## Problem Solving: Simplify the Problem

### What Is It?

Simplifying a mathematics problem is a strategy that often is used along with other problem-solving strategies. When a problem is too complex to solve in one step, it often helps to divide it into simpler problems and solve each one separately. Creating a simpler problem from a more complex one may involve rewording the problem; using smaller, simpler numbers; or using a more familiar scenario to understand the problem and find the solution. For example, consider the problem:

A soccer team won 24 of 36 games in the first season. If the team had the same ratio of wins to games in the second season, and they won 16 games, how many games did they play in the second season?

The answer can be found by simplifying the ratio of 24:36 to 2:3, and then cross-multiplying to find the total number of games in the second season, 24 games.

### Why Is It Important?

This is a problem-solving strategy that can be used with difficult concepts such as manipulating ratios or fractions. If a problem is confusing, the numbers can be rounded, or simpler numbers can be used to help make a plan to solve it.

### How Can You Make It Happen?

Introduce a problem to students that is complex and might be easier to solve if it were simplified. For example:

On your way to visit a friend, you leave your house at 2:45 P.M. and travel 1 3/4 miles to the train, 12 1/2 miles on the train, and 3/4 mile to your friend's house from the train station. If you get there at 4:15 P.M., how many miles per hour did you travel?

**Understand the Problem**Demonstrate that the first step is understanding the problem. This involves identifying the key pieces of information needed to find the answer. Students may need to read the problem several times and/or put the problem into their own words.

I know I left at a certain time, arrived at a certain time, and traveled a certain distance. I need to find how many miles per hour I traveled.

**Choose a Strategy**For this problem, it might be helpful for students to use simpler numbers to learn the steps they need to follow to solve it. Have students change the problem to:

I left the house 1:00, traveled 12 miles, and arrived at 4:00. How many miles per hour did I travel?

**Solve the Problem**First, have students solve the problem using the simpler numbers.

I left the house 1:00, traveled 12 miles, and arrived at 4:00. How many miles per hour did I travel?

I traveled 12 miles.

It took 3 hours.

To find the miles per hour, I divide 12 by 3 to get 4 miles per hour.Next, have them write down the steps they used to solve the problem.

Find the distance traveled.

Find the time spent.

Divide to find the miles per hour.

Then, have them use the actual numbers from the problem and follow the same steps.

Find the distance traveled.

1 3/4 + 12 1/2 + 3/4 = 15 milesFind the time spent.

The time from 2:45 to 4:15 is 1 hour and 30 minutes, or 1 1/2 hours.Divide to find the miles per hour.

15 divided by 1 1/2 = 10 miles per hour