Proportion Explorer

Pre-Algebra · Axiom Academy

A proportion is two ratios that are equal — and a balance scale shows it perfectly: when the ratios match, the scale sits dead level. When two ratios are equal, the scale balances You meet ratios everywhere a comparison stays the same while the amounts grow: 2 cups of flour to 3 of water, doubled to 4 and 6, tripled to 6 and 9. A proportion is just a claim that two of those ratios are equal — and there is no better way to feel "equal" than a balance scale. Watch a ratio sit on each pan of a scale. They start unequal, so it tips. Then the right side climbs until it matches the left, and the moment the two ratios are equal, the beam goes perfectly level. Keep an eye on the two cross-products underneath: they land on the very same number exactly when the scale balances. Equal ratios → a level beam. That level beam is a proportion. Find every ratio that balances 2/3 The left pan is locked at 2/3 . Drag the two sliders to set the right ratio, or tap a quick option. The beam tips toward whichever side is heavier and goes level only when the right ratio equals 2/3. How many different right ratios can you find that balance it? Every ratio that balances 2/3 is just 2/3 with both parts scaled by the same number — an equivalent ratio. Cross-products: the two diagonals must match

This is the written version of the interactive lesson above. See the full Pre-Algebra course.