Writing Algebraic Expressions

Contributor: Marlene Vogel. Lesson ID: 10324

This lesson focuses on real-life situations where you would use algebra expressions, using many fun activities!


Expressions and Equations, Operations and Algebraic Thinking, Pre-Algebra

learning style
Auditory, Visual
personality style
Beaver, Golden Retriever
Grade Level
Intermediate (3-5), Middle School (6-8)
Lesson Type
Quick Query

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Rafael raked r bags of leaves. Nicole raked 5 bags. How many bags of leaves were raked altogether? Can you write an algebraic expression to represent this word problem?

Take a look at the word problem at the beginning of this lesson.

Can you write an algebraic expression to represent it? Review some information about algebra, then write an algebraic expression for the word problem.

When working with word problems in math, it is important to know how and why words may be turned into numbers and operation signs to solve an equation. This rule applies when writing algebraic expressions. Remember, an expression is a group of numbers and operations signs, but NO = sign.

When writing the algebraic expression, you need to pay close attention to the words in the word problem, so you can translate them properly. Refer to the document entitled “Translating Word Problems” to refresh your memory about word phrases and the operations they refer to. Download it using the Download button in the right-hand sidebar.

Take a look at the following phrases and see if you can translate them into algebraic expressions:

  1. What is the product of 20 and k?

  1. What is the difference of g and 6?

To translate the first example, look at the entire phrase and identify the key words that tell you what to do.

What is the product of 20 and k? As you can see, the word product, the number 20, and the letter k are identified in the phrase. These three items help you write the algebraic expression.

Product tells you the operation that needs to be performed is multiplication. Remember, in algebra we no longer use the x to represent multiplication. Use a dot between the number and the variable, or write them side-by-side. The 20 and the k are what we are multiplying together. Your algebraic expression will look like either of the examples below:

20 • k or 20k

Try #2. What is the difference of g and 6? What are the key words you identified in this phrase? If you said difference, g, and 6, you are correct! What operation does the word difference represent? If you said subtraction, you are correct! So now you know you need to write an algebraic expression that involves subtraction. Your algebraic expression should look like the following:

6 - g

Watch the KHAN Academy video How to Write Expressions with Variables below for more instruction on writing expressions:

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