Equivalent ratios and ratio tables
A recipe, a mix or a map scale works at one size. How do you get other amounts that keep exactly the same comparison?
Where you are 5 inside
What this area is about
Two ratios are equivalent when they describe the same comparison: 3 : 7 and 9 : 21 make the same cordial, one jug three times the size of the other. You get from one to the other by multiplying both amounts by the same positive number. This area is that one move, and three pictures that keep track of it.
How these fit together
The core moves. Scaling a ratio up or down multiplies both amounts by the same number, so the mix stays the same. Finding a missing value in a pair of equal ratios uses that move backwards: when three of four numbers are known, find the scaling number and apply it.
Ways to see it. Ratio tables list equivalent ratios in rows, one column per quantity. The double number line draws two number lines one above the other, zero under zero, so matching points show equal ratios. Tape diagrams draw equal blocks for each part of a ratio, which makes a total easy to share out in that ratio.
A path through it
Scaling a ratio comes first, then finding a missing value, then ratio tables. The double number line can be taken at any point, and tape diagrams once part-to-part ratios are known.
Finish here and you are ready for comparing two ratios, rates and unit rates, proportions and percent as a rate per hundred.