Ratio, Proportion & Percent Lab
Visualize ratios with bar models, solve proportions step by step using cross-multiplication, and explore percent change with real-world examples. Discover why a 50% increase followed by a 50% decrease does not return to the original.
Guided Experiment: Discovering Cross-Multiplication
If two fractions are equal (a/b = c/d), what relationship holds between the products a×d and b×c? Will this always let you find one unknown value?
Write your hypothesis in the Lab Report panel, then click Next.
Bar Model
Controls
Results
| Multiplier | A | B |
|---|---|---|
| ×2 | 6 | 10 |
| ×3 | 9 | 15 |
| ×4 | 12 | 20 |
| ×5 | 15 | 25 |
| ×6 | 18 | 30 |
Data Table
(0 rows)| # | Type | Input Values | Result | Steps | Simplified |
|---|
Reference Guide
Ratios & Equivalent Ratios
A ratio a:b compares two quantities. Equivalent ratios are found by multiplying or dividing both parts by the same number.
The simplest form of a ratio is found by dividing both parts by their GCD.
Cross-Multiplication
To solve a proportion a/b = c/d with one unknown, cross-multiply to get ad = bc, then solve for the missing value.
This works because multiplying both sides by bd eliminates both denominators.
Percent Change
Percent change measures the relative difference between an original value and a new value.
A positive result is a percent increase. A negative result is a percent decrease.
Percent Change Asymmetry
A common mistake is thinking that a percent increase followed by the same percent decrease returns to the original. It does not.
The decrease is applied to the larger number, so it removes more than the increase added.