Introduction: Rational Numbers

Q. The number 0.318564318564318564….. is:

1. a natural number
2. a rational number
3. an irrational number
4. an integer

Q.

What number should be added to $\frac{-5}{8}$ so as to get $\frac{-3}{2}$?

Q.

Question 49

State whether the given statement is True or False.

Every integer is a rational number but every rational number need not be an integer.

Q.

Which of the following is not true?
(i) Whole numbers are closed under subtraction.
(ii) Integers are not closed under division.
(iii) Rational numbers are closed under division.

1. (i), (ii), (iii)

2. (ii), (iii)

3. (i), (iii)

4. (i), (ii)

Q.

$0$ is the smallest rational number. True or False. Why?

1. True
2. False

Q.

Question 58

State whether the given statement is True or False.

Every fraction is a rational number.

Q.

Question 50

State whether the given statement is True or False.

Every negative integer is not a negative rational number.

Q.

Question 03

Which of the following rational numbers is negative?

(a)$-\left(\frac{-3}{7}\right)$
(b) $\frac{-5}{-8}$
(c) $\frac{9}{8}$
(d) $\frac{3}{-7}$

Q.

Which of the following statements is incorrect?

1. Every integer is a rational number.

2. Every rational number is not an integer.

3. Every whole number is a rational number

4. Zero is a whole number, not a rational number.

Q. State whether the given statement is true of false:

(i) Zero is the smallest rational number.
(ii) Every integer is a rational number.
(iii) The quotient of two integers is always a rational number.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction.

Q.

Whole numbers are also called_________________

1. All of the above

2. Non-negative Integers

3. Non- Positive Integers

4. Natural Numbers

Q.

Question 91 (a)

In the following case, write the rational number whose numerator and denominator are respectively as under:
5 - 39 and 54 - 6

Q.

Question 02

Which of the following rational number is positive?

(a)$\frac{-8}{7}$
(b) $\frac{19}{-13}$
(c) $\frac{-3}{-4}$
(d) $\frac{-21}{13}$

Q.

Difference between fraction and rational number

Q.

Question 84

Write a rational number in which the numerator is less than ${}^{\prime }-7\times {11}^{\prime }$ and the denominator is greater than ${}^{\prime }12+4^{\prime }.$

Q.

Which of the following pairs represent the same rational number?

(i) (ii) (iii)

(iv) (v) (vi)

(vii)

Q. If $\frac{x}{y}$ and $\frac{y}{x}$ are rational numbers, then which of the following options are not correct?

1. $x\ne 0$, y can be 0
2. x can be 0, $y\ne 0$
3. $x\ne 0,y\ne 0$
4. both x and y can be 0

Q. Express the following rational number in the standard form: $\left(i\right)\frac{-7}{-8}$

Q.

Question 88 (f)

Write the following number in the form $\frac{p}{q}$, where p and q are integers.
opposite of three -fifths

Q. 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 $\frac{a}{b}=\frac{a\times m}{b\times m}$
(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) $\frac{2}{3}\mathrm{is}\mathrm{equal}\mathrm{to}\frac{4}{6}.$

Q.

Give four rational numbers equivalent to:

(i) (ii) (iii)

Q.

What is the difference between rational numbers and fractions? Or are they same?

Q.

Write four more rational numbers in each of the following patterns:

(i) (ii)

(iii) (iv)

Q.

Question 08

Which of the following is equivalent to $\frac{4}{5}$
(a) $\frac{5}{4}$
(b) $\frac{16}{25}$
(c) $\frac{16}{20}$
(d) $\frac{15}{25}$

Q. Express the following rational number in the standard form: $\left(ii\right)\frac{5}{-12}$

Q.

State whether the statement is given in question is true or False:

If $\frac{p}{q}$ is a rational number and $m$ is a non-zero integer, then$\left(\frac{p}{q}\right)=\frac{(p\times m)}{(q\times m)}$

1. True
2. False

Q. What are rational numbers? Give examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.

Q.

Question 91 (d)

In the following case, write the rational number whose numerators and denominator are respectively as under:
$25+15and81÷40$

Q.

Which of the following statements are true?

(i) Every whole number is a rational number.

(ii) Every integer is a rational number.

(iii) 0 is a whole number but it is not a rational number.

1. (i), (ii), (iii)

2. (i), (ii)

3. (ii), (iii)

4. (i)

Q. Write each of the following integers as a rational number. Write the numerator and the denominator in each case.

(i) 5
(ii) −3
(iii) 1
(iv) 0
(v) −23