The document discusses translating verbal phrases and sentences into algebraic expressions and equations. It provides examples of translating phrases involving addition, subtraction, multiplication, and division. It also gives examples of translating sentences into algebraic equations, such as "Five times a number y increased by 3, is 23" which translates to 5y + 3 = 23. The document emphasizes that being able to translate between verbal and algebraic representations is an important skill.

1.
Translating Verbal Phrases
Jennifer Duggan
Verbal Phrases/Operation

2. Addition: The sum of a number and 8 x 8
Five is added to a number x 5
Two more than a number x 2
A number increased by 3 x 3
Subtraction: Four is subtracted from a number x 4
Three less than a number x 3
The difference between 7 and a number 7 x
A number decreased by 2 x 2
Multiplication: The product of 5 and a number 5x
Twice a number 2x
One-half of a number x
Five percent of a number 0.05x
Division: The ratio of a number to 6
The quotient of 5 and a number
Three divided by some number.
There is often more than one unknown quantity in a problem, but a
relationship between the unknown quantities is given. For example, if one
unknown number is 5
more than another unknown number, we can use
x and x 5,
to represent them. Note that x and x 5 can also be used to represent two
unknown
numbers that differ by 5, for if two numbers differ by 5, one of the numbers
is 5
more than the other.
How would you represent two numbers that have a sum of 10? If one of
the
numbers is 2, the other is certainly 10 ­ 2, or 8. Thus if x is one of the

3. numbers,
then 10 ­ x is the other. The expressions
x and 10 ­ x
have a sum of 10 for any value of x.
Verbal Phrase
Algebraic Language
4 more than x
x + 4
8 less than m
m - 8
the product of 5 and x
5x
y divided by 6
y/6
two times z increased by x
2z + x
4 times y, decreased by 3 times x
the sum of 6 times x, and 7
4y - 3x
6x + 7
All of the examples involved translating a verbal phrase
into an algebraic expression.
It is also important to be able to translate a verbal sentence into an
algebraic equation.
Let's look at a few of those examples....
Five times a number y increased by 3, is 23.
5y + 3 = 23
17 diminished by twice a number x is 1.

4. 17 - 2x = 1
The quotient of sixteen and x is 8
16/x = 8
If five is increased by the product of three and x,
the result is 26
5 + 3x = 26
If a number y is added to three times y
the result is thirty-six.
3y + y = 36