Finding rational numbers between two numbers: Class 8 practice
Between any two rational numbers there are infinitely many more. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Equivalent fractions
The idea behind finding rational numbers between two numbers
Between any two rational numbers there are infinitely many more. Write both with a common (larger) denominator and pick fractions in between, or take the average (a + b)/2.
Step-by-step method
- Write both numbers with a common denominator.
- Multiply numerator and denominator by 10 if you need more room.
- List fractions whose numerators lie strictly between.
Worked example 1 (Basic)
Find the rational number halfway between 3/5 and 2/3.
- (3/5 + 2/3) ÷ 2
- Answer: 19/30
Worked example 2 (Standard)
Find 3 rational numbers between 1/6 and 2/6.
- Common denominator 360: 60/360 and 120/360
- Pick numerators between
- Answer: 5/24, 1/4, 7/24
Worked example 3 (Challenge)
Find 5 rational numbers between 1/6 and 1/3.
- Common denominator 180: 30/180 and 60/180
- Pick numerators between
- Answer: 7/36, 2/9, 1/4, 5/18, 11/36
Common mistakes and misconceptions
- Including the end points
- Not using a common denominator
Practice questions
- (Basic) Find the rational number halfway between 1/5 and 3/4.
- (Basic) Find the rational number halfway between 3/4 and 5/6.
- (Standard) Find 3 rational numbers between 1/2 and 7/8.
- (Standard) Find 3 rational numbers between 1/8 and 3/6.
- (Challenge) Find 5 rational numbers between 1/6 and 3/6.
- (Challenge) Find 5 rational numbers between 5/7 and 3/4.
Answer key with full working
- Q1: (1/5 + 3/4) ÷ 2 → Answer: 19/40
- Q2: (3/4 + 5/6) ÷ 2 → Answer: 19/24
- Q3: Common denominator 160: 80/160 and 140/160 → Pick numerators between → Answer: 19/32, 11/16, 25/32
- Q4: Common denominator 480: 60/480 and 240/480 → Pick numerators between → Answer: 7/32, 5/16, 13/32
- Q5: Common denominator 360: 60/360 and 180/360 → Pick numerators between → Answer: 2/9, 5/18, 1/3, 7/18, 4/9
- Q6: Common denominator 280: 200/280 and 210/280 → Pick numerators between → Answer: 201/280, 29/40, 41/56, 103/140, 26/35
Syllabus note
This skill is listed under "Rational Numbers" for Class 8 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is finding rational numbers between two numbers in?
"Rational Numbers", Class 8 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.