Translate Verbal Phrases into
Variable Expressions
Jen Kershaw
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Printed: January 10, 2015
AUTHOR
Jen Kershaw
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C HAPTER
Chapter 1. Translate Verbal Phrases into Variable Expressions
1
Translate Verbal Phrases
into Variable Expressions
Here you’ll learn to translate verbal phrases into variable expressions.
Have you ever had to figure out a math problem that was described in words? Look at this dilemma.
Kelly and her brother sold lemonade and cookies at the school fair. They sold the lemonade for two dollars per glass
and the cookies for one dollar and fifty cents a piece. When finished, Kelly realized that they had sold fifty glasses
of lemonade and twenty cookies. She said this to her brother.
"We sold fifty times two dollars and twenty times one dollar and fifty cents."
Kelly’s brother isn’t sure how to write this expression. Pay attention and you will be able to help him at the end of
the Concept.
Guidance
Do you know how to take a verbal phrase and write it as a variable expression?
To accomplish this task, you will need to think about what different words mean. A verbal expression is a mathematical statement that is expressed in words.
You will have to work as a detective to figure out what different words mean. Once you know what those words
mean, you will be able to write different variable expressions.
Let’s start by looking at some mathematical operations written as words.
Addition
Sum
Plus
Increased by
More
Subtraction
Difference
Less than
1
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Take away
Multiplication
Product
Times
Division
Quotient
Split up
This list does not include ALL of the ways to write the operations, but it will give you a good place to start.
Take a few minutes and write these words down in your notebook.
Now we can look at the following chart which starts with a verbal phrase and writes it as a variable expression.
TABLE 1.1:
Verbal Phrase
Three minus a number
A number increased by seven
The difference between an unknown quantity and
twenty-six
A number decreased by nine
Ten times a number plus four
Variable Expression
3−x
n+7
s − 26
w−9
10 f + 4
Notice that words like “a number” and “an unknown quantity” let us know that we need to use a variable.
Example A
Write a variable expression that reads “The product of a number and six plus four.”
Solution: 6x + 4
Example B
Write a variable expression that reads “Ninety divided by a number minus eight.”
Solution:
2
90
b
−8
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Chapter 1. Translate Verbal Phrases into Variable Expressions
Example C
Write a variable expression that reads “Two less than a number, multiplied by thirty-six.”
Solution: 36(n − 2)
Now let’s go back to the dilemma from the beginning of the Concept. Kelly explained the sales to her brother in this
way.
"We sold fifty times two dollars and twenty times one dollar and fifty cents."
First, use the information in the statement to write an expression.
50(2.00) + 20(1.50)
Notice that we have fifty times two dollars plus twenty times one dollar and fifty cents. This shows the number of
glasses of lemonade and cookies times each price.
Next, we can figure out how much money they made.
$130.00
This is our final answer.
Vocabulary
Variable Expression
A variable expression is a mathematical phrase that contains at least one variable or unknown quantity.
Variable
A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a,
b, x, y, m, and n.
Constant
A constant is a value that does not change. In Algebra, this is a number such as 3, 12, 342, etc., as opposed to
a variable such as x, y or a.
Verbal Expression
A verbal expression uses language to describe a mathematical expression instead of numbers, symbols and
variables.
Guided Practice
Here is one for you to try on your own.
Write a variable expression that reads “Eighty-five divided by a number minus thirteen.”
Solution
We could do this in several different ways. We could use a symbol, ÷, to show division or we could use a fraction
bar to show division.
Because you are moving toward Algebra, let’s use a fraction bar.
The answer is
85
a
− 13.
Video Review
3
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MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/58521
Writing Basic Algebraic Expressions
Explore More
Directions: Write a variable expression for each verbal expression.
1. The sum of a number and twelve.
2. The difference between a number and eight.
3. Three times a number
4. A number squared plus five
5. A number divided by two plus seven
6. Four times the quantity of a number plus six
7. A number times two divided by four
8. A number times six plus the same number times two
9. A number squared plus seven take a way four
10. A number divided by three plus twelve
11. A number times five and another number times six
12. Sixteen less than a number times negative four
13. A number times eight divided by two
14. A number divided by six and another number times negative five
15. A number divided by four plus another number divided by sixteen
4