Class 7 Maths Chapter 9 Rational Numbers NCERT Solutions

Class 7 Maths Chapter 9 Rational Numbers NCERT Solutions

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercise 9.1
Ex 9.1 Class 7 Maths Question 1.
List five rational numbers between:
(i) -1 and 0
(ii) -2 and -1
(iii) \(\frac{-4}{5} \text { and } \frac{-2}{3}\)
(iv) \(\frac{1}{2} \text { and } \frac{2}{3}\)
Solution:
(i) -1 and 0
Converting each of rational numbers as a denominator 5 + 1 = 6, we have

Hence, the required five rational numbers between -1 and 0 are \(\frac{-5}{6}, \frac{-2}{3}, \frac{-1}{2}, \frac{-1}{3} \text { and }-\frac{1}{6}\)

(ii) -2 and -1
Converting each of rational numbers as a denominator 5 + 1 = 6, we have

(iii) \(\frac{-4}{5} \text { and } \frac{-2}{3}\)
Converting each of the rational numbers as a denominator 5 × 3 = 15, we have

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

(iv) \(\frac{1}{2} \text { and } \frac{2}{3}\)
Converting each of the rational numbers in their equivalent rational numbers, we have

Ex 9.1 Class 7 Maths Question 2.
Write four more rational numbers in each of the following patterns:

Solution:

Ex 9.1 Class 7 Maths Question 3.
Give four rational numbers equivalent to:

Solution:

Ex 9.1 Class 7 Maths Question 4.
Draw a number line and represent the following rational numbers on it:

Solution:

Ex 9.1 Class 7 Maths 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.

Solution:
Rational numbers represented by P, Q, R and S.
\(\frac{7}{3}, \frac{8}{3}, \frac{-4}{3} \text { and } \frac{-5}{3}\) respectlvely.

Ex 9.1 Class 7 Maths Question 6.
Which of the following pairs represent the same rational number?


Solution:

Ex 9.1 Class 7 Maths Question 7.
Rewrite the following rational numbers in the simplest form:

Solution:

Ex 9.1 Class 7 Maths Question 8.
Fill in the boxes with the correct symbol out of >, < and =.

Solution:

Ex 9.1 Class 7 Maths Question 9.

Which is greater in each of the following:

Solution:

Ex 9.1 Class 7 Maths Question 10.
Write the following rational numbers in ascending order:

Solution:

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Class 7 Maths Chapter 9 Exercise 9.2

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercise 9.2
Ex 9.2 Class 7 Maths Question 1.
Find the sum:

Solution.

Ex 9.2 Class 7 Maths Question 2.
Find:

Solution:

Ex 9.2 Class 7 Maths Question 3.
Find the product:

Solution:

Ex 9.2 Class 7 Maths Question 4.
Find the value of:

Solution:

Rational Numbers Class 7 Extra Questions Very Short Answer Type

Question 1.
Find three rational numbers equivalent to each of the following rational numbers.
(i) −25
(ii) 37
Solution:

Question 2.
Reduce the following rational numbers in standard form.
(i) 35−15
(ii) −36−216
Solution:

Question 3.
Represent 32 and −34 on number lines.
Solution:

Question 4.
Which of the following rational numbers is greater?
(i) 34, 12
(ii) −32, −34
Solution:

Question 5.
Find the sum of

Solution:

Question 6.
Subtract:

Solution:

Question 7.
Find the product:

Solution:

Rational Numbers Class 7 Extra Questions Short Answer Type

Question 8.
If the product of two rational numbers is −916 and one of them is −415, find the other number.
Solution:
Let the required rational number be x.

Question 9.
Arrange the following rational numbers in ascending order.

Solution:

Question 10.
Insert five rational numbers between:

Solution:

Rational Numbers Class 7 Extra Questions Long Answer Type

Question 11.
Evaluate the following:

Solution:

Question 12.
Subtract the sum of −56 and -135 from the sum 223 and -625.
Solution:

Question 13.

Solution:
We have

Question 14.
Divide the sum of -21517 and 3534 by their difference.
Solution:

Question 15.
During a festival sale, the cost of an object is ₹ 870 on which 20% is off. The same object is available at other shops for ₹ 975 with a discount of 623 %. Which is a better deal and by how much?
Solution:
The cost of the object = ₹ 870
Discount = 20% of ₹ 870 = 20100 × 870 = ₹ 174
Selling price = ₹ 870 – ₹ 174 = ₹ 696
The same object is available at other shop = ₹ 975

Selling price = ₹ 975 – ₹ 65 = ₹ 910
Since ₹ 910 > ₹ 696
Hence, deal at first shop is better and by ₹ 910 – ₹ 696 = ₹ 214

Rational Numbers Class 7 Extra Questions Higher Order Thinking Skills (HOTS) Type

Question 16.
Simplify:
21.5 ÷ 5 – 15 of (20.5 – 5.5) + 0.5 × 8.5
Solution:
Using BODMAS rule, we have
21.5 ÷ 5 – 15 of (20.5 – 5.5) + 0.5 × 8.5
= 21.5 ÷ 5 – 15 of 15 + 0.5 × 8.5
= 21.5 × 15 – 15 × 15 + 0.5 × 8.5
= 4.3 – 3 + 4.25
= 4.3 + 4.25 – 3
= 8.55 – 3
= 5.55

Question 17.
Simplify:

Solution:
Using BODMAS rule, we have
2.3 – [1.89 – {3.6 – (2.7 – 0.77)}]
= 2.3 – [1.89 – {3.6 – 1.93}]
= 2.3 – [1.89 – 1.67]
= 2.3 – 0.22
= 2.08

Question 18.

Solution:
Using BODMAS rule, we have