Basic Concepts
In a nutshell: Proportions show when two ratios are equal and help solve for unknowns.
## What Is a Proportion?
A proportion is when two ratios are equal. It helps us find missing values and solve problems where things change at the same rate.
## Writing Proportions
If \(\frac{a}{b} = \frac{c}{d}\), then these ratios form a proportion.
## Solving Proportions
To find a missing number, use cross-multiplication:
\[
\frac{a}{b} = \frac{c}{d} \implies a \times d = b \times c
\]
## Everyday Uses
Proportions help you scale recipes, convert measurements, or determine distances on a map.
Examples
- If 3 pencils cost $6, how much do 5 pencils cost? Set up the proportion: 3/6 = 5/x.
- On a map, 1 inch represents 8 miles. If two cities are 3.5 inches apart, they are 28 miles apart.