# Worksheet on Finding Rational Numbers between Two Rational Numbers

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Worksheet for finding Rational Numbers between Two Rational Numbers covers the questions for finding Rational Numbers between Two Rational Numbers having either the same or different denominators. Check out Rational Numbers Worksheets to get conceptual knowledge on several concepts underlying.

1. Find out the Rational Numbers between 1/4 and 5/3?

Solution:

Check the denominators of given Rational Numbers.

If they aren’t the same firstly equate the denominators by finding the LCM.

LCM(4, 3) = 12

1/4 =1*3/4*3 = 3/12

5/3 = 5*4/3*4 = 20/12

Therefore, Rational Numbers between 4/12, 5/12, 6/12, 7/12, 8/12, 9/12, 10/12, 11/12, 12/12, 13/12, 14/12, 15/12, 16/12, 17/12, 18/12, 19/12.

2. Find at least 5 Rational Numbers lying between 1/3 and 4/3?

Solution:

Since the difference between numbers is small it is hard to write rational numbers between them. So multiply the given numbers with multiples of 10.

1/3 = 1*10/3*10 = 10/30

4/3 = 4810/3810 = 40/30

Therefore, the 5 Rational Numbers between 10/30 an 40/30 is 11/30, 12/30, 13/30, 14/30, 15/30.

3. What is the Property of inserting infinitely many rational numbers between Two Rational Numbers?

Solution:

Dense Property

4. There exists always a Rational Number Between Two Distinct Rational Numbers. Is it True or False?

Solution:

True

5. Find 4 Rational Numbers between 2/5 and 7/5?

Solution:

Since the denominators are the same and numerators differ by a large value you can simply increment the numerator by 1 and keep the denominator unchanged.

3/5, 4/5, 5/5, 6/5.

6. Find a Rational Number between 4/3 and 5/4?

Solution:

You can find a Rational Number between 4/3 and 5/4 using the average.

= (4/3+5/4)/2

=(16+15) /12)/2

= (31/12)/2

= 31/12*1/2

= 31/24

7. Find out 4 Rational Number between -1/3 and 1/4?

Solution:

Since the Denominators are not the same find out the LCM first

LCM(3,4) = 12

-1/3 = -1*4/3*4 = -4/12

1/4 = 1*3/4*3 = 3/12

Rational numbers between -1/3 and 1/4 are -3/12, -2/12, -1/12, 0.

8. Find Rational Numbers between 3/4 and 8/4?

Solution:

Since the denominators are the same and numerators differ by a large value you can simply increment the numerator by 1 and keep the denominator unchanged.

Rational Numbers between 3/4 and 8/4 is 4/4 5/4, 6/4, 7/4.