RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS WORKSHEET

Problem 1 : 

Find a rational number between 3/4 and 4/5.

Problem 2 :

Find two rational numbers between -3/5 and 1/2.

Problem 3 :  

Find one rational number between 4/3 and 2/5. 

Problem 4 :  

Find one rational number between -2/7 and 5/6. 

Problem 5 :

Find two rational numbers between 2/7 and 3/5. 

Problem 6 :

Find two rational numbers between -1/6 and 1/3.

Problem 7 :

Find three rational numbers between 1/4 and 1/2.

Problem 8 :

Find three rational numbers between 7/10 and 2/3. 

Solutions

Problem 1 :

Find a rational number between 3/4 and 4/5.

Solution : 

Formula Method : 

Let a = 3/4 and b = 4/5.

Let q be the rational number between 3/4 and 4/5. 

Then, we have 

q  =  1/2 x (a + b)

q  =  1/2 x (3/4 + 4/5)

q  =  1/2 x (15 + 16) / 20

q  =  1/2 x 31/20

q  =  31/40

So, the rational number between 3/4 and 4/5 is 31/40.

Same Denominator Method :

Let a = 3/4 and b = 4/5.

L.C.M of the denominator (4, 5) is 20.

So, we can write "a" and "b" as given below

a  =  3/4 x 5/5  =  15/20

and

b  =  4/5 x 4/4  =  16/20 

To find a rational number between 15/20 and 16/20 , we have to multiply the numerator and denominator by 10.

Then, we have

15/20 x 10/10  =  150/200

16/20 x 10/10  =  160/200

Therefore, the rational numbers between 150/200 and 160/200 are 151/200, 152/200, 153/200, 154/200, 155/200, 156/200, 157/200, 158/200 and 159/200.

Problem 2 :

Find two rational numbers between -3/5 and 1/2.

Solution : 

Let a = -3/5 and b = 1/2.

Let q₁ and q₂ be the rational number between -3/5 and 1/2. 

First, let us get q₁.

q₁  =  1/2 x (a + b)

q₁  =  1/2 x (-3/5 + 1/2)

q₁  =  1/2 x (-6 + 5) / 10

q₁  =  1/2 x (-1/10)

q₁  =  -1/20

Now, let find q₂.

q₂  =  1/2 x (a + q1)

q₂  =  1/2 x (-3/5 - 1/20)

q₂  =  1/2 x (-12 - 1) / 20

q₂  =  1/2 x (-13/20)

q₂  =  -13/40

So, the two rational number are -1/20 and -13/40.

Note : 

The two rational numbers can be inserted as 

-3/5 < -13/40 < -1/20 < 1/2

Solution for Other Problems :

3)  13/15

4)  23/84

5)  31/70 and 51/140

6)  -1/24 and 1/12

7)  3/8, 5/16, 9/32

8)  41/60, 83/120, 167/240

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