Two lines that move together
Two cups of flour to three of water. Double both and it is the same recipe: four and six. One slider here runs through both scales at once, so you cannot change the flour without changing the water. What survives all that changing is the ratio.
8 : 12
- In lowest terms
- 2 : 3
- For every 1 of flour
- 1 : 1.5
The recipe
Drag the upright line along. Both scales are read where it crosses them.
Ready to try some? Equivalent ratio worksheets
Where it usually goes wrong
A ratio is read as a pair of numbers rather than as a relationship, so it gets scaled by adding: 2 : 3 becomes 3 : 4 by adding one to each, and the recipe is ruined. Both quantities have to be multiplied by the same thing, which is what keeps 2 : 3 and 8 : 12 the same ratio.
Try this
- Press 2 : 3 and drag the line out to 8 : 12. Neither number ever gains on the other.
- Read the “for every 1” line as you go. It does not change, and that is the thing a ratio actually is.
- Try adding one to each side in your head and check it against the tool. 3 : 4 is a different place on the line.
Where this goes next
Scaling a recipe, reading a map, converting a currency and every unit rate are this, and so is nearly all of the proportional reasoning that comes after.