# CHAPTER – 9 Rational Numbers

## Exercise – 9.1

Q1. List five rational numbers between:

• -1 and 0

Solution:-

The five rational numbers between 1- and 0 are,

= -1<(-2/3)<(-3/4)<(-4/5)<(-5/6)<(-6/7)<0

• -2 and 1

Solution:-

The first five rational numbers between -2 and 1- are ,

= -2<(-8/7)<(-9/8)<(-10/9)<(-11/10)<(-12/11)<-1

• -4/5 and -2/3

Solution:-

The first five rationals numbers between -4/5 and -2/3 are,

= -4/5<(-13/12)<(-14/13)<(-15/14)<(-16/15)<(-17/16)<-2/3

• -1/2 and 2/3

Solution:-

The first five rationals numbers between -1/2 and 2/3 are,

= -1/2<(-1/6)<(0)<(1/3)<(1/2)<(20/36)<2/3

Q2. Write four more rationals numbers in each of the following patterns:

• -3/5, -6/10, -9/15,-12/20……

Solution:-

=  -15/25 , -18/30 , -21/35 , -24/40.

• -1/4 , -2/8 , -3/12 , …….

Solution:-

= -4/16 ,

-5/20 , -6/24 , -7/28 …….

• -1/6 , 2/-12 , 3/-18 , 4/-24

Solution:-

= 5/-30 , 6/-36 , 7/-42 , 8/-48….

• -2/3 , 2/-3 , 4/-6 , 6/-9 …..

Solution:-

= 8/-12 , 10/-15 , 12/-18 , 14/-21 …..

Q3. Give four rational numbers  equivalent to:

• -2/7

Solution:-

= -4/14 , -6/21 , -8/28 , -10/35

• 5/-3

Solution:-

= 10/-6 , 15/-9 , 20/-12 , 25/-15

• 4/9

Solution:-

= 8/18, 12/27, 16/36, 20/45

Q4. Draw the number line and represent the following rational numbers on it:

• 3/4

Solution:-

We know that 3/4 is grater than 0 and less than 1 .

It lies between 0 and 1 It can be represented on number line as,

• -5/8

Solution: –

We know that -5/8 is less than the 0 and greater than -1

It lies between 0 and -1 It can be represented on number line as,

• -7/4

Solution:-

Now above question can be written as,

= (-7/4) =

We know that (-7/4) is less than -1 and greater than -2

It lies between -1 and -2 .It can be represented on number line as,

• 7/8

Solution:-

We know that 7/8 is greater than 0 and less than 1.

It lies between 0 and 1 It can be represented on number line as,

Q5. The points P,Q,R,S,,T,U,A and B on the number line are such that, TR= RS = SU and AP = PQ = QB . Name the rational numbers represented by P,Q,R and S .

Solution:-

By observing the figure we can say that,

The distance between A and B = 1 unit

And it is divided into 3 equal parts = AP = PQ = QB = 1/3

P = 2+(1/3)

= (6+1)/3

= 7/3

Q= 2+(2/3)

= (6+2)/3

= 8/3

Similarly,

The distance between U and T = 1 unit.

And it is divided into 3 equal parts = TR = RS = SU = 1/3

R = -1 -(1/3)

= (-3-1) /3

= -4/3

S = -1 – (2/3)

= -3 -2)/3

= -5/3

Q6. Which of the following pairs represent the same rational number?

• (-7/21) and (3/9)

Solution:-

We have to check if the given pair represents the same rational numbers.

Then,

-7/21 = 3/9

-1/3 = 1/3

-7/21 not equal to 3/9

So, the given pair does not represent the same rational number.

• (-16/20) and (20/-25)

Solution:-

We have to check if the given pair represents the same rational numbers .

Then,

-16/20 = 20/-25

-4/5 =  -4/5

=16/20 = 20/-25

So, the given pair represents the same rational numbers.

Then,

-2/3 = 2/3

-2/3 = 2/3

So, the given pair represents the same rational numbers

(iv) (-3/5) and (-12/20)

Solution:-

We have to check if the given pair represents the same rational numbers .

Then,

-3/5 = -12/20

-3/5 = -3/5

-3/5 = -3/5

-3/5 = -12/20

So, the given pair represents the same rational numbers.

• (8/-5) and (-24/15)

Solution:-

We have to check if the given pair represents thee same rational numbers.

Then,

8/-5 = -24/15

8/-5 = -8/5

8/-5 = -24/15

So, the given pair represents the same rational numbers

• (1/3) and (-1/9)

Solution:-

We have to check if the given pair represents the same rational numbers.

Then,

1/3 = -1/9

1/3 not equal to -1/9

So, the given pair does not represents the same rational number.

• (-5/-9) and (5/-9)

Solution:-

We have to check if the the given pair represents the same rational number.

Then,

-5/-9 = 5/-9

5/9  not equal to -5/9

So, the given pairs does not represent the same rational numbers

Q7. Rewrite the following rational numbers in the simplest form:

• -8/6

Solution:-

The given rational numbers can be simplified further,

Then,

= -4/3 [ Divide both numerator and denominator by 2]

• 25/45

Solution:-

The given rational numbers can be simplified further,

Then,

= 5/9 [ Divide both numerator and denominator by 5]

• -44/72

Solution:-

The given rational numbers can be simplified further,

Then,

= -11/8 [ Divide both numerator and denominator by 4 ]

• -8/10

Solution:-

The given rational numbers can be simplified further,

Then,

= -4/5 [ Divide both numerator and denominator by 2]

Q8. Fill in the blanks with the correct symbol out of <,> and =.

• -5/7[ ] 2/3

Solution:-

-5/7 [<] 2/3

• -4/5[] -5/7

Solution:-

-4/5 [<] -5/7

• -7/8 [] 14/-16

Solution:-

-7/8 [ = ] 14/-16

• -8/5 [] -7/4

Solution:-

-8/5 [>] -7/4

• 1/3 [] -1/4

Solution:-

1/3 [<] -1/4

• 5/-11 [] -5/11

Solution:-

5/-11 [ = ] -5/11

• 0 [] -7/6

Solution:-

= 0 [>] -7/6

Q9. Which is greater in each of the following

• 2/3 , (5/2)

Solution:-

2/3 < 5/2

• -5/6 , (-4/3)

Solution:-

-5/6 > -12/6

• -3/4 , 2/-3

Solution:-

-3/4 < 2/-3

• -1/4 , 1/4

Solution:-

-1/4 < 1/4

Q10. Write the following rational numbers in ascending order:

• -3/5 , -2/5 , -1/5

Solution:-

(-3/5) < (-2/5) < (-1/5)

• -1/3 , -2/9 , -4/3

Solution:-

To convert the given rational numbers into like fractions we have to find LCM,

LCM of 3,9,3 is 9

(-4/3) < (-1/3) < (-2/9).

• -3/7 , -3/2 , -3/4

Solution:-

To convert the given rational numbers into like fractions we have to find LCM,

LCM of 7,2 and 4 is 28

(-3/2) < (-3/4) < (-3/7)