Writing Algebraic Expressions

Lesson 2-3

Word phrases can be written as algebraic expressions.

Use the words to determine what operation you are using.

Use a variable for the phrase “a number.”

Adding Phrases

Plus More than Sum Increased by Added to Total

Subtracting Phrases

Minus Difference of Subtracted from Decreased by Less than Less

Multiplying Phrases Times Product of Multiply Twice Of

Dividing Phrases Divided by Quotient Into ratio

Example: 7 decreased by b

“Decreased by” means subtract.

7 - b

Example: The product of 19 and k

“Product” means multiply. We show multiplication by placing the factor right next to the variable.

19k

Less than, more than

Some word phrases contain the words “less than” or “more than.”

When you see those words, start with the second part of the phrase.

Example: 23 less than m

m - 23

Example: 32 less than 5 times c

The 32 is less than the 5 times c, which means we subtract 32 from the 5 times c. So, start with 5 times c.

5c - 32

Tables

When you are given a table of values, determine how to get from the first column to the second column.

Describe that pattern with an algebraic expression.

Example

n ?3 127 2811 44

Compare from left to right.

How do we get from 3 to 12? Add 9 or multiply by 4.

How do we get from 7 to 28? Multiply by 4. If we multiply 11 by 4, we get 44.

The pattern is to multiply our number, n, by 4.

The algebraic expression to describe this is:

4n

Describing Unknown Numbers

When you don’t know what a number is, let a variable stand for that number.

Use an algebraic expression to describe what you’re looking for.

Example

Write an algebraic expression to describe Jerry’s age. Use the following information:

Jerry is 4 years younger than his brother Steve.

First, we have to know how old Steve is. We do not have an age for Steve, so we will use a variable:

Let s = Steve’s age.

Now that we have determined Steve’s age (s), we can use it to determine Jerry’s age. Jerry is 4 years younger than Steve.

s - 4

If Steve is 22 years old, then how old is Jerry?

s - 422 - 418

Jerry is 18 years old.

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