Lesson 3: Representing Equivalent Ratios

Property

A double number line is simply two number lines aligned so that they start at the same location and the first marks represent the ratio in question.

Examples

• A car travels 120 miles in 2 hours. A double number line would align 0 miles with 0 hours, 120 miles with 2 hours, and 240 miles with 4 hours, showing the constant relationship.
• A recipe calls for 3 cups of flour for every 2 eggs. Using a double number line, you can see that if you use 4 eggs, you will need 6 cups of flour.
• An old printer prints 40 pages in 5 minutes. A double number line shows that in 10 minutes, it would print 80 pages, and in 15 minutes, it would print 120 pages.

Explanation

Ratios can connect different kinds of measurements, like miles and hours. A double number line is a great visual tool that places these two measurements side-by-side, helping you see how they increase together at a constant rate.

Property

A unit rate is a rate with a denominator of 1 unit.
To convert a rate to a unit rate, we divide the numerator by the denominator.
This gives us a denominator of 1.

Examples

• If Anita was paid 384 dollars for 32 hours, her hourly (unit) pay rate is $\frac{384 \text{ dollars}}{32 \text{ hours}} = 384 \div 32 = 12$ dollars per hour.

• If a car travels 455 miles using 14 gallons of gasoline, its unit rate is $\frac{455 \text{ miles}}{14 \text{ gallons}} = 455 \div 14 = 32.5$ miles per gallon (mpg).