HOW TO FIND THER IN PROPORTION
Answers
Learning Objective(s)
· Determine whether a proportion is true or false.
· Find an unknown in a proportion.
· Solve application problems using proportions.
Introduction
A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale.
For example, imagine you want to enlarge a 5-inch by 8-inch photograph to fit a wood frame that you purchased. If you want the shorter edge of the enlarged photo to measure 10 inches, how long does the photo have to be for the image to scale correctly? You can set up a proportion to determine the length of the enlarged photo.
Determining Whether a Proportion is True or False
A proportion is usually written as two equivalent fractions. For example:
Notice that the equation has a ratio on each side of the equal sign. Each ratio compares the same units, inches and feet, and the ratios are equivalent because the units are consistent, and is equivalent to .
Proportions might also compare two ratios with the same units. For example, Juanita has two different-sized containers of lemonade mix. She wants to compare them. She could set up a proportion to compare the number of ounces in each container to the number of servings of lemonade that can be made from each container.
Since the units for each ratio are the same, you can express the proportion without the units:
When using this type of proportion, it is important that the numerators represent the same situation – in the example above, 40 ounces for 10 servings – and the denominators represent the same situation, 84 ounces for 21 servings.
Juanita could also have set up the proportion to compare the ratios of the container sizes to the number of servings of each container.
Sometimes you will need to figure out whether two ratios are, in fact, a true or false proportion. Below is an example that shows the steps of determining whether a proportion is true or false.
Example
Problem
Is the proportion true or false?
miles (check)
The units are consistent across the numerators.
gallons (check)
The units are consistent across the denominators.
Write each ratio in simplest form.
Since the simplified fractions are equivalent, the proportion is true.
Answer
The proportion is true.
Identifying True Proportions
To determine if a proportion compares equal ratios or not, you can follow these steps.
1. Check to make sure that the units in the individual ratios are consistent either vertically or horizontally. For example, or are valid setups for a proportion.
2. Express each ratio as a simplified fraction.
3. If the simplified fractions are the same, the proportion is true; if the fractions are different, the proportion is false.
Sometimes you need to create a proportion before determining whether it is true or not. An example is shown below.
Example
Problem