# Quantitative Reasoning: Definition & Strategies Video

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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

This lesson will discuss quantitative reasoning. It will define this type of reasoning, look at a four-step process for solving problems with this type of reasoning, and examples of using quantitative reasoning strategies to solve problems.

## Quantitative Reasoning

In an effort to develop a program to decrease the amount of sugar the people in the city of Stoneville are eating, the mayor is gathering facts about the town's residents. He finds that the city's population is 12,322, and that the city's stores sell a total of 19,820 pounds of candy each year. He wants to figure out how much candy the average resident buys in a year.

He first notes that if he could divide the number of pounds out evenly between the residents, then the amount assigned to each resident would equal the average number of pounds that resident bought. Ah-ha! He simply needs to divide the number of pounds of candy by the number of residents, so this is the plan he devises to solve the problem.

Now, he just needs to carry out the plan.

19,820 / 12,322 â‰ˆ 1.6

It looks like, on average, each resident of the city buys 1.6 pounds of candy per year. The mayor decides that this makes sense based on the facts of the problem, so he has his answer.

The reasoning that the mayor used in this scenario is an example of using quantitative reasoning to solve a real-world problem. Quantitative reasoning is the act of understanding mathematical facts and concepts and being able to apply them to real-world scenarios.

## Quantitative Reasoning Strategies

Many standardized tests have a quantitative reasoning section. Tackling these types of problems can be done using a number of strategies. First and foremost, when dealing with any type of quantitative reasoning problem, it's a good idea to have a plan.

Thankfully, there's a nice four-step process that George Polya, a Hungarian mathematician, developed to solve problems in general, and it can often be used to organize your thoughts and develop a plan to solve a given problem.

1. Understand the problem: Reword it in your own words and read it as many times as necessary to understand it.
2. Devise a plan: Come up with a way to solve the problem based on the information given, such as drawing a picture or diagram, translating the problem into numerical expressions, or working backwards, to name a few.
3. Carry out the plan: Carry out the plan that you devised.
4. Look back: Check your answer with the original problem. Make sure that it makes sense with the problem and that you carried out your plan correctly. If it checks out, great! If not, start over.

This process can aid in quantitative reasoning in that it gives a nice strategy on ways to think about the problem in an organized manner. If we look back at how the mayor solved his problem, we see that he used this process.

This process can be used for any type of problem, but the quantitative reasoning comes in at steps two and three when we devise a plan and carry it out. Knowing how to identify the relationships among the quantities in the problem and connect those relationships to appropriate operations is quantitative reasoning at its finest. Consider another example.

## Example

Suppose that the distance around a rectangular flower garden is 22 feet. The length of the garden is 7 feet, but we don't know the width, and we'd like to figure it out. Let's take it through our steps!

First, we make sure that we understand the problem. Well, let's see. The garden is a rectangle, and we know that its length is 7 feet. This tells us that two of the sides of the garden that are opposite one another have lengths of 7 feet. We also know that the distance around the garden, or its perimeter, is 22 feet. Okay, I think we can move on to Step 2 and devise a plan.

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