Grade 7 · Grade 7: Proportional Reasoning and Rational Numbers · Proportional Relationships and Percent
Percent Change: Tax, Discount, Interest and Error
Solve multi-step percent problems using multipliers, and interpret percent increase, decrease and error.
Learning objectives
- Solve markup, discount, tax, tip and commission problems.
- Use a single multiplier for repeated percent change.
- Calculate simple interest.
- Calculate and interpret percent error.
AERO Mathematics alignment
AERO.M7.NS.4
Use proportional relationships to solve multi-step ratio and percent problems, including simple interest, tax, markup, discount, commission, tips and percent error.
MYP criteria
- Criterion A — Knowing and understanding
- Criterion D — Applying mathematics in real-life contexts
ENGAGE
Start here
A phone costs 2000 QAR. In a sale it drops 20%. The next month the price rises 20% again.
Think about it
Is the phone back at 2000 QAR? Predict first, then calculate.
Hint: The 20% rise is applied to the sale price, not the original.
EXPLAIN
Multipliers, interest and error
Every percent change is a multiplication. An increase of p% multiplies by (1 + p/100); a decrease multiplies by (1 − p/100).
| Change | Multiplier | Example on 2000 |
|---|---|---|
| 20% decrease | 0.8 | 1600 |
| 20% increase | 1.2 | 2400 |
| 20% down then 20% up | 0.8 × 1.2 = 0.96 | 1920 |
| 8% tax added | 1.08 | 2160 |
Simple interest
Simple interest is I = Prt, where P is the principal, r the annual rate as a decimal and t the time in years. 5000 QAR at 4% for 3 years earns 5000 × 0.04 × 3 = 600 QAR.
Percent error
Percent error compares a measurement with the true value: |measured − actual| ÷ actual × 100. Measuring 98 cm when the true length is 100 cm is a 2% error.
Remember
Percent changes never simply add up. 20% down then 20% up gives 0.96, a 4% loss overall.
INVESTIGATION
Try it yourself
Track one advertised price over two weeks, or model it. Calculate each percent change using multipliers, then find the single multiplier equivalent to the whole period and express it as one overall percent change.
Watch
Finding a Percent of a Number
Math Antics · 7:00
Revisit percent of a number before working with multipliers and interest.
Before you watch: What single number multiplies a price to add 8% tax?
- Find the multiplier for a 30% decrease.
- Calculate simple interest on 2000 at 4% for 3 years.
Interactive simulation · PhET
Unit Rates
Compare prices before and after a percent change, using multipliers.
While you explore
- Which single multiplier gives a 15% increase?
- Does a 20% rise followed by a 20% fall return you to the original price? Test it.
Key vocabulary
- Simple interest
- Interest calculated only on the original amount.
- Percent error
- How far a measurement is from the true value, as a percent.
Practice questions
0/1 correct
Level 1 · Criterion A
Which multiplier increases a price by 12%?
MYP criterion tasks
Level 2 · Criterion D
A price rises 10% then falls 10%. Find the overall percent change and explain.
Reflect & track
Your learning log
Saved privately in this browser — no account needed.
How confident do you feel?