Learn with Amar
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 check division using a missing factor.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Signed multiplication.
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
Find (−42)/(−6) and explain its sign without memorizing a separate division rule.
Why this math matters
A quotient is the factor that reproduces the dividend when multiplied by the nonzero divisor. Verify a quotient by multiplying it by its divisor, especially when several minus signs appear.
Set up the model
A useful answer starts with clear assumptions:
- The divisor is nonzero.
- The slash represents division of the entire signed numbers.
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.
Check division using a missing factor
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Find (−42)/(−6) and explain its sign without memorizing a separate division rule.
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
(−6)q = −42
Translate the quotient into an equivalent missing-factor question.
Apply the relationship
q = 7 because (−6)(7) = −42
A negative factor needs a positive partner to produce a negative product.
Check and interpret
(−42)/(−6) = 7
The quotient is positive when dividend and divisor have the same sign.
The result
(−42)/(−6) = 7
The quotient is positive when dividend and divisor have the same sign.
Common mistakes to catch
- A negative divisor alone does not determine the sign; compare both signs.
- Division by zero cannot be justified by the sign rules.
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 45/(−9).
Show a hint
Find the number that −9 multiplies to make 45.
Reveal answer and explanation
−5
(−9)(−5) = 45.
Practice 2
Why is 8/0 undefined?
Show a hint
Ask whether 0q can equal 8.
Reveal answer and explanation
No number multiplied by zero equals 8
The equation 0q = 8 has no solution, so the proposed quotient does not exist.
Take the idea with you
Verify a quotient by multiplying it by its divisor, especially when several minus signs appear.
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: Order negative fractions and decimals
Completion is your own study record, not a test score. It stays in this browser, does not sync to another device, and can be removed by clearing browser data.