Algebra 1 / Unit 2: Solving Equations
2.5 Ratios, Rates and Proportions
Notes
- A ratio compares two quantities: 3 to 4, $3:4$ or $\displaystyle \frac{3}{4}$.
- A rate compares quantities with different units, like miles per hour. A unit rate has a denominator of 1.
- A proportion says two ratios are equal. Solve with cross products: if $\displaystyle \frac{a}{b} = \frac{c}{d}$, then $ad = bc$.
Practice
Solve $\displaystyle \frac{x}{8} = \frac{15}{24}$.
$24x = 120$, so $x = 5$.
A car travels 210 miles on 7 gallons. At that rate, how far on 12 gallons?
Unit rate: $210 \div 7 = 30$ mi/gal, and $30 \cdot 12 = 360$.
Which is the better buy?
$0.25 per ounce versus $0.22 per ounce.
Ready for more? Take the Unit 2 test.