Grade 7 an Introduction to Rational Number Worksheet Questions and Answers (For CBSE, ICSE, IAS, NET, NRA 2022)

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(1) Box the Rational Numbers to the Left of Zero on the Number Line.

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

(a)

(b)

(c)

(3) Answer the Following

(a) Between which two consecutive integer does lies?

(b) What is the larger of the two integer between which lies?

(4) Answer the Following

(a) Which integer lies immediately right of on the number line?

(b) Write as a decimal number round off to two decimal places and mark it on number line.

(5) Write Two Rational Numbers That Are Equivalent to the One Given.

(a)

(b)

(6) Write Two Rational Numbers That Are Equivalent to the One Given.

(a)

(b)

(7) Fill the Boxes with Integer to Make the Rational Number Equivalent.

(a)

(b)

(8) Fill the Boxes with Integer to Make the Rational Number Equivalent.

(a)

(b)

(9) Answer the Following Question.

(a) Write as a rational number with numerator 200.

(b) Write as a rational number with denominator 63.

(10) Indicate (√ /X) Whether the Given Statement is True or False.

(a) Every integer number is also a rational number.

(b) Division of two rational number is not a rational number.

(c) There are only 10 rational number lies between to .

(11) Indicate (√ /X) Whether the Given Rational Number is in Its Lowest Form or Not.

(a)

(b)

(c)

(12) Circle the Rational Number That Are in Their Standard Form.

(a)

(b)

(13) Circle the Rational Number That Are in Their Standard Form.

(a)

(b)

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

(a)

(15) Rewrite Each Rational Number in Its Lowest Form (L) and Its Standard Form (s) .

(a)

(16) Rewrite Each Rational Number in Its Lowest Form (L) and Its Standard Form (s) .

(a)

(17) Rewrite Each Rational Number in Its Lowest Form (L) and Its Standard Form (s) .

(a)

(18) Compare the Given Rational Numbers. Use < , > , or = .

(a)

(b)

(c)

(19) Compare the Given Rational Numbers. Use < , > , or = .

(a)

(b)

(c)

(20) Order the Given Rational Number.

(a)

(b)

(21) Write Three Rational Number between Given Two Rational Number.

(a)

(22) Write Three Rational Number between Given Two Rational Number.

(a)

(23) Write a Series of 15 Rational Number between:

(a)

(24) Write a Series of 15 Rational Number between:

(a)

(25) Indicate (√ /X) Whether the Given Statement is True or False.

(a) There are infinite number of rational number between two integers.

(b) Every rational number is a integer.

(c) There is only one rational number between and .

Answers and Explanations

Answer (1)

Any rational number that stated left side of Zero on number line are negative rational number.

So, for given rational number, negative rational number are the rational number which stated left side of Zero on number line.

So, answer is,

Here is actually a positive rational number.

Answer 2 (a)

Given rational number

Ad representation of number on number line is as below.

Ad Representation of Number on Number Line

Answer 2 (B)

Given rational number

Ad representation of number on number line is as below.

Ad Representation of Number on Number Line

Answer 2 (C)

Given rational number

Ad representation of number on number line is as below.

Ad Representation of Number on Number Line

Answer 3 (a)

Given rational number is

To find out between which two consecutive integer given rational number lies, we must convert it to decimal number.

So,

So, integer immediate lies to the right to the given rational number on number line is 3

Integer immediate lies to the left to the given rational number on number line is 2

So, given rational lies between 2 and 3 consecutive integers.

Answer 3 (B)

Given rational number is

To find out largest of the two integers between which given rational number lies, we must convert it to decimal number.

So,

So, integer immediate lies to the right to the given rational number on number line is 2

Integer immediate lies to the left to the given rational number on number line is 1

So, among these two integers 2 is largest integer.

Answer 4 (a)

Given rational number is

To find out the integer which lies immediate to right of given rational number on number line, we must convert it to decimal number.

So,

So, integer immediate lies to the right to the given rational number on number line is

Integer immediate lies to the left to the given rational number on number line is

So, lies immediately right of on the number line

Answer 4 (B)

Given rational number is .

To convert it in to decimal number we divide numerator by denominator.

Now, round off to two decimal places of given rational (decimal) number is as below.

Round off to Two Decimal Places

Answer 5 (a)

Given rational number

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 5 (B)

Given rational number

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 (a)

Given rational number

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)

Given rational number

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 (a)

So, equivalent rational number,

Answer 7 (B)

Given rational number for equivalent rational number,

First Consider only,

Now Consider,

So, equivalent rational number,

Answer 8 (a)

So, equivalent rational number,

Answer 8 (B)

Given rational number for equivalent rational number,

First consider only,

Now consider,

So, equivalent rational number

Answer 9 (a)

To write as a rational number with numerator 200, means equivalent rational number of given rational number having numerator 200. ;

So, can be written as rational number with numerator 200:

Answer 9 (B)

To write as a rational number with denominator 63, means equivalent rational number of given rational number having denominator 63;

So, can be written as rational number with denominator 63:

Answer 10 (a)

Given statement: Every integer number is also a rational number.

We can write every integer number as a rational number by simply writing 1 as a denominator.

By writing 1 as a denominator its value remain as it is and can be read as a rational number like,

So, given statement is true.

So, every integer number is also a rational number.

Answer 10 (B)

Given statement: Division of two rational number is not a rational number

Suppose these two rational numbers are

Now for division of rational number

Here is a rational number, means division of rational number is also a rational number.

So, given statement is wrong.

So, Division of two rational number is not a rational number

Answer 10 (C)

Given statement: There are only 10 rational number lies between to

Given rational number are

Now write its equivalent rational number by simply multiplying its numerator and denominator by 100.

So,

Now rational number between these two rational numbers are,

So, there is infinite rational number between given rational number

So, there are only 10 rational number lies between to

Answer 11 (a)

Given rational number is

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

To check given rational number is in its lowest form or not we should 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,

So given rational number is not in its lowest form.

So ,

Answer 11 (B)

Given rational number is

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

To check given rational number is in its lowest form or not we should 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,

So given rational number is in its lowest form.

So ,

Answer 11 (C)

Given rational number is

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

To check given rational number is in its lowest form or not we should 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,

So given rational number is not in its lowest form.

So ,

Answer 12 (a)

Given set of rational number are,

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.

For : its denominator is negative so, this rational number is not its standard form

For : The lowest form of given rational number is , so this rational number is not in its standard form.

For : The rational number is in its standard form.

For : The rational number is in its standard form.

Now,

Answer 12 (B)

Given set of rational number are,

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.

For : The lowest form of given rational number is , this rational number is not its standard form

For : The rational number is in its standard form.

For : The Denominator od given rational number is negative, so rational number is not in its standard form.

For : The rational number is in its standard form.

Now,

Answer 13 (a)

Given set of rational number are,

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.

For : The rational number is in its standard form.

For : The lowest form of given rational number is , so this rational number is not in its standard form.

For : The lowest form of given rational number is , so this rational number is not in its standard form.

For : The rational number is in its standard form.

Now,

Answer 13 (B)

Given set of rational number are,

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.

For : its denominator is negative so, this rational number is not its standard form

For : The rational number is in its standard form.

For : The rational number is in its standard form.

For : The lowest form of given rational number is , so this rational number is not in its standard form.

Now,

Answer 14 (a)

Given rational number is:

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.

The lowest form of given rational number is:

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)

Given rational number is:

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.

The lowest form of given rational number is:

is a Standard form of given rational number?

Answer 16 (a)

Given rational number is:

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.

The lowest form of given rational number is:

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 17 (a)

Given rational number is:

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.

The lowest form of given rational number is:

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 18 (a)

Here denominator is same for both the rational number,

And for numerator is greater than

So,

Answer 18 (B)

For the rational number

So, both rational numbers are equivalent rational number.

So,

Answer 18 (C)

Here is a positive rational number and is a negative rational number, so obvious positive rational number is greater than negative rational number,

So,

Answer 19 (a)

Here denominator is same for both the rational number,

And for numerator is greater than

So,

Answer 19 (B)

For rational number

And for rational number :

So, from above

Answer 20 (a)

To write give rational number in ascending order first we convert this rational number to decimal number,

So,

Now from above its clear that,

Answer 20 (B)

To write give rational number in descending order first we convert this rational number to decimal number,

So,

Now from above its clear that,

Answer (21)

Given two rational number is

The number lies between and ;

Now, Number lies between and ;

Now, Number lies between and ;

So, three number lies between and are

Answer (22)

Given two rational number is

The number lies between and ;

Now, Number lies between and ;

Now, Number lies between and ;

So, three number lies between and are

Answer (23)

Given rational number are

To write 15 rational number between given rational number; multiply numerator and denominator by 100 so,

Rational number are

Now 15 rational number between give rational number are:

And many more, means this way one can find many rational numbers between given two rational number.

Answer (24)

Given rational number are

To write 15 rational number between given rational number; multiply numerator and denominator by 10 so,

Rational number are

Now 15 rational number between give rational number are:

And many more, means this way one can find many rational numbers between given two rational number.

Answer 25 (a)

Given statement that: There are infinite number of rational numbers between two integers.

It՚s true that there are infinite number of rational numbers between two rational number

There are infinite number of rational numbers between two integers.

Answer 25 (B)

Given statement that: Every rational number is an integer.

Given statement is wrong not every rational number is an integer but every integer is a rational number.

So, every rational number is an integer.

Answer 25 (C)

Given statement that: There is only one rational number between and .

Now, multiply numerator and denominator by 100 to both rational numbers so,

Rational number are

Now rational number between give rational number are:

Same way can be finding out many more by multiplying 1000 and many more to numerator and denominator.

So, there are infinite number of rational numbers between two rational number

There is only one rational number between and .

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