GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 2
REVERSE — Division as reverse multiplication
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with your own idea.
Which number must multiply 25 to produce −100?
Write or sketch a prediction before you read on. Use the model below to test it.
Understand
Division asks for a missing factor. Check a quotient by multiplying it by the divisor. Division by zero is undefined, and dividing two integers need not give an integer.
Key Ideas
Do not swap dividend and divisor. For example, 8 ÷ 2 = 4 but 2 ÷ 8 = .
Visualise
Division: find the missing factor
Method
Rewrite the division as a missing-factor multiplication. Find the factor and check the product. Always check that the divisor is nonzero.
Worked Example
Given
−100 divided by 25.
To Find
The quotient (−100) ÷ 25.
Reasoning
25 × q = −100.
Solution
- 25 × 4 = 100.
- 25 × (−4) = −100.
- Check: divisor × quotient = dividend.
Result
(−100) ÷ 25 = −4.
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
Find (−96) ÷ (−12), then verify.
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 38