Comparing rational numbers: Class 7 practice
To compare rational numbers, write them with positive denominators and a common denominator, then compare numerators. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Integers
- Equivalent fractions
The idea behind comparing rational numbers
To compare rational numbers, write them with positive denominators and a common denominator, then compare numerators. Any negative number is less than any positive number, and between two negatives the one further from zero is smaller.
Step-by-step method
- Make denominators positive.
- Use the LCM as common denominator.
- Compare numerators, remembering signs.
Worked example 1 (Basic)
Compare -4/6 and 4/3.
- Common denominator 6: -4/6 and 8/6
- -4 < 8
- Answer: -4/6 < 4/3
Worked example 2 (Standard)
Compare -2/6 and -6/4.
- Common denominator 12: -4/12 and -18/12
- -4 > -18
- Answer: -2/6 > -6/4
Worked example 3 (Challenge)
Compare -5/3 and -7/9.
- Common denominator 9: -15/9 and -7/9
- -15 < -7
- Answer: -5/3 < -7/9
Common mistakes and misconceptions
- Thinking −3/4 < −4/5
- Ignoring the sign
Practice questions
- (Basic) Compare 7/5 and 4/9.
- (Basic) Compare 2/6 and -8/4.
- (Standard) Compare -5/6 and -5/5.
- (Standard) Compare -3/2 and -7/2.
- (Challenge) Compare -7/2 and -5/3.
- (Challenge) Compare -2/5 and -2/3.
Answer key with full working
- Q1: Common denominator 45: 63/45 and 20/45 → 63 > 20 → Answer: 7/5 > 4/9
- Q2: Common denominator 12: 4/12 and -24/12 → 4 > -24 → Answer: 2/6 > -8/4
- Q3: Common denominator 30: -25/30 and -30/30 → -25 > -30 → Answer: -5/6 > -5/5
- Q4: Common denominator 2: -3/2 and -7/2 → -3 > -7 → Answer: -3/2 > -7/2
- Q5: Common denominator 6: -21/6 and -10/6 → -21 < -10 → Answer: -7/2 < -5/3
- Q6: Common denominator 15: -6/15 and -10/15 → -6 > -10 → Answer: -2/5 > -2/3
Syllabus note
This skill is listed under "Rational Numbers" for Class 7 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 comparing rational numbers in?
"Rational Numbers", Class 7 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.