# Rational Numbers - Class 8 - Mathematics

Renews every month. Cancel anytime

### Your personal doubt-solving assistant

Chatterbot AI gives you 100% accurate answers to your questions in an instant.

## Extra Questions - Rational Numbers | NCERT Exemplar | Mathematics | Class 8

Solve the following: Select the rational numbers from the list which are also the integers.

$$\frac{9}{4}, \frac{8}{4}, \frac{7}{4}, \frac{6}{4}, \frac{9}{3}, \frac{8}{3}, \frac{7}{3}, \frac{6}{3}, \frac{5}{2}, \frac{4}{2}, \frac{3}{1}, \frac{3}{2}, \frac{1}{1}, \frac{0}{1}, \frac{-1}{1}, \frac{-2}{1}, \frac{-3}{2}, \frac{-4}{2}, \frac{-5}{2}, \frac{-6}{2}$$

To solve the given problem, we determine which rational numbers from the list are also integers. A rational number represented as a fraction $$\frac{a}{b}$$ is an integer if the division (a \div b) results in a whole number (i.e., no remainder).

Let's calculate the division for each fraction in the list and check which results are integers:

$$\frac{9}{4} = 2.25$$ (not an integer)

$$\frac{8}{4} = 2$$ (integer)

$$\frac{7}{4} = 1.75$$ (not an integer)

$$\frac{6}{4} = 1.5$$ (not an integer)

$$\frac{9}{3} = 3$$ (integer)

$$\frac{8}{3} \approx 2.67$$ (not an integer)

$$\frac{7}{3} \approx 2.33$$ (not an integer)

$$\frac{6}{3} = 2$$ (integer)

$$\frac{5}{2} = 2.5$$ (not an integer)

$$\frac{4}{2} = 2$$ (integer)

$$\frac{3}{1} = 3$$ (integer)

$$\frac{3}{2} = 1.5$$ (not an integer)

$$\frac{1}{1} = 1$$ (integer)

$$\frac{0}{1} = 0$$ (integer)

$$\frac{-1}{1} = -1$$ (integer)

$$\frac{-2}{1} = -2$$ (integer)

$$\frac{-3}{2} = -1.5$$ (not an integer)

$$\frac{-4}{2} = -2$$ (integer)

$$\frac{-5}{2} = -2.5$$ (not an integer)

$$\frac{-6}{2} = -3$$ (integer)

The rational numbers from the list that are also integers are:

$$ \frac{8}{4}, \frac{9}{3}, \frac{6}{3}, \frac{4}{2}, \frac{3}{1}, \frac{1}{1}, \frac{0}{1}, \frac{-1}{1}, \frac{-2}{1}, \frac{-4}{2}, \frac{-6}{2} $$

Select those which can be written as a rational number with denominator 4 in their lowest form:

$\frac{7}{8}, \frac{64}{16}, \frac{36}{-12}, \frac{-16}{17}, \frac{5}{-4}, \frac{140}{28}$

### Improve your grades!

Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.

Sign up now### Improve your grades!

Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.

Sign up now### Improve your grades!

Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.

Sign up now### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

Verify the property $x \times(y \times z)=(x \times y) \times z$ of rational numbers by using and What is the name of this property?

(a) $x=1, y=\frac{-1}{2}$ and $z=\frac{1}{4}$

(b) $x=\frac{2}{3}, y=\frac{-3}{7}$ and $z=\frac{1}{2}$

(c) $x=\frac{-2}{7}, y=\frac{-5}{6}$ and $z=\frac{1}{4}$

(d) $x=0, y=\frac{1}{2}$

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

$\frac{7}{11}$ of all the money in Hamid's bank account is Rs. 77,000 . How much money does Hamid have in his bank account?

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

Find the multiplicative inverse of

(i) $-1 \frac{1}{8}$

(ii) $3 \frac{1}{3}$

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

Find two rational numbers whose absolute value is $\frac{1}{5}$.

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

The diagram shows the wingspans of different species of birds. Use the diagram to answer the question given below:

(a) How much longer is the wingspan of an Albatross than the wingspan of a Sea gull?

(b) How much longer is the wingspan of a Golden eagle than the wingspan of a Blue jay?

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

Here is a table which gives the information about the total rainfall for several months compared to the average monthly rains of a town. Write each decimal in the form of rational number $\frac{p}{q}$.

Month | Above/Below |
---|---|

May | 2.6924 |

June | 0.6096 |

July | -6.9088 |

August | -8.636 |

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

## Fill ups - Rational Numbers | NCERT Exemplar | Mathematics | Class 8

The equivalent of $\frac{5}{7}$, whose numerator is 45 is ______________.

To find the equivalent fraction of $ \frac{5}{7} $ with a numerator of 45, we use the property of equivalent fractions where both the numerator and denominator are multiplied by the same number to keep the value of the fraction unchanged.

Given: $$ \frac{5}{7} \quad \text{and numerator} = 45 $$

Let's determine the number that 5 is multiplied by to get 45: $$ 45 = 5 \times k $$ Solving for ( k ): $$ k = \frac{45}{5} = 9 $$

Now, we multiply both the numerator and the denominator of $ \frac{5}{7} $ by 9: $$ \frac{5 \times 9}{7 \times 9} = \frac{45}{63} $$

Thus, the equivalent fraction of $\frac{5}{7} $ with a numerator of 45 is: $$ \frac{45}{63} $$

The equivalent rational number of $\frac{7}{9}$, whose denominator is 45 is ______________________.

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

$(213 \times 657)^{-1}=213^{-1} \times$ ______________________.

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

The reciprocal of $\frac{-5}{7}$ is ______________________.

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

## MCQ - Rational Numbers | NCERT Exemplar | Mathematics | Class 8

A number which can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$ is

(a) natural number.

(b) whole number.

(c) integer.

(d) rational number.

A number which can be expressed in the form $$\frac{p}{q}$$ where $ p $ and $ q$ are integers and $ q \neq 0$, is defined as a **rational number**. The definition includes any case where both $ p $ and $ q $ are integers, which allows for the representation of fractions, whole numbers, and integers, depending on the values of $ p$ and $ q$. For example:

If $ p = 2 $ and $ q = 1 $, then $\frac{p}{q} = 2 $, which is a whole number and an integer.

If $ p = 1 $ and $ q = 2 $, then $\frac{p}{q} = 0.5 $, which is neither a whole number nor an integer but is a rational number.

Therefore, the correct answer to the question is: (d) rational number.

A number of the form $\frac{p}{q}$ is said to be a rational number if

(a) $p$ and $q$ are integers.

(b) $p$ and $q$ are integers and $q \neq 0$

(c) $p$ and $q$ are integers and $p \neq 0$

(d) $p$ and $q$ are integers and $p \neq 0$ also $q \neq 0$.

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

Multiplicative inverse of a negative rational number is

(a) a positive rational number.

(b) a negative rational number.

(c) 0

(d) 1

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

The reciprocal of 0 is

(a) 1

(b) -1

(c) 0

(d) Not defined

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

## True/False - Rational Numbers | NCERT Exemplar | Mathematics | Class 8

If $\frac{x}{y}$ is a rational number, then $y$ is always a whole number. (True/False)

False.

The statement, "If $\frac{x}{y}$ is a rational number, then $y$ is always a whole number," is false. A rational number is defined as a number that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers, where $p$ (numerator) is an integer, $q$ (denominator) is a nonzero integer. The denominator $y$ in $\frac{x}{y}$ only needs to be a nonzero integer, not necessarily a whole number. For example, $y$ could be negative, and as long as $x$ is also an integer, the fraction $\frac{x}{y}$ will be rational. Thus, $y$ does not have to be a whole number; it can be any nonzero integer.

If $\frac{p}{q}$ is a rational number, then $p$ cannot be equal to zero. (True/False)

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

The additive inverse of $\frac{1}{2}$ is -2 . (True/False)

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

The negative of 1 is 1 itself. (True/False)

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

For any rational number $x, x+(-1)=-x$. (True/False)

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

All positive rational numbers lie between 0 and 1000 . (True/False)

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

Every fraction is a rational number. (True/False)

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

0 is whole number but it is not a rational number. (True/False)