Lesson 3: Solving Ratio Problems with Models

Property

To solve ratio problems using tape (or bar) diagrams: 

1. Draw: Sketch identical rectangular boxes to represent the ratio of each quantity.
2. Identify: Locate the known quantity in the problem. This could be the amount of one specific part (Part-to-Part) or the total amount of all parts combined (Part-to-Whole).
3. Calculate: Find the value of a single box by dividing the known quantity by its corresponding number of boxes:

4. Solve: Multiply this single-part value by the number of boxes for any unknown quantity you need to find.

Examples

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.