# One- & Two-Step Word Problems: Fractions & Decimals

Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

In this lesson, we will briefly review fractions and decimal numbers. We will then look at one and two-step word problems that involve these types of numbers and show examples of how to solve them.

## Fractions and Decimals

Suppose that a clothing store is having a half-off everything sale. You've been eyeing a shirt there for a while, so you decide to take advantage of the discount. As you're heading to the store, you are trying to calculate what the sale price of the shirt will be.

You know that the original price is \$45.50, so you simply need to determine half of this. We can do this by multiplying \$45.50 by 1/2 or by 0.5. In other words, if we let x be the sale price of the shirt, then we have the following:

x = 1/2 × 45.50 or x = 0.5 × 45.50

The numbers involved in this problem are decimal numbers and fractions, and both of them represent a portion of something.

A fraction is a ratio of two integers, with the bottom number not equal to 0.

In our example, 1/2 is a fraction.

A decimal number is simply a number containing a decimal point. It can also be thought of as a fraction in which the division has been performed.

In our example, 0.5 is a decimal number.

The number 45.50 in our problem is also a decimal number, so we see that this problem involves decimal numbers and fractions. Now that we are familiar with the types of numbers that are involved in this problem, let's take a deeper look at the problem itself.

## One and Two-Step Word Problems

Word problems are often classified by how many steps it takes to solve them. For example, the problem of finding the sale price of the shirt you want is an example of a one-step word problem, because it takes one step to solve the problem. We simply multiply the original price of the shirt by 1/2 or 0.5.

We get that the sale price of the shirt is \$22.75, and it only takes one step to come upon that answer.

A two-step word problem is a word problem that takes two steps to solve. For example, suppose that when you go to check out at the store, the cashier asks if you want to donate \$5 to a charity that they are supporting. You say sure, and right then, the cash register goes down, so the cashier has to ring you up manually. To figure out your total cost, we know that the shirts original cost is 45.50, and you get half off of that. You also have to add on the \$5 that you are donating to the charity. Therefore, we need to use two steps to solve the problem:

1. Multiply 45.50 by 1/2 or 0.5.
2. Add 5 to the result.

In other words, if we let the total cost be C, then we have the following:

• C = (1/2) × 45.50 + 5

It takes two steps to simplify this expression, and they are the same two steps that we mentioned.

All together, your total cost is \$27.75.

Let's take a look at a couple more examples of one and two-step word problems involving fractions and decimals.

## Examples

Let's start with a one-step word problem. Suppose that two brothers, Paul and Nathan go to get a check-up at their family doctor. Paul goes in first, and finds out that he is 73 inches tall. Nathan follows, and the doctor tells him that his height is 94%, or 17/18, of his brother's height. The doctor then leaves the room before telling Nathan what that is in inches, so Nathan has to figure out how tall he is on his own.

Hmmm…well, if Nathan's height is 17/18 of Paul's height, all we have to do to find Nathan's height is multiply Paul's height (73 inches) by 17/18. Just one simple step!

• Nathan's Height = (17/18) × 73 ≈ 69

We get that Nathan is 69 inches tall. Now, let's consider a two-stepper.

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