Distinguish a part-to-whole ratio from a part-to-part ratio

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Distinguish a part-to-whole ratio from a part-to-part ratio

If blue: whole = 3: 5, the unlisted gold part represents the remaining two shares. This is equivalent to blue: gold = 3: 2. Adding 3 and 5 would incorrectly count the blue part twice.

A given amount for one part can determine the total. If the three blue shares equal 24, one share is 8 and the five-share whole is 40. State whether each ratio entry is a part or the whole before calculating.

Concentration and composition descriptions often use this distinction. A stated part-to-whole fraction gives the amount relative to the total; it is not automatically the same as a ratio between two ingredients.

Worked example: Blue: whole is 3: 5 and blue equals 24 units. Find the whole.

Divide 24 by 3 to find one share.

Multiply that share by 5.

Answer: 40 units.

Check your understanding: What is blue: gold here?

Answer: 3: 2.

Why: Gold is the whole minus the blue share.