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Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to use a pattern to justify a negative product.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Multiplication by whole numbers and signed addition.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Explain why (−4)(−3) = 12 using the products (−4)×2, (−4)×1, and (−4)×0.
Why this math matters
The sign rules for multiplication preserve distributivity and consistent numerical patterns. Track sign and magnitude separately when evaluating a long product.
Set up the model
A useful answer starts with clear assumptions:
- Standard arithmetic distributivity applies.
- Each successive second factor decreases by one.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Use a pattern to justify a negative product
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Explain why (−4)(−3) = 12 using the products (−4)×2, (−4)×1, and (−4)×0.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
(−4)×2 = −8; (−4)×1 = −4; (−4)×0 = 0
Each one-step decrease in the second factor increases the product by four.
Apply the relationship
(−4)×(−1) = 4; (−4)×(−2) = 8
Continue the same increase across zero rather than changing the rule.
Check and interpret
(−4)×(−3) = 12
Two negative factors produce a positive product, consistent with the pattern.
The result
(−4)×(−3) = 12
Two negative factors produce a positive product, consistent with the pattern.
Common mistakes to catch
- Two negative terms being added remain negative; the positive result rule concerns multiplication.
- Ignoring the number of negative factors can reverse the final sign.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Evaluate (−7)(5).
Show a hint
Exactly one factor is negative.
Reveal answer and explanation
−35
Seven negative groups of magnitude five give a negative product of magnitude 35.
Practice 2
Evaluate (−2)(−3)(−4).
Show a hint
Multiply two factors first, then track the remaining sign.
Reveal answer and explanation
−24
(−2)(−3) = 6, and 6(−4) = −24; an odd number of negative factors gives a negative product.
Take the idea with you
Track sign and magnitude separately when evaluating a long product.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Check division using a missing factor
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