Translate Verbal Phrases into
Variable Expressions
Brenda Meery
Jen Kershaw
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Printed: June 22, 2016
AUTHORS
Brenda Meery
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Translate Verbal Phrases into Variable Expressions
1
Translate Verbal Phrases
into Variable Expressions
In this concept, you will learn to change words into variable expressions.
Twins Larry and Terry want to buy their dad a great gift for his upcoming birthday. Both boys have been saving all
of their dimes and quarters for several months. “I count 928 dimes,” Larry announces. “Great! I count 515 quarters,”
Terry says. “But how do we go from knowing the number of coins to the amount of money?” How can Larry and
Terry use a mathematical expression to figure out how much money they have in total?
In this concept, you will learn to change words into variable expressions.
Translating Phrases into Expressions
Many problems can be solved using mathematical methods. In order to do this, you must be able to translate words
into mathematical expressions. More often than not, the words can be expressed as a variable expression which can
be evaluated to solve a problem.
You know the symbols+, −, ×, ÷, represent the four most commonly used mathematical operations. The operation
of multiplication can be represented by the symbol(×)or by#( )or( )( ). Division can be represented by the
symbol(÷)or ## .
In addition to the words add, subtract, multiply and divide, there is a variety of other words that also correspond to
these mathematical operations.
Let’s start by creating a list of words that could translate into each of the mathematical operations.
TABLE 1.1: Mathematical Operations
Addition
Add
Increased by
Plus
Sum
Total
More
Subtraction
Subtract
Decreased by
Minus
Difference
Reduced by
Less than
Multiplication
Multiply
Product
Times
Twice
Of
Division
Divide
Quotient
Shared
Split between
Divided by
Let’s look at an example of translating words into a variable expression.
Remember that a variable expression has one or more variables (letters) that represent an unknown quantity.
Write the following as a mathematical expression with one variable:
A number increased by four.
First, name the variable. Let ’n’ represent the number.
Next, represent the mathematical operation by its symbol.+
Then, insert the constant after the symbol.4
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A
by four
| number
{z } increased
|
{z
} |{z}
n
4
+
The variable expression is n + 4.
Let’s look at one more example.
Write the following as a mathematical expression with two variables:
Twice the length less three times the width.
First, name the variables. Let ’l’ represent length and let ’w’ represent width.
Next, represent any operations performed on the variables.2land 3w
Then, represent the mathematical operation by its symbol.−
Twice the length |{z}
less three
times
|
{zthe width}
|
{z
}
2l
−
3w
The variable expression is2l − 3w.
Examples
Example 1
Earlier, you were given a problem about Larry and Terry and all their dimes and quarters.
Larry and Terry need to write a variable expression to show the value of ’d’ dimes and ’q’ quarters.
First, name the variables. Let ’d’ be the number of dimes. Let ’q’ be the number of quarters.
Next, express the value of the coins as decimals. Ten cents is0.10and twenty-five cents is 0.25.
Next, represent any operation performed on the variables.0.10d and 0.25q
Then, represent the mathematical operation by its symbol.+
The variable expression is0.10d + 0.25q
How can Larry and Terry use this variable expression to figure out how much money they have?
They have counted the coins and they know they have 928 dimes and 515 quarters.
They have to evaluate the variable expression0.10d + 0.25q whend = 928 and q = 515.
First, substitute the valuesd = 928 and q = 515into the expression.
0.10(928) + 0.25(515)
Next, multiply to clear the parenthesis:
0.10(928) = 92.80 and 0.25(515) = 128.75
Then, add:
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Chapter 1. Translate Verbal Phrases into Variable Expressions
92.80 + 128.75 = $221.55
The answer is$221.55
Larry and Terry can spend$221.55on their dad’s gift.
Example 2
Write the following as a mathematical expression with one variable:
One-half of Adam’s age six years ago.
First, name the variable. Let ’x’ represent Adam’s age.
Next, represent any operation performed on the variable.−6
Then, represent the mathematical operation by its symbol. 12 ( )
One-half
age six years ago
|
{z of} Adam’s
|
{z
}
1
2
(x−6)
The variable expression is 21 (x − 6).
Example 3
Write the following as a mathematical expression with two variables:
Four times the number of dimes less twice the number of quarters.
First, name the variables. Let ’d’ represent the number of dimes. Let ’q’ represent the number of quarters.
Next, represent any operation performed on the variables.
4dand2q
Then represent the mathematical operation by its symbol.[U+0080][U+0093]
Four
times the {z
number of dimes} |{z}
less twice the number of quarters
|
|
{z
}
4d
−
2q
The answer is4d − 2q.
Example 4
Write the following as a mathematical expression with two variables:
The total tax from the first purchase at 5% and the second purchase at 9%.
First, name the variables. Let ’a’ represent the first purchase. Let ’b’ represent the second purchase.
Next, represent any operation performed on the variables.+5%aand 9%b.
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Then, represent the mathematical operation by its symbol.+
The total
form the first purchase at 5% and the second purchase at 9%
|{z} tax
|
{z
}
|
{z
}
+
5%a
9%b
The answer is+5%aand 9%b.
This answer is incorrect. You must multiply by the percent expressed as a decimal. The total is the sum of the taxes
on each of the purchases.
5
= 0.05
100
9
= 0.09
9% =
100
5% =
The total
form the first purchase at 5% |{z}
and the second purchase at 9%
|{z} tax
|
{z
}
|
{z
}
0.05%a
+
The answer is0.05a + 0.09b.
Review
Write a variable expression to represent each of the following:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
The sum of a number and twelve.
The difference between a number and eight.
Three times a number
A number squared plus five
A number divided by two plus seven
Four times the quantity of a number plus six
A number times two divided by four
A number times six plus the same number times two
A number squared plus seven take a way four
A number divided by three plus twelve
A number times five and another number times six
Sixteen less than a number times negative four
A number times eight divided by two
A number divided by six and another number times negative five
A number divided by four plus another number divided by sixteen
Review (Answers)
To see the Review answers, open this PDF file and look for section 1.9.
4
0.09%b
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Chapter 1. Translate Verbal Phrases into Variable Expressions
Resources
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