Algebraic Expressions

Lesson 6.02

After completing this lesson, you will be able to say:

• I can use numbers and variables to write expressions.

• I can translate written phrases into algebraic expressions.

• I can translate algebraic expressions into written phrases

Key Terms

Verbal expression: A mathematical expression in which all mathematical operations are written using words; also called a mathematical phrase; an example is the product of three and a number.

Variable: A letter that holds the place for some unknown value in an algebraic expression, such as x or y.

Algebraic expression: An expression that contains numbers, variables, and mathematical operations like addition, subtraction, etc; an example is x + 2

Verbal Phrases

This chart groups commonly used phrases by their meaning

Tricks of Translating

An algebraic expression uses numbers, letters, and symbols instead of words. All you will need to do is change the words into math.

Since algebraic expressions contain variables like the letter x, you should no longer use x to represent multiplication

Tricks of Translating

It is important to pay attention to the order of quantities when translating

When the phrases “less than” and “subtracted from” are translated to an algebraic expression, the order of the numbers must be reversed.

Translating expressions

Sam invited 40 friends, but his mom mentioned that some might not come. This means he would have “forty minus some number.”

First, identify the action phrase in the verbal expression to know what operation is being used. In this expression, the action phrase is “minus,” which means to subtract. So the verbal expression written in algebraic form is:

Example

Rewrite “the quotient of eight and an unknown value” into an algebraic expression

In this expression, the action phrase is "quotient", meaning division.

Try It

Translate the verbal expression “seven less than a number” into an algebraic expression

Check your work

Remember, the “less than” tells you to subtract from, so switch the order.

x − 7

Translating Expressions

How do you translate the expression: “Double the total number of brownies and cookies?”

Example

Sam has to pay a $5 admissions fee for each person who attends the party. Sam’s expression now contains two operations. The verbal expression for the cost of admissions is “the product of five and the quantity forty minus a number.”

The first operation is to determine the total number of friends. The second operation is to multiply by five. Adding the parentheses around the first operation will ensure that Sam subtracts before he multiplies. Sam can write the algebraic expression as:

Try it

Translate the verbal expression “a number to the power of five times 3” into an algebraic expression.

Check your work

In this expression, the action phrases are “power” and “times”, showing an exponent and multiplication.

Notice this verbal expression contains an exponent. The standard way of writing this expression would be 3x5, and it would not need to contain the multiplication dot or parentheses

Algebraic expressions as Verbal expressions

To translate an algebraic expression into a verbal expression, you simply replace the symbols with words, or action phrases

The easiest way to translate a complex algebraic expression is to say it out loud. This will help you identify all the operations and numbers.

This expression can be read as the sum of a number and 2 divided by 4

Reading it aloud allows you to write it as a verbal expression. This one could be written as:

“the sum of a number and two divided by four,” “the total of a number and two divided by four,” “the quotient of a number plus two divided by four.”

Try it

Translate the algebraic expression shown below into a verbal expression.

2x − 7

Check your Work

The operations being performed in this expression are multiplication and subtraction. Here is how to read each operation within the expression:

So you can write this algebraic expression as “the product of a number and two minus seven” or “seven less than twice a number.”

Now that you completed this lesson, you should be able to say:

• I can use numbers and variables to write expressions.

• I can translate written phrases into algebraic expressions.

• I can translate algebraic expressions into written phrases