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.

Answer:

Yes, \(\frac{2}{-3}\) is a rational number,

∵ 2 and -3 are integers and -3 ≠ 0.

Question 2.

List ten rational numbers.

Answer:

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:

Answer:

Question 2.

Is 5 a positive rational number?

Answer:

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.

Answer:

\(\frac{1}{7}, \frac{3}{8}, \frac{5}{17}, \frac{2}{9}\) and \(\frac{5}{18}\) and are positive rational numbers.

NCERT In-text Question Page No. 176

Question 1.

Is -8 a negative rational number?

Answer:

(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.

Answer:

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) \(\frac{-2}{-9}\)

Answer:

(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) \(\frac{-12}{18}\)

Answer:

(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 \(\frac{-3}{8}\)

Answer:

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) \(\frac{-19}{5}+\frac{-7}{5}\)

Answer:

Question 2.

Find:

(i) \(\frac{-3}{7}+\frac{2}{3}\)

(ii) \(\frac{-5}{6}+\frac{-3}{11}\)

Answer:

(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 \(\frac{3}{9} ?, \frac{-9}{11} ?, \frac{5}{7} ?\)

Answer:

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) \(2 \frac{1}{5}-\left(\frac{-1}{3}\right)\)

Answer:

(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) \(-\frac{6}{5} \times(-2) ?\)

Answer:

(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) \(\frac{2}{3} \times \frac{-5}{9}\)

Answer:

(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 \(\) ?

Answer:

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) \(\frac{-6}{7} \times \frac{5}{7}\)

Answer:

(i) \(\frac{2}{3} \times \frac{-7}{8}=\frac{-7}{12}\)

(ii) \(\frac{-6}{7} \times \frac{5}{7}=\frac{-30}{49}\)