Class9 mathematics

CBSE 9 th standard Mathematics Chapter 1 Number System Example 1 Are the following statements true or false? Give reasons for your answers Every whole number is a natural number. Every integer is a rational number Every rational number is an integer Solution: i. False, because zero is a whole number but not a natural number. ii. True. because every integer m can be expressed in the form m/1 and so it is a rational number. False because 3/5 is not integer. Example 2 Solution 1 Find five rational numbers between 1 and 2 Take 1 as r and 2 as s add r and s and divide the sum by 2 that is (r+s)/2 = (1+2)/2 Therefor 3/2 is a number between 1 and 2 Other four numbers are 5/4, 11/8,13/8 and 7/4 Solution 2 Find five rational numbers between 1 and 2 Convert 1 and 2 into fraction form 1/1 and 2/1 If they ask 5 rational numbers multiply numerator and denominator of both fractions by 6 5 + 1 = 6 1/1 × 6/6 and 2/1 ×6/6 That is 6/6 and 12/6 Now write 5 rational numbers between them they are 7/6 , 8/(6 ) , 9/6 , 10/6, ( 11)/6 they can be written in simplified way Final Answer is 7/6 , 4/(3 ) , 3/2 , 5/3, ( 11)/6 Exercise 1.1 Question number 1 Is zero a rational number? Can you write it in the form of p/q where p and q are integers and q ≠ 0 Answer Yes 0 is a rational number since q ≠ 0 It can be written in p/q form as 0/1 , 0/2 ,0/3,0/4 etc Question Number 2 Find six rational numbers between 3 and 4 Convert 3 and 4 into fraction form 3/1 and 4/1 If they ask 6 rational numbers multiply numerator and denominator of both fractions by 7 6 + 1 = 7 3/1 × 7/7 and 4/1 ×7/7 That is 21/6 and 28/6 Now write 6 rational numbers between them They are 22/7 , 23/7 , 24/7 , 25/7, ( 26)/7 27/7 Final Answer is 22/7 , 23/7 , 24/7 , 25/7, ( 26)/7 27/7 Question number 3 Find five rational numbers between 3/5 and 4/5 Solution Since rational numbers have common denominator 3/5 and 4/5 If they ask 5 rational numbers multiply numerator and denominator of both fractions by 6 5 + 1 = 6 3/5 × 6/6 and 4/5 ×6/6 That is 18/30 and 24/30 Now write 5 rational numbers between them They are 19/30 , 20/30 , 21/30 , 22/30, ( 23)/( 30) write them in simplified way Final Answer is 19/30 , 2/3 , 7/10 , 11/15, ( 23)/( 30) Question number 4 State whether the following statements are true or false. Give reasons for your answer Every natural number is whole number. True. Since all natural numbers are included in whole number Every integer is a whole number. False. Negative integers are not whole numbers Every rational number is a whole number. False. All fractional numbers are included in rational number not in whole number. Extra questions Find five rational numbers between 2/3 and 3/4 Solution Since denominators are not common, convert them into common denominator 2/3 × 4/4 3/4 ×3/3 8/12 9/12 Multiply numerator and denominator of both fractions by 6 5 + 1 = 6 8/12 × 6/6 and 9/12 ×6/6 That is 48/72 and 54/72 Now write 5 rational numbers between them They are 49/72 , 50/72 , 51/72 , 52/72, ( 53)/( 72) write them in simplified way Final Answer is 49/72 , 25/36 , 17/24 , 13/18, ( 53)/( 72) 2.Find six rational numbers between 1/7 and 1/5 Solution Since denominators are not common, convert them into common denominator 1/7 × 5/5 1/5 ×7/7 5/35 7/35 Multiply numerator and denominator of both fractions by 7 6 + 1 = 7 5/35 × 7/7 and 7/35 ×7/7 That is 35/245 and 49/245 Now write 6 rational numbers between them They are 36/245 , 37/245 , 38/245 , 39/245, ( 40)/( 245) ,( 41)/( 245) write them in simplified way Final Answer is 36/245 , 37/245 , 38/245 , 39/245, ( 8)/( 49) ,( 41)/( 245) Solve Find six rational numbers between -2 and 1/5 Find six rational numbers between 1/2 and 2/3 Find six rational numbers between -1 and 1 Find six rational numbers between 3/11 and 1/3