1.9: 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
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.
Verbal Phrase | Variable Expression |
---|---|
Three minus a number |
\begin{align*}3 - x\end{align*} |
A number increased by seven |
\begin{align*}n + 7\end{align*} |
The difference between an unknown quantity and twenty-six |
\begin{align*}s - 26\end{align*} |
A number decreased by nine |
\begin{align*}w - 9\end{align*} |
Ten times a number plus four |
\begin{align*}10f + 4\end{align*} |
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: \begin{align*}6x+4\end{align*}
Example B
Write a variable expression that reads “Ninety divided by a number minus eight.”
Solution: \begin{align*}\frac{90}{b}-8\end{align*}
Example C
Write a variable expression that reads “Two less than a number, multiplied by thirty-six.”
Solution: \begin{align*}36(n - 2)\end{align*}
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.
\begin{align*}50(2.00) + 20(1.50)\end{align*}
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.
\begin{align*}$130.00\end{align*}
This is our final answer.
Vocabulary
- Variable Expression
- a group of numbers, operations and variables without an equal sign.
- Variable
- a letter used to represent an unknown number
- Constant
- a number in an expression that does not have a variable.
- Verbal Expression
- using language to write 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, \begin{align*}\div\end{align*}
Because you are moving toward Algebra, let’s use a fraction bar.
The answer is \begin{align*}\frac{85}{a}-13\end{align*}
Video Review
Writing Basic Algebraic Expressions
Practice
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
Evaluate
To evaluate an expression or equation means to perform the included operations, commonly in order to find a specific value.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.Verbal Expression
A verbal expression (or verbal model) uses words to decipher the mathematical information in a problem. An equation can often be written from a verbal model.Image Attributions
Here you'll learn to translate verbal phrases into variable expressions.