Example 1
Is -7 a rational number?
- Write -7 as a fraction with denominator 1: -7/1.
- Here p = -7 and q = 1, both are integers and q is not zero.
Answer: Yes
📗 Class 7 maths · session 8 of 12 · 60 minutes · 🎁 free with an account
Rational numbers
Welcome aboard Captain Calc's math mission on rational numbers! Today we will explore numbers in p/q form, compare them, and master fractions with positive and negative signs.
🤖 Written with Google's Gemini AI. A second AI solved all 55 questions without seeing the answers, and both agree. One of our teachers has not read it yet, so if something looks wrong, please tell us.
A complete lesson · 60 minutes
Teach it, see it, practise it, all on this page.
Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.
- Warm-up3 min
- Warm-up games5 min
- Understanding Rational Numbers8 min
- Equivalent Forms and Standard Form7 min
- Comparing Rational Numbers7 min
- Operations on Rational Numbers7 min
- Captain Calc's Standard Form Converter6 min
- Hero Number Line Comparison5 min
- Energy Zap Operations6 min
- Quiz5 min
- Set the project1 min
By the end you can
- Define rational numbers in p/q form.
- Convert rational numbers to standard form.
- Compare rational numbers using common denominators.
- Add, subtract, multiply, and divide rational numbers.
Before you start
- Operations on positive and negative integers.
- Basic operations on proper and improper fractions.
Have ready
- Notebook and pencil for rough work.
- Ruler for drawing number lines.
Class 7 · CBSE, ICSE and state boards
Warm-up · think first
Captain Calc has a debt of ₹3 divided equally among 4 friends. Express each friend's share in rupees as a fraction.
Show the answer
-3/4 because debt is represented as negative 3 divided into 4 equal parts.
Teacher tip: Ask students what negative money values represent in real life.
🎮 Warm-up games · 5 quick games
Play with Captain Calc
Six minutes with Captain Calc. Vote, say why, then show the answer.
- Which one does not belong with the others? (-3/4 · 6/-8 · -9/12 · -4/5)
Answer: -4/5 because all the other numbers are equivalent to -3/4. - Would you rather gain ₹1/2 or lose ₹1/4? (Gain ₹1/2 · Lose ₹1/4)
Answer: Gain ₹1/2 because gaining money adds a positive value to your total. - An integer is a rational number. (Always · Sometimes · Never)
Answer: Always. Any integer n can be written in p/q form as n/1, where 1 is not zero. - I am a negative rational number in standard form. My denominator is 5 and my numerator is -2. What number am I?
Answer: -2/5 - How are rational numbers useful when sharing money or measuring temperatures?
Answer: They allow us to show parts of whole quantities with positive or negative direction, like temperature below zero or splitting costs.
Part 1 of 4 · learn, see, practise
Understanding Rational Numbers
A rational number is any number that can be written in the form p/q, where p and q are integers and q is not zero.
If p and q have the same sign, the rational number is positive. If they have opposite signs, it is negative.
All integers and fractions are rational numbers.
Example 2
Express 0 as a rational number with denominator 5.
- Zero divided by any non-zero integer equals zero.
- Write 0 with denominator 5 as 0/5.
Answer: 0/5
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Core
Stretch 🔥
Stretch 🔥
Answers (for the teacher)
- -9/1
- No
- positive
- 0
- 15/-3
- -15/-20
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Unlocking the rest of this lesson gives you:
- Part 2: Equivalent Forms and Standard Form, with practice at three levels
- Part 3: Comparing Rational Numbers, with practice at three levels
- Part 4: Operations on Rational Numbers, with practice at three levels
- Class activity 1: Captain Calc's Standard Form Converter
- Class activity 2: Hero Number Line Comparison
- Class activity 3: Energy Zap Operations
- A 10-question quiz
- After-class project: Captain Calc's City Budget Mission
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
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FAQ
Rational numbers: questions
What is a rational number in Class 7 maths?
A rational number is any number that can be expressed in p/q form where p and q are integers and q is not zero.
Is every fraction a rational number?
Yes, every fraction is a rational number, but rational numbers also include negative fractions and negative integers.
Why is 5/0 not a rational number?
Division by zero is not defined in mathematics, so the denominator q can never be zero.
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