NCERT Solutions for Class 7 Math Chapter 9 - Rational Numbers

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Mathematics NCERT Grade 7, Chapter 9: Rational Numbers- As the name suggests, the chapter deals with rational numbers. A detailed explanation about rational numbers is given in the chapter. Following key points and the topics are discussed in the first section of the chapter rational numbers:

Need for rational numbers
What are rational numbers?

A number that can be expressed in the form p/q, where p and q are integers and q $\neq$ 0, is called a rational number. All integers and fractions are rational numbers.
Examples: -2/7, 3/8, etc.

Numerator and denominator

In p/q, the integer p is the numerator, and the integer q (≠ 0) is the denominator.

Equivalent rational numbers: By multiplying the numerator and denominator of a rational number by the same non zero integer, we obtain another rational number equivalent to the given rational number.
Positive rational numbers: When the numerator and denominator both are positive
negative rational numbers: When the numerator is positive and denominator is negative.
The number 0 is neither a positive nor a negative rational number.
Subsequently, the concept of rational numbers on a number line is also explained.

After this, in the first half of the chapter, some more topics like rational numbers in standard form, comparison of rational numbers and rational numbers between two rational numbers are explained.

The standard form of rational numbers must be studied which states that a rational number is in the standard form if its denominator is a positive integer and the numerator and denominator have no common factor other than 1.
There are an unlimited number of rational numbers between two rational numbers.

In the other half of the chapter, Operations on rational numbers are discussed. OPERATIONS discussed in the chapter are:
1. Addition
2. Additive inverse
3. Subtraction
4. Multiplication
5. Division
The chapter Rational numbers end with the summary.

Page No 182:

Question 1:

List five rational numbers between:

(i) − 1 and 0 (ii) − 2 and − 1

(iii) (iv)

Answer:

(i) −1 and 0

(ii) −2 and −1

Five rational numbers are

(iii)

Five rational numbers are

(iv)

Five rational numbers are

Page No 182:

Question 2:

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

(i) (ii)

(iii) (iv)

Answer:

(i)

It can be observed that the numerator is a multiple of 3 while the denominator is a multiple of 5 and as we increase them further, these multiples are increasing. Therefore, the next four rational numbers in this pattern are

(ii)

The next four rational numbers in this pattern are

(iii)

The next four rational numbers in this pattern are

(iv)

The next four rational numbers in this pattern are

Video Solution for rational numbers (Page: 182 , Q.No.: 2)

NCERT Solution for Class 7 math - rational numbers 182 , Question 2

Page No 183:

Question 3:

Give four rational numbers equivalent to:

(i) (ii) (iii)

Answer:

(i)

Four rational numbers are

(ii)

Four rational numbers are

(iii)

Four rational numbers are

Page No 183:

Question 4:

Draw the number line and represent the following rational numbers on it:

(i) (ii)

(iii) (iv)

Answer:

(i)

This fraction represents 3 parts out of 4 equal parts. Therefore, each space between two integers on number line must be divided into 4 equal parts.

can be represented as

(ii)

This fraction represents 5 parts out of 8 equal parts. Negative sign represents that it is on the negative side of number line. Therefore, each space between two integers on number line must be divided into 8 equal parts.

can be represented as

(iii)

This fraction represents 1 full part and 3 parts out of 4 equal parts. Negative sign represents that it is on the negative side of number line. Therefore, each space between two integers on number line must be divided into 4 equal parts.

can be represented as

(iv)

This fraction represents 7 parts out of 8 equal parts. Therefore, each space between two integers on number line must be divided into 8 equal parts.

can be represented as

Video Solution for rational numbers (Page: 183 , Q.No.: 4)

NCERT Solution for Class 7 math - rational numbers 183 , Question 4

Page No 183:

Question 5:

The points P, Q, R, S, T, U, A and B on the number line are such that,

TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.

Answer:

Distance between U and T = 1 unit

It is divided into 3 equal parts.

TR = RS = SU =

R =

S =

Similarly,

AB = 1 unit

It is divided into 3 equal parts.

P =

Q =

Video Solution for rational numbers (Page: 183 , Q.No.: 5)

NCERT Solution for Class 7 math - rational numbers 183 , Question 5

Page No 183:

Question 6:

Which of the following pairs represent the same rational number?

(i) (ii) (iii)

(iv) (v) (vi)

(vii)

Answer:

(i)

As, therefore, it does not represent same rational numbers.

(ii)

Therefore, it represents same rational numbers.

(iii)

Therefore, it represents same rational numbers.

(iv)

Therefore, it represents same rational numbers.

(v)

Therefore, it represents same rational numbers.

(vi)

As, therefore, it does not represent same rational numbers.

(vii)

Page No 183:

Question 7:

Rewrite the following rational numbers in the simplest form:

(i) (ii)

(iii) (iv)

Answer:

(i)

(ii)

(iii)

(iv)

Page No 183:

Question 8:

Fill in the boxes with the correct symbol out of >, <, and =

(i) (ii) (iii)

(iv) (v) (vi)

(vii)

Answer:

(i)

As −15 < 14,

Therefore,

(ii)

As −28 < −25

Therefore,

(iii) Here,

Therefore,

(iv)

As −32 > −35,

Therefore,

(v)

As −4 < −3,

Therefore,

(vi)

(vii)

Page No 184:

Question 9:

Which is greater in each of the following?

(i) (ii) (iii)

(iv) (v)

Answer:

(i)

By converting these into like fractions,

As 15 > 4, therefore, is greater.

(ii)

(iii)

By converting these into like fractions,

(iv)

(v)

By converting these into like fractions,

Page No 184:

Question 10:

Write the following rational numbers in ascending order:

(i) (ii) (iii)

Answer:

(i)

As −3 < −2 < −1,

(ii)

By converting these into like fractions,

As −12 < −3 < −2,

(iii)

By converting these into like fractions,

As −42 < −21 < −12,

Video Solution for rational numbers (Page: 184 , Q.No.: 10)

NCERT Solution for Class 7 math - rational numbers 184 , Question 10

Page No 190:

Question 1:

Find the sum:

(i) (ii) (iii)

(iv) (v) (vi)

(vii)

Answer:

(i) $\frac{4}{5} + (\frac{- 11}{4}) = \frac{4}{5} - \frac{11}{4} = \frac{16 - 55}{20} = \frac{- 39}{20}$

(ii)

L.C.M of 3 and 5 is 15.

(iii)

L.C.M of 10 and 15 is 30.

(iv)

L.C.M of 11 and 9 is 99.

(v)

L.C.M of 19 and 57 is 57.

(vi)

(vii) =

L.C.M of 3 and 5 is 15.

Video Solution for rational numbers (Page: 190 , Q.No.: 1)

NCERT Solution for Class 7 math - rational numbers 190 , Question 1

Page No 190:

Question 2:

Find

(i) (ii) (iii)

(iv) (v)

Answer:

(i)

L.C.M of 24 and 36 is 72.

(ii)

L.C.M of 63 and 7 is 63.

(iii)

L.C.M of 13 and 15 is 195.

(iv)

L.C.M of 8 and 11 is 88.

(v)

L.C.M of 9 and 1 is 9.

Page No 190:

Question 3:

Find the product:

(i) (ii) (iii)

(iv) (v) (vi)

Answer:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Page No 190:

Question 4:

Find the value of:

(i) (ii) (iii)

(iv) (v) (vi)

(vii)

Answer:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

Video Solution for rational numbers (Page: 190 , Q.No.: 4)

NCERT Solution for Class 7 math - rational numbers 190 , Question 4

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