5.4 Ratios and rates: summary of key concepts

Summary of key concepts

Denominate numbers ( [link] )

Like and unlike denominate numbers ( [link] )

Pure numbers ( [link] )

Comparing numbers by subtraction and division ( [link] )

Comparing pure or like denominate numbers by subtraction ( [link] )

Ratio rate ( [link] )

Proportion ( [link] )

$\frac{3\text{ people}}{\text{2 jobs}}=\frac{6\text{ people}}{\text{4 jobs}}$ is a proportion.

Solving a proportion ( [link] )

Proportions involving rates ( [link] )

$\frac{\text{unit type 1}}{\text{unit type 2}}=\frac{\text{unit type 1}}{\text{unit type 2}}\text{ or }\frac{\text{unit type 1}}{\text{unit type 1}}=\frac{\text{unit type 2}}{\text{unit type 2}}$

Five-step method for solving proportions ( [link] )

1. By careful reading, determine what the unknown quantity is and represent it with some letter. There will be only one unknown in a problem.
2. Identify the three specified numbers.
3. Determine which comparisons are to be made and set up the proportion.
4. Solve the proportion.
5. Interpret and write a conclusion.

Percents ( [link] )

Conversion of fractions, decimals, and percents ( [link] )

Applications of percents:

Base ( [link] )

Percentage ( [link] )

Percent ( [link] )

Solving problems ( [link] )