Part-to-Part Ratios

A part-to-part ratio compares two parts of a group directly to each other – like the ratio of cats to dogs at a shelter. It answers “how does this group compare to that group?” rather than “how does this group compare to everything?” (which is a part-to-whole ratio, covered on the next page). Recognising which type of ratio a problem is asking about is often the trickiest part of solving it correctly.

What Is a Part-to-Part Ratio?

A part-to-part ratio compares two specific parts of a group to each other, without referencing the group's total size directly.

A shelter has cats and dogs in the ratio 3:5. If there are 12 cats, how many dogs are there?

Scale factor = 12 ÷ 3 = 4. Dogs = 5 × 4 = 20.

Finding a Total from Two Parts

A cake recipe uses flour to sugar in the ratio 5:2. If 500 g of flour and 200 g of sugar are used, what is the total weight?

500 g + 200 g = 700 g in total.

Real-Life Application

Sports: the ratio of wins to losses on a team.
Business: the ratio of full-time to part-time employees.
Cooking: oil to vinegar ratio in a salad dressing.

Key Takeaways

A part-to-part ratio directly compares two portions of a group to each other.
Knowing one part's actual value lets you scale up to find the other, using the scale factor.
Adding both parts together gives the group's total – the bridge to part-to-whole ratios, covered next.

Practice: Part-to-Part Ratios

Find the Other Part