Grade 6 · Grade 6: Number, Ratio and Percent · Ratio, Rate and Percent
Percent and Unit Conversion
Treat percent as a rate per hundred, find parts and wholes, and convert measurement units using ratio reasoning.
Learning objectives
- Find a percent of a quantity as a rate per 100.
- Find the whole when given a part and the percent.
- Convert measurement units by multiplying by a ratio equal to 1.
- Solve discount, tax and tip problems.
AERO Mathematics alignment
AERO.M6.NS.4
Find a percent of a quantity as a rate per 100, and solve problems involving finding the whole given a part and the percent.
AERO.M6.NS.5
Use ratio reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities.
MYP criteria
- Criterion A — Knowing and understanding
- Criterion D — Applying mathematics in real-life contexts
ENGAGE
Start here
A jacket is marked 240 QAR. A sign says 25% off, and tax of 5% is added at the till.
Think about it
Is 25% off then 5% tax the same as 20% off overall?
Hint: Try the calculation with multipliers: 0.75 then 1.05.
EXPLAIN
Percent as a rate per hundred
Percent means per hundred. 25% is the ratio 25:100, the fraction 25/100 and the decimal 0.25. Because percent is a rate, every percent problem is a ratio problem in disguise.
Three question types
| Question | Method | Example |
|---|---|---|
| Find the part | part = percent × whole | 15% of 240 = 0.15 × 240 = 36 |
| Find the whole | whole = part ÷ percent | 36 is 15% of 36 ÷ 0.15 = 240 |
| Find the percent | percent = part ÷ whole | 36 out of 240 = 0.15 = 15% |
Multipliers
A 25% discount multiplies by 0.75. Adding 5% tax multiplies by 1.05. Doing both gives 0.75 × 1.05 = 0.7875, so the final price is 240 × 0.7875 = 189 QAR — not the same as a single 20% discount, which would give 192.
Unit conversion is ratio reasoning
To convert, multiply by a ratio equal to 1. For example 5 km × (1000 m / 1 km) = 5000 m. Writing the units in the fraction shows which ones cancel.
Remember
Percent changes always refer to a starting amount. A 20% rise followed by a 20% fall does not return you to the start, because the second change is applied to a bigger number.
INVESTIGATION
Try it yourself
Choose three items you might buy. Apply a discount of your choice and then 5% tax, using multipliers only. Then work backwards: given the final price, recover the original. Explain which direction was harder and why.
Watch
Finding a Percent of a Number
Math Antics · 7:00
Shows percent as a rate per hundred, exactly the idea behind every discount.
Before you watch: What does the word percent literally mean?
- Find 15% of 240.
- A jacket costs 180 after a 25% discount. What was the original price?
Interactive simulation · PhET
Unit Rates
Use the shopping screen to find the price per single item, then compare two offers.
While you explore
- Which item is the better value, and how does the unit rate prove it?
- How would a 20% discount change each unit rate?
Key vocabulary
- Multiplier
- The single number you multiply by to apply a percent change.
- Percent
- A number out of one hundred.
Practice questions
0/1 correct
Level 1 · Criterion A
A 300 QAR item is reduced by 20%. What is the new price?
MYP criterion tasks
Level 2 · Criterion D
After a 25% discount an item costs 180 QAR. Find the original price and explain your method.
Reflect & track
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