs and positive number is greater than the negative number. Thus, it is on the right of the negative number.

#### Question 1:

Write down the numerator of each of the following rational numbers:
(i) $\frac{-7}{5}$
(ii) $\frac{15}{-4}$
(iii) $\frac{-17}{-21}$
(iv) $\frac{8}{9}$
(v) 5

Numerators are:
(i) $-$7
(ii) 15
(iii) $-$17
(iv) 8
(v) 5

#### Question 2:

Write down the denominator of each of the following rational numbers:
(i) $\frac{-4}{5}$
(ii) $\frac{11}{-34}$
(iii) $\frac{-15}{-82}$
(iv) 15
(v) 0

Denominators are:
(i) 5
(ii) $-$34
(iii) $-$82
(iv) 1
(v) 1

#### Question 3:

Write down the rational number whose numerator is (−3) × 4, and whose denominator is (34 − 23) × (7 − 4).

According to the question:

Numerator = ($-$3) × 4 = $-$12

Denominator = (34 $-$ 23) × (7 $-$ ​4) = 11 × 3 = 33

∴ Rational number = $\frac{-12}{33}$

#### Question 4:

Write the following rational numbers as integers:

Integers are 7, $-$12, 34, $-$73 and 95.

#### Question 5:

Write the following integers as rational numbers with denominator 1:

Rational numbers of given integers with denominator 1 are:

#### Question 6:

Write down the rational number whose numerator is the smallest three digit number and denominator is the largest four digit number.

Smallest three-digit number = 100

Largest four-digit number = 9999

∴ Required rational number = $\frac{100}{9999}$

#### Question 7:

Separate positive and negative rational numbers from the following rational numbers:

Given rational numbers can be rewritten as:

Thus, positive rational numbers are:

or,

Negative rational numbers are:

or,

#### Question 8:

Which of the following rational numbers are positive:
(i) $\frac{-8}{7}$
(ii) $\frac{9}{8}$
(iii) $\frac{-19}{-13}$
(iv) $\frac{-21}{13}$

The numbers can be rewritten as:

Positive rational numbers are (ii) and (iii), i.e., .

#### Question 9:

Which of the following rational numbers are negative?
(i) $\frac{-3}{7}$
(ii) $\frac{-5}{-8}$
(iii) $\frac{9}{-83}$
(iv) $\frac{-115}{-197}$

The  numbers can be rewritten as:

Negative rational numbers are (i) and (iii).

#### Question 1:

Express each of the following as a rational number with positive denominator:
(i) $\frac{-15}{-28}$
(ii) $\frac{6}{-9}$
(iii) $\frac{-28}{-11}$
(iv) $\frac{19}{-7}$

Rational number with positive denominators:

(i) Multiplying the number by $-$1, we get:

$\frac{-15}{-28}=\frac{-15×-1}{-28×-1}=\frac{15}{28}$

(ii) Multiplying the number by $-$1, we get:

$\frac{6}{-9}=\frac{6×-1}{-9×-1}=\frac{-6}{9}$

(iii) Multiplying the number by $-$1, we get:

$\frac{-28}{-11}=\frac{-28×-1}{-11×-1}=\frac{28}{11}$

(iv) Multiplying the number by $-$1, we get:

$\frac{19}{-7}=\frac{19×-1}{-7×-1}=\frac{-19}{7}$

#### Question 2:

Express $\frac{3}{5}$ as a rational number with numerator:
(i) 6
(ii) −15
(iii) 21
(iv) −27

Rational number with numerator:

(i) 6 is:

(ii)

(iii)

(iv)

#### Question 3:

Express $\frac{5}{7}$ as a rational number with denominator:
(i) −14
(ii) 70
(iii) −28
(iv) −84

$\frac{5}{7}$ as a rational number with denominator:
(i) −14 is:

(ii) 70 is:

(iii) −28 is:

(iv) −84 is:

#### Question 4:

Express $\frac{3}{4}$ as a rational number with denominator:
(i) 20
(ii) 36
(iii) 44
(iv) −80

3/4 as rational number with denominator:

(i)

(ii)

(iii)

(iv)

#### Question 5:

Express $\frac{2}{5}$ as a rational number with numerator:
(i) −56
(ii) 154
(iii) −750
(iv) 500

2/5 as a rational number with numerator:

(i)

(ii)

(iii)

(iv)

#### Question 6:

Express $\frac{-192}{108}$ as a rational number with numerator:
(i) 64
(ii) −16
(iii) 32
(iv) −48

Rational number with numerator:

#### Question 7:

Express $\frac{168}{-294}$ as a rational number with denominator:
(i) 14
(ii) −7
(iii) −49
(iv) 1470

Rational number with denominator:

#### Question 8:

Write $\frac{-14}{42}$ in a form so that the numerator is equal to:
(i) −2
(ii) 7
(iii) 42
(iv) −70

Rational number with numerator:

#### Question 9:

Select those rational numbers which can be written as a rational number with numerator 6:

Given rational numbers that can be written as a rational number with numerator 6 are:

#### Question 10:

Select those rational numbers which can be written as a rational number with denominator 4:

Given rational numbers that can be written as a rational number with denominator 4 are:

122 (On multiplying by 6) = 613223 (On multiplying by 3) = 6934 (On multiplying by 2) = 6867 (On multiplying by 1) = 67

#### Question 11:

In each of the following, find an equivalent form of the rational number having a common denominator:
(i)
(ii)
(iii)

Equivalent forms of the rational number having common denominator are:

(i)  .

(ii)

(iii)

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