What is a Ratio?

Pre-Algebra · Axiom Academy

Compare two quantities, write the same ratio three ways, and tell part-to-part from part-to-whole. Imagine a bag of colored counters: 3 red and 4 blue . A ratio simply compares those two amounts — it tells us how many red there are next to how many blue. Here, the ratio of red to blue is 3 to 4. The same comparison — 3 red to 4 blue — can be written three different ways. They all mean exactly the same thing. All three notations describe the same set of counters: for every 3 red, there are 4 blue. When we compare the red counters to the blue counters, we are comparing one part of the group to another part . That is a part-to-part ratio . The ratio of apples to oranges is 5:3 — a part-to-part ratio comparing apples (one part) to oranges (another part). When we compare the red counters to all the counters (red + blue), we are comparing one part to the whole group. That is a part-to-whole ratio . The ratio of apples to all fruits is 5:8 — a part-to-whole ratio comparing apples (one part) to all fruits (the whole group). Here is the key idea: the same counters give two different ratios depending on what we compare them to. Watch both comparisons spring from one shared set. Compares one color to the other color — for every 3 red, there are 4 blue. Compares one color to all the counters — 3 out of 7 counters are red. (3 red + 4 blue = 7 total.) A class has 12 boys and 15 girls. Part-to-part: boys to girls = 12:15 , which simplifies to 4:5 .

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