Adding and subtracting rational numbers: Class 7 practice
Rational numbers add like fractions, but signs matter: rewrite each with a common positive denominator, add the signed numerators, then simplify.. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Integer addition
- LCM
The idea behind adding and subtracting rational numbers
Rational numbers add like fractions, but signs matter: rewrite each with a common positive denominator, add the signed numerators, then simplify.
Step-by-step method
- Write each number with a positive denominator.
- Convert to the LCM of the denominators.
- Add or subtract signed numerators.
- Simplify.
Worked example 1 (Basic)
Find 5/8 + (-3/6).
- LCM 24
- 15/24 + (-12/24)
- = 3/24 = 1/8
- Answer: 1/8
Worked example 2 (Standard)
Find 9/3 + (1/9).
- LCM 9
- 27/9 + (1/9)
- = 28/9 = 28/9
- Answer: 28/9
Worked example 3 (Challenge)
Find -4/5 − (2/5).
- LCM 5
- -4/5 − (2/5)
- = -6/5 = -6/5
- Answer: -6/5
Common mistakes and misconceptions
- Losing a negative sign
- Subtracting a negative incorrectly
Practice questions
- (Basic) Find 2/10 + (5/10).
- (Basic) Find 5/8 + (-5/10).
- (Standard) Find -9/9 + (8/4).
- (Standard) Find 9/5 + (-5/6).
- (Challenge) Find -5/3 − (-3/2).
- (Challenge) Find 2/11 − (6/2).
Answer key with full working
- Q1: LCM 10 → 2/10 + (5/10) → = 7/10 = 7/10 → Answer: 7/10
- Q2: LCM 40 → 25/40 + (-20/40) → = 5/40 = 1/8 → Answer: 1/8
- Q3: LCM 36 → -36/36 + (72/36) → = 36/36 = 1 → Answer: 1
- Q4: LCM 30 → 54/30 + (-25/30) → = 29/30 = 29/30 → Answer: 29/30
- Q5: LCM 6 → -10/6 − (-9/6) → = -1/6 = -1/6 → Answer: -1/6
- Q6: LCM 22 → 4/22 − (66/22) → = -62/22 = -31/11 → Answer: -31/11
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 adding and subtracting 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.