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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to choose the base of a percentage change.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Fractions, decimals, and percentages.
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
A fictional club grows from 40 members to 50 members. Find the percentage increase and the percentage decrease needed to return from 50 to 40.
Why this math matters
A percentage change compares a difference with the original value, so reversing a change uses a different base. When reading growth claims, identify the baseline before comparing percentages.
Set up the model
A useful answer starts with clear assumptions:
- The counts refer to the same club.
- Each percentage uses the count at the start of that particular change.
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.
Choose the base of a percentage change
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A fictional club grows from 40 members to 50 members. Find the percentage increase and the percentage decrease needed to return from 50 to 40.
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
increase = 50 − 40 = 10
First find the absolute change in members.
Apply the relationship
10/40 × 100% = 25%
The growth starts at 40, so 40 is the reference amount.
Check and interpret
return decrease = 10/50 × 100% = 20%
The return starts at 50. Equal absolute changes need not have equal percentages.
The result
return decrease = 10/50 × 100% = 20%
The return starts at 50. Equal absolute changes need not have equal percentages.
Common mistakes to catch
- Dividing the increase by the final value answers a different question.
- Equal increase and decrease percentages do not generally cancel.
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
A length changes from 80 cm to 68 cm. Find the percentage decrease.
Show a hint
Divide the lost length by 80.
Reveal answer and explanation
15%
The loss is 12 cm; 12/80 = 0.15.
Practice 2
After a 10% increase, a score of 60 becomes 66. Does a 10% decrease restore 60?
Show a hint
Apply the decrease to 66.
Reveal answer and explanation
No; it becomes 59.4
66 × 0.90 = 59.4 because the second percentage uses a larger base.
Take the idea with you
When reading growth claims, identify the baseline before comparing percentages.
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: Work backward from a discounted amount
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