Grade 8 the Basic of Rational Number Worksheet Questions and Answers (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Mark the Given Rational Numbers on the Number Line.

(a)

(b)

(c)

(2) Indicate (√ /X) Whether the Given Statement is Correct or Not.

(a) Every integer is a rational number.

(b) Natural number include ZERO.

(c) The Natural number lies right side of ZERO on number line

(3) Write the Two Consecutive Integers between Which the Given Rational Number Lies.

(a)

(b)

(c)

(d)

(4) Answer the Following Questions.

(a) Which is the first integer to the left of the rational number

(b) Which integer is closest to the rational number

(5) Answer the Following Questions.

(a) Which is the smaller of the two consecutive integers between which lies?

(6) Write Two Equivalent Rational Numbers for Each Number.

(a)

(b)

(7) Write Two Equivalent Rational Numbers for Each Number.

(a)

(b)

(8) Fill Each Box with an Integer to Make the Rational Numbers Equivalent.

(a)

(b)

(9) Fill Each Box with an Integer to Make the Rational Numbers Equivalent.

(a)

(b)

(10) Write a Rational Number Equivalent to Whose

(a) Numerator is

(b) Denominator is .

(11) Write Each Rational Number in Both Its Lowest Form (L) and Standard Form (s) .

(a)

(12) Write Each Rational Number in Both Its Lowest Form (L) and Standard Form (s) .

(a)

(13) Write Each Rational Number in Both Its Lowest Form (L) and Standard Form (s) .

(a)

(14) Write Each Rational Number in Both Its Lowest Form (L) and Standard Form (s) .

(a)

(15) Write Each Rational Number in Its Decimal Form.

(a)

(b)

(c)

(16) Write Each Rational Number in Its Decimal Form.

(a)

(b)

(c)

(17) Write Each Decimal Number in the Form P/Q.

(a)

(b)

(c)

(18) Compare the Given Rational Numbers.

(a)

(b)

(c)

(19) Compare the Given Rational Numbers.

(a)

(b)

(c)

(20) Order the Given Rational Numbers.

(a)

(b)

(21) Write a Series of 10 Rational Numbers between:

(a)

(b)

(22) Indicate (√ /X) Whether the Given Statement is True or Not.

(a) Between any to two consecutive integers, there are many rational numbers

(b)

(c)

Answers and Explanations

Answer 1 (a)

Given rational number:

Representation of Rational number on number line is as below.

Representation of Rational Number on Number Line

Answer 1 (B)

Given rational number:

Representation of Rational number on number line is as below.

Representation of Rational Number on Number Line

Answer 1 (C)

Given rational number:

Representation of Rational number on number line is as below.

Representation of Rational Number on Number Line

Answer 2 (a)

Integer number are the number that include whole number plus minus series number that is - and so on

But it does not include any rational number like etc.

But rational numbers include all integer number plus any in between rational number like etc.

So, in another way we can say that integer number is a part of rational number.

An integer can be written as a fraction simply by giving it a denominator of one, so any integer is a rational number.

So, every integer is a rational number.

Answer 2 (B)

Natural number are the number that generally used to count something, starting from and so on.

This number is the number, we generally learn when we are child and love to speak or learn and so on.

This number does not include 0 (ZERO)

So, Natural number includes ZERO.

Answer 2 (C)

Representation of Number line is as below.

Representation of Number Line

From Figure it is clear shows that Natural number lies right side of ZERO on number line, so given statement is right.

So, the Natural number lies right side of ZERO on number line

Answer 3 (a)

Given rational number,

Here numerator is lower than the denominator that means its value is higher than one but lower than one.

So,

Answer 3 (B)

First, we simplify the given rational number;

So,

Answer 3 (C)

First, we simplify the given rational number;

So,

Answer 3 (D)

First, we simplify the given rational number;

So,

Answer 4 (a)

Given rational number:

So, lies between two integer number are

Representation of integer number on number line is as below.

From above it is clear that first integer to the left of the rational number is

Answer 4 (B)

First, we simplify the given rational number;

So, from this one thing we can conclude that is number lies between two integer number is

Now, to identify the colure number we must find the middle number of two integer number ; and middle number is

Now, the given rational number is higher than the middle number; so, closure number to the given rational number is 7.

So, integer number is closest to the rational number

Answer 5 (a)

First, we simplify the given rational number;

So, from this one thing we can conclude that is number lies between two integer number is

Now, Representation of integer number on number line is as below.

On the number line as we move left side starting from ZERO (0) the value of numbers decrease accordingly.

That means

So, the smaller of the two consecutive integers between which lies is

Answer 6 (a)

Equivalent to any rational number can be find out by multiplying or dividing by the same integer number to its numerator and denominator.

So,

So,

Answer 6 (B)

Equivalent to any rational number can be find out by multiplying or dividing by the same integer number to its numerator and denominator.

So,

Therefore,

Answer 7 (a)

Equivalent to any rational number can be find out by multiplying or dividing by the same integer number to its numerator and denominator.

So,

So,

Answer 7 (B)

Equivalent to any rational number can be find out by multiplying or dividing by the same integer number to its numerator and denominator.

So,

So,

Answer 8 (a)

Equivalent to any rational number can be find out by multiplying or dividing by the same integer number to its numerator and denominator.

So, here

Now to get multiplied integer number we divide second rational number՚s numerator by first rational number՚s numerator,

So, here given rational number multiplied by 3 to get equivalent rational number.

So, denominator of first rational number

So,

Answer 8 (B)

Given equation:

Now to get multiplied integer number we divide second rational number՚s numerator by first rational number՚s numerator,

So, here given rational number multiplied by 7.5 to get equivalent rational number.

So, denominator of first rational number

So,

Answer 9 (a)

Given equation:

Now to get multiplied integer number we divide First rational number՚s denominator by second rational number՚s denominator,

So, here given rational number Divided by 8 to get equivalent rational number.

So, Numerator of first rational number

So,

Answer 9 (B)

Given equation:

Now to get multiplied integer number we divide First rational number՚s denominator by second rational number՚s denominator,

So, here given rational number Divided by 3 to get equivalent rational number.

So, Numerator of second rational number

So,

Answer 10 (a)

Given Rational number

And demanded equivalent rational number whose numerator is

So, common multiplied number to given rational number is,

So, Denominator of second rational number

So, Rational number that equivalent to and whose Numerator is is

Therefore, the answer is

Answer 10 (B)

Given Rational number

And demanded equivalent rational number whose denominator is

So, common multiplied number to given rational number is,

So, Numerator of second rational number

So, Rational number that equivalent to and whose Denominator is is

Answer 11 (a)

Lowest Form: Lowest form of rational number is equivalent rational number than cannot be divided by any further common factor of numerator and denominator.

To get lowest form of given rational number first we figure out common factor of numerator and denominator.

Common factor of numerator as below,

And Common Factor of denominator is as below,

Now, for lowest form,

is lowest form of given rational number.

Standard form: Standard form of rational number is equivalent rational number than cannot be divided by any further common factor of numerator and denominator, and having Denominator is a positive integer.

To get standard form of given rational number first we figure out common factor of numerator and denominator.

Common factor of numerator as below,

And Common Factor of denominator is as below,

Now, for standard form,

is Standard form of given rational number.

NOTE: Standard form of any rational number can be a lowest form of rational number but lowest form of rational number cannot be standard form.

Answer 12 (a)

Lowest Form:

To get lowest form of given rational number first we figure out common factor of numerator and denominator.

Common factor of numerator as below,

And Common Factor of denominator is as below,

Now, for lowest form,

is lowest form of given rational number.

Standard Form:

To get Standard form of given rational number first we figure out common factor of numerator and denominator.

Common factor of numerator as below,

And Common Factor of denominator is as below,

Now, for lowest form,

Now, Denominator of standard form cannot be minus integer.

That՚s why to get Standard form of we multiply numerator and denominator by

is a Standard form of given rational number?

Answer 13 (a)

Lowest Form:

To get lowest form of given rational number first we figure out common factor of numerator and denominator.

Common factor of numerator as below,

And Common Factor of denominator is as below,

Now, for lowest form,

is lowest form of given rational number.

Standard Form:

To get Standard form of given rational number first we figure out common factor of numerator and denominator.

Common factor of numerator as below,

And Common Factor of denominator is as below,

Now, for Standard form,

Now, Denominator of standard form cannot be minus integer.

That՚s why to get Standard form of we multiply numerator and denominator by

is a Standard form of given rational number?

Answer 14 (a)

Lowest Form:

To get lowest form of given rational number first we figure out common factor of numerator and denominator.

Common factor of numerator as below,

And Common Factor of denominator is as below,

Now, for lowest form,

is lowest form of given rational number.

Standard Form:

To get Standard form of given rational number first we figure out common factor of numerator and denominator.

Common factor of numerator as below,

And Common Factor of denominator is as below,

Now, for Standard form,

Now, Denominator of standard form cannot be minus integer.

That՚s why to get Standard form of we multiply numerator and denominator by

is a Standard form of given rational number?

Answer 15 (a)

To find out decimal form of given rational number, must divide numerator by denominator.

Answer 15 (B)

To find out decimal form of given rational number, must divide numerator by denominator.

Answer 15 (C)

To find out decimal form of given rational number, must divide numerator by denominator.

Answer 16 (a)

To find out decimal form of given rational number, must divide numerator by denominator.

Answer 16 (B)

To find out decimal form of given rational number, must divide numerator by denominator.

Answer 16 (C)

To find out decimal form of given rational number, must divide numerator by denominator.

Answer 17 (a)

Given form is decimal form and demanded number in Rational number form.

So,

So, given decimal number 1.88 in form of is

Answer 17 (B)

Given form is decimal form and demanded number in Rational number form.

So,

So, given decimal number 1.6 in form of is .

Answer 17 (C)

Given form is decimal form and demanded number in Rational number form.

So,

So, given decimal number in form of is .

Answer 18 (a)

To compare rational number, we have to convert it in to decimal form for easy of identification.

So, Decimal number of

And Decimal Number of

So,

So,

Answer 18 (B)

To compare rational number, we must convert it in to decimal form for easy of identification.

So, Decimal number of

And Decimal of

So, 0.8 is higher than 0.75.

So,

Answer 18 (C)

To compare rational number, we must convert it in to decimal form for easy of identification.

So, Decimal number of

And decimal of,

So,

So,

Answer 19 (a)

To compare rational number, we must convert it in to decimal form for easy of identification.

So, Decimal number of

And decimal of,

So, 2.75 is higher than 1.6.

So,

Answer 19 (B)

To compare rational number, we must convert it in to decimal form for easy of identification.

So, Decimal number of

And decimal of,

So, and is same.

So,

Answer 19 (C)

To compare rational number, we must convert it in to decimal form for easy of identification.

So, Decimal number of,

And Decimal Number of,

So, is higher than .

So,

Answer 20 (a)

In order to arrange given rational number in Ascending order first we must convert them in to decimal number for easy of understanding.

So, decimal number of given,

So, Arrangement of number is as below.

Answer 20 (B)

In order to arrange given rational number in Ascending order first we must convert them in to decimal number for easy of understanding.

So, decimal number of given,

So, arrangement of number is as below.

Answer 21 (a)

Rational number between:

And

So, 10 rotational number between

Answer 21 (B)

Rational number between:

And

So, 10 Rotational number between are as below.

Answer 22 (a)

Between any two-consecutive integer, there any infinite rational number; this can be understanding as below.

Two consecutive number are 0

And rational number these two numbers in the form of decimal number are as below,

0.1,0.2,0.3,0.4,0.5 … plus 0.01,0.02,0.03,0.04,0.05,0.06 … plus 0.001,0.002,0.003 0.004 … and likewise so on …

Between any to two consecutive integers, there are many rational number

Answer 22 (B)

Here rational number

And for rational number

So, its

So,

Answer 22 (C)

Given rational number,

So,

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