# NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers InText Questions

These NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers InText Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers InText Questions

NCERT In-text Question Page No. 174

Question 1.
Is the number $$\frac{2}{-3}$$ rational? Think about it.
Yes, $$\frac{2}{-3}$$ is a rational number,
∵ 2 and -3 are integers and -3 ≠ 0.

Question 2.
List ten rational numbers.
Following are ten rational numbers:
$$\frac{1}{3}, \frac{-2}{3}, \frac{4}{5}, \frac{1}{-6}, \frac{-3}{-4}, 5.8,2 \frac{4}{5}$$, 0.93, 18 and 11.07
Note: 1. ‘0’ can be written as $$\frac{0}{2}$$ or $$\frac{0}{15}$$ etc.
Hence, it is a rational number.
2. A natural number can be written as
5 = $$\frac{5}{1}$$ or 108 = $$\frac{108}{1}$$ Hence, it is also a rational number.

NCERT In-text Question Page No. 175

Question 1.
Fill in the boxes:

Question 2.
Is 5 a positive rational number?
Yes, 5 or $$\frac{5}{1}$$ is having both its numerator
and denominator as positive.
∴ It is a positive rational number.

Question 3.
List five more positive rational numbers.
$$\frac{1}{7}, \frac{3}{8}, \frac{5}{17}, \frac{2}{9}$$ and $$\frac{5}{18}$$ and are positive rational numbers.

NCERT In-text Question Page No. 176

Question 1.
Is -8 a negative rational number?
(i) Yes, -8 or $$\frac{-8}{1}$$ is a negative rational number, because its numerator is a negative integer.

Question 2.
List five more negative rational numbers.
Five negative rational numbers are as follows:
$$\frac{-5}{9}, \frac{-6}{11}, \frac{-3}{13}, \frac{3}{-10} \text { and } \frac{-1}{7}$$

Question 3.
Which of these are negative rational numbers?
(i) $$\frac{-2}{3}$$
(ii) $$\frac{5}{7}$$
(iii) $$\frac{3}{-5}$$
(iv) 0
(v) $$\frac{6}{11}$$
(vi) $$\frac{-2}{-9}$$
(i) $$\frac{-2}{3}$$ is a negative rational number.
(ii) $$\frac{5}{7}$$ is a positive rational number.
(iii) $$\frac{3}{-5}$$ is a negative rational number.
(iv) 0 is neither a positive nor a negative rational number.
(v) $$\frac{6}{11}$$ is a positive rational number.
(vi) $$\frac{-2}{-9}$$ is a positive rational number.
∴ (i) $$\frac{-2}{3}$$ and (ii) $$\frac{3}{-5}$$ are negative rational numbers.

NCERT In-text Question Page No. 178

Question 1.
Find the standard form of:
(i) $$\frac{-18}{45}$$
(ii) $$\frac{-12}{18}$$
(i) Since HCF of 18 and 45 is 9.
∴ $$\frac{-18}{45}=\frac{(-18) \div 9}{45 \div 9}=\frac{-2}{5}$$
Thus, the standard form of $$\frac{-18}{45}$$ is $$\frac{-2}{3}$$

(ii) Since HCF of 12 and 18 is 6.
∴ $$\frac{-12}{18}=\frac{(-12) \div 6}{18 \div 6}=\frac{-2}{3}$$
Thus, the standard form of $$\frac{-12}{18}$$ is $$\frac{-2}{3}$$

NCERT In-text Question Page No. 181

Question 1.
Find five rational numbers between $$\frac{-5}{7}$$ and $$\frac{-3}{8}$$
First we convert the given rational numbers with common denominators,
∴ LCM of 7 and 8 is 56.

Thus, the five rational numbers, between $$\frac{-5}{7}$$ and $$\frac{-3}{8}$$ are:

NCERT In-text Question Page No. 185

Question 1.
Find:
(i) $$\frac{-13}{7}+\frac{6}{7}$$
(ii) $$\frac{-19}{5}+\frac{-7}{5}$$

Question 2.
Find:
(i) $$\frac{-3}{7}+\frac{2}{3}$$
(ii) $$\frac{-5}{6}+\frac{-3}{11}$$
(i) $$\frac{-3}{7}+\frac{2}{3}$$
∴ LCM of 7 and 3 is 21

NCERT In-text Question Page No. 186

Question 1.
What will be the additive inverse of $$\frac{3}{9} ?, \frac{-9}{11} ?, \frac{5}{7} ?$$
Additive inverse of $$\frac{-3}{9}$$ is $$\frac{3}{9}$$.
Additive inverse of $$\frac{-9}{11}$$ is $$\frac{9}{11}$$.
Additive inverse of $$\frac{5}{7}$$ is $$\frac{-5}{7}$$.

NCERT In-text Question Page No. 187

Question 1.
Find
(i) $$\frac{7}{9}-\frac{2}{5}$$
(ii) $$2 \frac{1}{5}-\left(\frac{-1}{3}\right)$$
(i) $$\frac{7}{9}-\frac{2}{5}$$
L.C.M of 9 and 5 is 45.

(ii) $$2 \frac{1}{5}-\left(\frac{-1}{3}\right)$$
L.C.M of 5 and 3 is 15.

NCERT In-text Question Page No. 188

Question 1.
What will be
(i) $$-\frac{3}{5} \times 7$$
(ii) $$-\frac{6}{5} \times(-2) ?$$
(i) $$-\frac{3}{5} \times 7=\frac{(-3) \times 7}{5}=\frac{-21}{5}=-4 \frac{1}{5}$$
(ii) $$\frac{-6}{5} \times(-2)=\frac{(-6) \times(-2)}{5}=\frac{12}{5}=2 \frac{2}{5}$$

Question 2.
(i) $$\frac{-3}{4} \times \frac{1}{7}$$
(ii) $$\frac{2}{3} \times \frac{-5}{9}$$
(i) $$\frac{-3}{4} \times \frac{1}{7}=\frac{-3 \times 1}{4 \times 7}=\frac{-3}{28}$$
(ii) $$\frac{2}{3} \times \frac{-5}{9}=\frac{-2 \times 5}{3 \times 9}=\frac{-10}{27}$$

NCERT In-text Question Page No. 189

Question 1.
What wTill be the reciprocal of  and  ?
Reciprocal of $$\frac{-6}{11}$$ is $$\frac{-11}{6}$$
Reciprocal of $$\frac{-8}{5}$$ is $$\frac{-5}{8}$$

NCERT In-text Question Page No. 190

Question 1.
Find
(i) $$\frac{2}{3} \times \frac{-7}{8}$$
(ii) $$\frac{-6}{7} \times \frac{5}{7}$$
(i) $$\frac{2}{3} \times \frac{-7}{8}=\frac{-7}{12}$$
(ii) $$\frac{-6}{7} \times \frac{5}{7}=\frac{-30}{49}$$