Learn with Amar
Teaching video
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Browse grades and teaching videos01 · Read and understand
What you will learn
- Translate a percentage reduction into a multiplier.
- Apply a later percentage to the updated amount.
- Distinguish percentage change from percentage-point change.
Before you start
Decimal multiplication and the meaning of percent.
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 $80 backpack is discounted by 25%. In this classroom example, an 8% tax is then applied to the discounted price. What is the final total?
Why this math matters
A percentage has meaning only in relation to a base. Tracking that base helps with store comparisons, changes in measurements, and data reports. Writing each change as a multiplier makes multi-step percentage problems easier to check.
Original price
$80.00
The first base
After 25% off
$60.00
Multiply by 0.75
After 8% tax
$64.80
Multiply $60 by 1.08
Set up the model
A useful answer starts with clear assumptions:
- The discount applies to the entire $80 price.
- The fictional 8% tax applies to the discounted price; this is an arithmetic assumption, not a statement of local tax rules.
- There are no other fees. Final currency is reported to the nearest cent.
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.
Work out a discount, then a tax
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A fictional $80 backpack is discounted by 25%. In this classroom example, an 8% tax is then applied to the discounted price. What is the final total?
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.
Find the discount
discount = 0.25 × $80 = $20
Twenty-five percent is one quarter. The discount is an amount removed from the original price.
Find the sale price
sale price = $80 − $20 = $60 = $80 × 0.75
After removing 25%, 75% of the original price remains. The multiplier is 1 − 0.25 = 0.75.
Apply tax to the sale price
tax = 0.08 × $60 = $4.80
The new base is $60. Applying 8% to the original $80 would contradict this problem's stated order and tax base.
Find and check the total
total = $60 × 1.08 = $64.80
The combined multiplier is 0.75 × 1.08 = 0.81. The total is 81% of the original price, so it is 19% below that original price.
The result
The final total is $64.80 under the example's discount and tax assumptions.
Subtracting 25% and adding 8% does not give a 17% net reduction, because the 8% applies to a changed base. Also, a rate increasing from 8% to 10% rises by 2 percentage points, but by 25% relative to its old rate: (10 − 8)/8 = 0.25.
Common mistakes to catch
- A 25% discount means paying 75% of the original price, not paying 25%.
- Successive percentage changes multiply; simply adding the signed percentages usually gives the wrong net change.
- A 20% decrease followed by a 20% increase gives 0.8 × 1.2 = 0.96, so it does not restore the starting amount.
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
In another fictional example, a $120 item has a 15% discount followed by a 5% tax on the discounted price. Find the final total.
Show a hint
Multiply 120 by 0.85, then by 1.05.
Reveal answer and explanation
$107.10
The discounted price is 120 × 0.85 = $102. Tax is 102 × 0.05 = $5.10, so the total is $107.10.
Practice 2
A $50 item is reduced by 20% and then by another 10%, with no tax or fees in this example. What is the final price and the overall percentage reduction?
Show a hint
The second discount applies to the price after the first. Use 0.8 × 0.9.
Reveal answer and explanation
$36; a 28% overall reduction
50 × 0.8 × 0.9 = $36. The saving is $14, and 14/50 = 0.28 = 28%, rather than 30%.
Take the idea with you
When reading any percentage claim, ask 'a percentage of what?' Write the base beside each step. For a change from old value to new value, divide the difference by the old value before converting to percent.
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: Read a supply-order expression in the right order
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