Types of Ratio Relationships

Ratio relationships exist between a variety of quantity types. The kind of connection between quantities determines the type of ratio relationship that exists. A ratio relationship (R) allows us to take a quantity we know (Q1) and change it (or convert it) to another quantity.

Q1 * R = Q2

Unit Relationship: This is based on the fact that 2 different units for the same kind of quantity (say, length) can express the same amount of that quantity. That means the amount in one unit is equivalent to the amount in the other unit. Ex: 100 cm = 1 m states that a 100 cm length is exactly the same length as 1 m. The size of 1 used to describe the length (the unit) has changed, but not the actual length.

So: 255 cm * ___1m___ = 2.55 m

100 cm

Q1 * R = Q2

System Relationship: This is a relationship between 2 different kinds of quantities that both describe the same system at the same time. The two quantities cannot be said to be equal (5 cats can't equal 5 dogs), but they can be simultaneously true about the system where one doubles when the other doubles.

We examined density as a system relationship. It expresses how much mass is associated with 1 unit of volume (typically 1 mL or 1 L or 1 cubic meter).

So: 255 mL * ___5 g___ = 1275 g

1 mL

Q1 * R = Q2

Pure Number Relationship: This relationship is between 2 of the same kind of quantity, same unit. Comparing two of the same kind of quantity reveal how much bigger one is than the other. The relative magnitude (how much bigger) is the concept of a pure number.

So: 250 mL compared to 125 mL = 2