GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 2
CANCEL — Tokens, subtraction and additive inverse
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with your own idea.
How can you remove 18 positive tokens when you start with only 7?
Write or sketch a prediction before you read on. Use the model below to test it.
Understand
A +1 token and a −1 token form a zero pair. Adding a zero pair changes the representation, not the value. Subtracting an integer has the same effect as adding its additive inverse.
Key Ideas
The additive inverse of a negative integer is positive. Zero is its own additive inverse.
Visualise
Zero-pair subtraction
Start with the given positive tokens.
Method
Represent the starting value. Add only the zero pairs needed. Remove the requested tokens and count what remains.
Worked Example
Given
7 positive tokens; subtract 18 positive tokens.
To Find
The value of 7 − 18.
Reasoning
A zero pair has value zero.
Solution
- Add 11 zero pairs: there are 18 positive and 11 negative tokens.
- Remove all 18 positive tokens.
- 11 negative tokens remain.
Result
7 − 18 = −11.
AIMS Method
- A — Attempt independently
Predict before calculating. - I — Investigate the idea
Identify signs, order and operation. - M — Make connections
Connect movements, tokens and expressions. - S — Scrutinise your reasoning
Check the sign, value and original conditions.
Think first. Use AI purposefully. Verify always.
Focused Practice
Explain 4 − (−12) using tokens.
Check & Feedback
Explain the key idea to someone who made the mistake described above. Use a model or a checked example.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Operations with Integers · printed page 28