All Labs

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

3:535simplified3:535original6:10610×29:15915×312:201220×415:251525×5
Part A
Part B

Controls

Results

Original Ratio
3:53 : 5
Simplified
3:53 : 5
A per B
0.6000
B per A
1.6667
Equivalent Ratios
MultiplierAB
×2610
×3915
×41220
×51525
×61830

Data Table

(0 rows)
#TypeInput ValuesResultStepsSimplified
0 / 500
0 / 500
0 / 500

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.

3:5=6:10=9:15=12:203:5 = 6:10 = 9:15 = 12:20

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.

ab=cd    ad=bc\frac{a}{b} = \frac{c}{d} \implies ad = bc

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.

Percent Change=NewOriginalOriginal×100%\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%

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.

100+50%15050%75100100 \xrightarrow{+50\%} 150 \xrightarrow{-50\%} 75 \ne 100

The decrease is applied to the larger number, so it removes more than the increase added.