# NCERT Solutions For Class 9 Math | Exercise 1.1

###### Chapter 1 | Number Systems | 4 Questions

Detailed solution to all exercise questions of NCERT book for CBSE Class 9 Math in Chapter 1 - Number Systems - exercise 1.1. The exercise comprises 4 questions.

Key concepts covered in this exercise include properties of rational numbers, natural numbers, whole numbers, and integers. Finding rational numbers between two numbers. Expressing rational numbers in the form $\frac{p}{q}$, where p and q are integers and q is not zero.

1. Is 0 a rational number? Can you write it in the form $\frac{p}{q}$, where p and q are integers and q ≠ 0?

Zero is a rational number.

Zero can be written in the form $\frac{p}{q}$, where p and q are integers and q ≠ 0 as $\frac{0}{1}$

2. Find six rational numbers between 3 and 4.

Step 1: To obtain six rational numbers between 3 and 4, we must multiply and divide both 3 and 4 by 7.
Why 7?
By multiplying and dividing by 7, we are increasing the gap between 3 and 4 by 7 times. So, 6 numbers can be fitted between them.
So, the rule is always to multiply and divide it by a number that is 1 more than the number of numbers to be fitted between the given numbers.

3 will consequently become $\frac{21}{7}$ and 4 will become $\frac{28}{7}$
Essentially, now we have to find 6 numbers between $\frac{21}{7}$ and $\frac{28}{7}$
Notice that between 21 and 28 we can fit 6 integers.

Step 2: Write integers from 22 to 27 and divide them by 7 to get the 6 numbers between 3 and 4.
The numbers are therefore, $\frac{22}{7}$, $\frac{23}{7}$, $\frac{24}{7}$, $\frac{25}{7}$, $\frac{26}{7}$, and $\frac{27}{7}$.

3. Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.

Step 1: To obtain five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$, we must multiply and divide both $\frac{3}{5}$ and $\frac{4}{5}$ by 6.
Why 6?
By multiplying and dividing by 6, we are increasing the gap between $\frac{3}{5}$ and $\frac{4}{5}$ 6 times. So, 5 numbers can be fitted between them.

$\frac{3}{5}$ will consequently become $\frac{18}{30}$ and $\frac{4}{5}$ will become $\frac{24}{30}$
Essentially, now we have to find 6 numbers between $\frac{18}{30}$ and $\frac{24}{30}$
Notice that between 18 and 24 we have 5 integers.

Step 2: Write integers from 19 to 23 and divide them by 30 to get the 5 numbers between $\frac{3}{5}$ and $\frac{4}{5}$.
The numbers are therefore, $\frac{19}{30}$, $\frac{20}{30}$, $\frac{21}{30}$, $\frac{22}{30}$, and $\frac{23}{30}$.

4. State whether the following statements are true or false with reasons.

i): Every natural number is a whole number.
TRUE. Whole numbers include 0 as well as all the natural numbers. So, every natural number is a whole number.

ii): Every integer is a whole number.
FALSE. Negative integers are not whole numbers.
However, note that all whole numbers are integers.

iii): Every rational number is a whole number.
FALSE. Whole numbers are non-negative numbers.
Negative rational numbers and rational numbers whose denominators ≠ 1 are not whole numbers.

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