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 combine quantities with matching variable parts.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Coefficients 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
Simplify 5a + 3b − 2a + 7 − b and explain why all terms cannot merge into one number of a's.
Why this math matters
Like terms can be combined because they count the same variable quantity; constants form a separate group. Before simplifying a formula, label the different types of term and combine only matching groups.
Set up the model
A useful answer starts with clear assumptions:
- a and b can vary independently.
- Only terms with identical variable parts are combined.
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.
Combine quantities with matching variable parts
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Simplify 5a + 3b − 2a + 7 − b and explain why all terms cannot merge into one number of a's.
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
(5a − 2a) + (3b − b) + 7
Reorder the sum while keeping each sign attached to its term.
Apply the relationship
(5 − 2)a + (3 − 1)b + 7
The implicit coefficient of b is one.
Check and interpret
3a + 2b + 7
The a terms, b terms, and constant represent three different types of quantity.
The result
3a + 2b + 7
The a terms, b terms, and constant represent three different types of quantity.
Common mistakes to catch
- Terms with the same letter but different exponents are not like terms.
- A subtraction sign must travel with the term when terms are rearranged.
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
Simplify 8x − 3 + 2x + 9.
Show a hint
Group x terms and constant terms separately.
Reveal answer and explanation
10x + 6
8x + 2x = 10x and −3 + 9 = 6.
Practice 2
Can 2x + 3x² be simplified to 5x²?
Show a hint
Compare x and x² as variable parts.
Reveal answer and explanation
No
x and x² are different powers; at x = 2 the original is 16 but 5x² is 20.
Take the idea with you
Before simplifying a formula, label the different types of term and combine only matching groups.
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: Undo operations in a two-step equation
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