NCERT Solutions For Class 9 Math | Exercise 1.1

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})

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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}).
   

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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}).
   

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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.