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**NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers: **In earlier classes, you have studied whole numbers, natural numbers, integer numbers. In this article, you will get CBSE NCERT rational numbers class 7 solutions. Fractions number is a rational number that contains only positive integers whereas the rational number contains positive and negative integers. All fractions are rational numbers but all rational numbers are not fractions.

This Story also Contains

- NCERT Solutions for Maths Chapter 9 Rational Numbers Class 7 - Important Formulae
- NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers - Important Points
- NCERT Solutions for Maths Chapter 9 Rational Numbers Class 7
- NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers (Intext Questions and Exercise)
- NCERT Solutions for Maths Chapter 9 Rational Numbers Class 7 Topic 9.3
- NCERT rational numbers class 7 solutions Topic 9.4
- NCERT Solutions for Class 7 Maths Chapter 9 Topic 9.6
- NCERT Solutions for Maths Chapter 9 Rational Numbers Class 7 Topic 9.8
- NCERT Solutions for Class 7 Chapter 9 Rational Numbers Maths Exercise 9.1
- NCERT Solutions for Chapter 9 Maths Class 7 Rational Numbers Topic 9.9.1
- NCERT Solutions for Chapter 9 Maths Class 7 Rational Numbers Topic 9.9.2
- NCERT Solutions for Class 7th Math Chapter 9 Rational Numbers Topic 9.9.3
- NCERT Solutions for Class 7th Math Chapter 9 Rational Numbers Topic 9.9.4
- NCERT Solutions for Class 7th Math Chapter 9 Rational Numbers Exercise: 9.2
- Rational Numbers Class 7 Maths Chapter 9-Topics

Once you go through NCERT Solutions for Class 7 you will get more clarity of the concepts. You must refer to the NCERT Syllabus for Class 7 Maths for better understanding. There are 14 questions in 2 exercises given in NCERT . In CBSE NCERT solutions for Class 7 Maths chapter 9 rational numbers, you will get all detailed explanations of all these questions including practice question given at end of the very topic. You can get NCERT Solutions by clicking on the above link. Here you will get solutions to two exercises of this chapter.

Rational number = p/q, Where p and q are integers and q ≠ 0.

Numerator and Denominator: In the p/q , p is the numerator and q is the denominator.

Comparison of Rational Numbers:

p/q < a/b If pb < aq

p/q > a/b If pb > aq

Operations on Rational Number:

Addition of rational numbers : (p/q) + (a/b) = ((p×b) + (a×q))/(q×b)

Subtraction of rational numbers: (p/q) - (a/b) = ((p×b) - (a×q))/(q×b)

Multiplication of rational numbers: p/q) × (a/b) = (p×a)/(q×b)

Division of rational numbers: (p/q) ÷ (a/b) = (p×b)/(q×a)

Reciprocal of p/q = q/p

(Rational number)(Reciprocal) = 1

A rational can be expressed in the form of p/q , Where p and q are integers and q ≠ 0.

**Numerator and Denominator:** In the p/q , p is the numerator and q is the denominator.

We obtain another **equivalent rational number** by multiplying the numerator and denominator with the same nonzero integer.

+ sign and positive integer: a position to the right of 0.

- sign and negative integer: a position to the left of 0.

**Rational Numbers in Standard Form: **

Its denominator is a positive integer.

The numerator and denominator have no common factor other than 1.

Examples: 3/5 , -5/8 , 2/7, etc.

**Comparison of Rational Numbers:**

p/q < a/b If pb < aq

p/q > a/b If pb > aq

**Operations on Rational Number:**

Addition of rational numbers : (p/q) + (a/b) = ((p×b) + (a×q))/(q×b)

Subtraction of rational numbers: (p/q) - (a/b) = ((p×b) - (a×q))/(q×b)

Multiplication of rational numbers: p/q) × (a/b) = (p×a)/(q×b)

Division of rational numbers: (p/q) ÷ (a/b) = (p×b)/(q×a)

**Reciprocal of a rational number: **

Reciprocal of p/q = q/p

Product of rational numbers with its reciprocal is always 1.

Free download **NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers PDF **for CBSE Exam.

** Question:1 ** Is the number rational? Think about it.

** Answer: **Yes , is a rational number because it is written in the form: , where .

** Question: ** Fill in the boxes:

(i) (ii)

** Answer: **

** (i) **

can be written as:

Hence, we have

** (ii) **

can be written as:

Hence, we have

** Question:1 ** Is 5 a positive rational number?

** Answer: ****Yes**, 5 can be written as a positive rational number , where 5 and 1 are both positive integers and denominator not equal to zero.

** Question:2 ** List five more positive rational numbers.

** Answer: **Five more positive rational numbers are:

** Question:1 ** Is – 8 a negative rational number?

** Answer: ****Yes**, is a negative rational number because it can be written as , where the numerator is negative integer and denominator is a positive integer.

** Question:2 ** List five more negative rational numbers.

** Answer: **Five more negative rational numbers are:

** Question: ** Which of these are negative rational numbers?

(i) (ii) (iii) (iv) 0 (v) (vi)

** Answer:** (i) here, the numerator is -2 which is negative and the denominator is 3 which is positive.

Hence, the fraction is negative.

(ii) here, the numerator is 5 which is positive and the denominator is 7 which is also positive.

Hence, the fraction is positive.

(iii) here, the numerator is 3 which is positive and the denominator is -5 which is negative.

Hence, the fraction is negative.

(iv) 0 zero is neither a positive nor a negative number.

(v) here, the numerator is 6 which is positive and the denominator is 11 which is also positive.

Hence, the fraction is positive.

(vi) here, the numerator is -2 which is negative and the denominator is -9 which is also a negative integer.

Hence, the fraction is overall a positive fraction.

** Question: ** Find the standard form of

(i) (ii)

** Answer: **(i) Given fraction .

We can make it in the standard form :

(i) Given fraction .

We can make it in the standard form :

** Question: ** Find five rational numbers between

** Answer: **LCM of 7 and 8 is 56.

Hence we can write given fractions as:

and

Therefore, we can find five rational numbers between .

** Question: ** ** 1(i) ** List five rational numbers between:

–1 and 0

** Answer: **To find five rational numbers between we will convert each rational numbers as a denominator , we have

So, we have five rational numbers between

Hence, the five rational numbers between -1 and 0 are:

** Question: ** ** 1(ii) ** List five rational numbers between:

–2 and –1

** Answer: **To find five rational numbers between we will convert each rational numbers as a denominator , we have

So, we have five rational numbers between

Hence, the required rational numbers are

** Question: ** ** 1(iii) ** List five rational numbers between:

** Answer: **To find five rational numbers between we will convert each rational numbers with the denominator as , we have

Since there is only one integer i.e., -11 between -12 and -10, we have to find equivalent rational numbers.

Now, we have five rational numbers possible:

Hence, the required rational numbers are

** Question: ** ** 1(iv) ** List five rational numbers between:

** Answer: **To find five rational numbers between we will convert each rational numbers in their equivalent numbers, we have

Making denominator as LCM(2,3)=6

that is

Now, we have five rational numbers possible:

Hence, the required rational numbers are

** Question: ** ** 2(i) ** Write four more rational numbers in each of the following patterns:

** Answer: **We have the pattern:

Now, following the same pattern, we have

Hence, the required rational numbers are:

** Question: ** ** 2(ii) ** Write four more rational numbers in each of the following patterns:

** Answer: **We have the pattern:

Now, following the same pattern, we have

Hence, the required rational numbers are:

** Question: ** ** 2(iii) ** Write four more rational numbers in each of the following patterns:

** Answer: **We have the pattern:

Now, following the same pattern, we have

Hence, the required rational numbers are:

** Question: ** ** 2(iv) ** Write four more rational numbers in each of the following patterns:

** Answer: **We have the pattern:

Now, following the same pattern, we have

Hence, the required rational numbers are:

** Question: ** ** 3(i) ** Give four rational numbers equivalent to:

** Answer: ** can be written as:

Hence, the required equivalent rational numbers are

** Question: ** ** 3(ii) ** Give four rational numbers equivalent to:

** Answer:** can be written as:

Hence, the required equivalent rational numbers are

** Question: ** ** 3(iii) ** Give four rational numbers equivalent to:

** Answer:** can be written as:

Hence, the required equivalent rational numbers are

** Question: ** ** 4(i) ** Draw the number line and represent the following rational numbers on it:

** Answer: **Representation of on the number line,

** Question: ** ** 4(ii) ** Draw the number line and represent the following rational numbers on it:

** Answer:** Representation of on the number line,

** Question: ** ** 4(iii) ** Draw the number line and represent the following rational numbers on it:

** Answer: **Representation of on the number line,

** Question: ** ** 4(iv) ** Draw the number line and represent the following rational numbers on it:

** Answer: **Representation of on the number line,

** Answer: **Given TR = RS = SU and AP = PQ = QB then, we have

There are two rational numbers between A and B i.e., P and Q which are at equal distances hence,

The rational numbers represented by P and Q are:

Also, there are two rational numbers between U and T i.e., S and R which are at equal distances hence,

The rational numbers represented by S and R are:

** Question: ** ** 6 ** Which of the following pairs represent the same rational number?

(i) (ii)

(iii) (iv)

(v) (vi)

(vii)

** Answer: **To compare we multiply both numbers with denominators:

(i) We have

Here, they are equal but are in opposite signs hence, do not represent the same rational numbers.

(ii) We have

So, they represent the same rational number.

(iii) We have

Here, Both represents the same number as these minus signs on both numerator and denominator of will cancel out and gives the positive value.

(iv) We have

So, they represent the same rational number.

(v) We have

So, they represent the same rational number.

(vi) We have

So, They do not represent the same rational number.

(vii) We have

Here, the denominators of both are the same but .

So, do not represent the same rational numbers.

** Question: ** ** 7 ** Rewrite the following rational numbers in the simplest form:

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

** Answer:** (i) can be written as:

(ii) can be written in the simplest form:

(iii) can be written as in simplest form:

** Question: ****8 ** Fill in the boxes with the correct symbol out of >, <, and =.

(i) (ii) (iii)

(iv) (v) (vi)

(vii)

** Answer:**** (i) **

Hence,

** (ii) **

Hence,

** (iii) **

Hence,

** (iv) **

Hence,

** (v) **

Hence,

** (vi) **

Hence,

** (vii) **

Zero is always greater than every negative number.

Therefore,

** Question: ** ** 9 ** Which is greater in each of the following:

(i) (ii)

(iii) (iv)

(v)

** Answer: ****(i) **

Since,

So,

** (ii) **

Since,

So,

** (iii) **

Since,

So,

** (iv) **

As each positive number is greater than its negative.

** (v) **

So,

** Question: ****10(i) ** Write the following rational numbers in ascending order:

** Answer: **(i) Here the denominator value is the same.

Therefore,

Hence, the required ascending order is

** Question: ** ** 10(ii) ** Write the following rational numbers in ascending order:

** Answer: **Given

LCM of .

Therefore, we have

Since

Hence, the required ascending order is

** Question: ** ** 10(iii) ** Write the following rational numbers in ascending order:

** Answer: **Given

LCM of .

Therefore, we have

Since

Hence, the required ascending order is

** Question: ** Find:

** Answer: **For the given sum:

Here the denominator value is same that is 7 hence we can sum the numerator as:

For the given sum:

Here also the denominator value is the same and is equal to 5 hence we can write it as:

** Question:(i) ** Find:

** Answer: **Given sum:

Taking LCM of 7 and 3 we get; 21

Hence we can write the sum as:

** Question:(ii) ** Find:

** Answer: **Given sum:

Taking LCM of 6 and 11 we get; 66

Hence we can write the sum as:

** Question:1 ** What will be the additive inverse of

-3/9, -9/11, 5/7

** Answer: **The additive inverse of

The additive inverse of

The additive inverse of

** Question:2 ** Find

** Answer: **

** Question: ** What will be

(i) (ii)

** Answer:** (i)

We can write the product as:

(i)

We can write the product as:

** Question: ** What will be the reciprocal of

** Answer: **The reciprocal of will be:

The reciprocal of will be:

** Question: ** ** 1(i) ** Find the sum:

** Answer:** Given sum:

Here the denominator is the same which is 4.

** Question: ** ** 1(ii) ** Find the sum:

** Answer:** Given sum:

Here the LCM of 3 and 5 is 15.

Hence, we can write the sum as:

** Question: 1(v) ** Find the sum :

** Answer: **Given sum:

Taking LCM of 19 and 57, we have 57

We can write the sum as:

** Question: ** ** 1(vi) ** Find the sum:

** Answer: **Given sum:

Adding any number to zero we get, the number itself

Hence,

- Need For Rational Numbers
- What Are The Rational Numbers?
- Positive And Negative Rational Numbers
- Rational Numbers On A Number Line
- Rational Numbers In A Standard Form
- Comparison Of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Operations On Rational Numbers

Chapter No. | Chapter Name |

Chapter 1 | |

Chapter 2 | |

Chapter 3 | |

Chapter 4 | |

Chapter 5 | |

Chapter 6 | |

Chapter 7 | |

Chapter 8 | Comparing quantities |

Chapter 9 | Rational Numbers |

Chapter 10 | |

Chapter 11 | |

Chapter 12 | |

Chapter 13 | |

Chapter 14 | |

Chapter 15 | Visualising Solid Shapes |

### You will study the different types of numbers which you should know in NCERT Class 7 Mathematics book .

- It will help you in your homework as all the practice questions including questions given below every topic are covered in this article.
- You will also learn addition, multiplication, subtraction, and division of rational numbers.
- You will also get solutions to the practice questions given below every topic which will give you conceptual clarity.
- You should practice all the NCERT questions including examples. If you facing difficulties in doing so, you can take help from the NCERT solutions for Class 7 Maths chapter 9 Rational Numbers.

** Happy learning!!! **

**Also Check NCERT Books and NCERT Syllabus here:**

1. What is rational number?

A number can be expressed in the form of p/q, where p and q are integers and q is not equal to 0 is called a rational number. Students can deeper understanding of rational number in class 7 math chapter 9. You can download rational numbers class 7 pdf to study both offline and online mode.

2. How do you perform operations with rational numbers?

- For addition and subtraction, find a common denominator, perform the operation on the numerators, and keep the denominator the same.
- For multiplication, multiply the numerators and denominators separately.
- For division, multiply by the reciprocal of the second number (divisor) and follow the multiplication rule.

3. How many exercises in NCERT solution Class 7 Maths chapter 9?

There are 2 exercises in NCERT solution Class 7 Maths chapter 9.

Rational Numbers Exercise 9.1- 10 questions

Rational Numbers Exercise 9.2- 4 questions

4. How do you convert a recurring decimal into a fraction?

- To convert a recurring decimal into a fraction, represent the recurring part as 'x' and subtract it from the whole decimal.
- Solve for 'x' to get an equation. Multiply both sides by the appropriate power of 10 to eliminate the recurring part.
- This will give you an equation that you can solve to find the fraction equivalent of the recurring decimal.

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