Notes On Unit Rates and Ratios

Unit Rate

A comparison of two different quantities where one quantity is equal to one.

Example of Unit Rate

If a car travels 150 miles in 3 hours, the unit rate is 50 miles per hour.

Ratio Representation

Ratios can be represented in the form a:b or as fractions to clarify the relationship between two quantities.

Proportions

Mathematical statements that assert two ratios or rates are equivalent.

Cross Products of Proportions

In valid proportions, the cross products are equal, represented as a × d = b × c.

Application of Proportions

Proportions can be used to solve for unknown variables in scenarios such as recipes or pricing.

Proportional Reasoning

Fundamental for scaling quantities accurately in practical applications like map scales and recipe adjustments.

Cost per Unit Example

Comparing costs to find unit rates. For instance, $4 for 2 pounds and $6 for 3 pounds both equate to $2 per pound.

Setting up Proportions

To find unknown variables, set up a proportion based on the relationship between quantities.

Conversion between Unit Rates and Ratios

Helps in solving proportional relationships for calculations involving speed, density, or pricing.