More English to
Algebra
Translating word problems
Translating Verbal Phrases



The key to translating verbal phrases it to
know what the English words mean
mathematically…
It’s expected that you know the words that
mean add, subtract, multiply and divide
Here are some more terms for the following…
Words that mean Add or Subtract
COPY THIS!
Addition
Subtraction
Plus
Minus
Increased by
Sum
Less
Subtract
In all
Fewer than
More than
Decreased by
together
combined
Total
Difference between/of
Less than (reverses the order of subtraction)
Words that mean Multiply or Divide
COPY THIS!
Multiply
Times
Divide
Product of
Out of
Divided
Rate
by a factor of
Quotient of
Each
A, An, in, or per
Of
Factors
Multiplied by
Separate
Ratio of
Percent (divide by 100)
Translating Verbal Phrases
COPY THIS!

The starting point to translate verbal phrases is to
identify the variable first…

Most often you will know what the variable is by the
phrase “a number”…

It doesn’t matter which order you add or
multiply…you will get the same results; however,
when subtracting or dividing it DOES matter which
order you place the numbers
Example # 1
Five years older than her brother
1.First identify the variable…in this case the
variable is her brother’s age…lets call that a
2. The term “older than” means to add
3. Five years means the number 5
So the above expression can be written as:
5+a
Strategies
COPY THIS!

Some strategies that you can use when
working with this concept are:



Read the expression or sentence more than
once…
Underline, circle, or box each of the terms as you
identify them
Lets look at some more examples….
Example # 2
Six dollars an hour times the number of hours
1.
2.
3.
Hour is the variable …let’s call it h
Times means to multiply
Six dollars means the number 6
The algebraic expression is:
6 ∙ h This can also be written as 6h
Example # 3
Three more than the quantity five times a number
1.
2.
3.
5 times a number is the variable …let’s call
it 5n
More than means to add
Three means the number 3
The algebraic expression is:
5n + 3
Example # 4
Two less than the sum of 6 and a number m
1.
2.
3.
4.
A number m is the variable
The sum of 6 and m means to add
Two less than means to subtract 2
In this instance you have to add before you
subtract…so the sum of 6 and m would go in
parenthesis
The algebraic expression is:
(6 + m) – 2
Example # 5
A number x decreased by the sum of 10 and the square of
a number y
1.
2.
3.
4.
A number x is the variable
Decreased means to subtract
The sum means to add
In this instance you have to add the sum of 10 and
the square of a number y. Since you have to
perform this function first before you subtract …10
and the square of y would go in parenthesis
The algebraic expression is:
x – ( 10 + y2)
Verbal Sentences into
Equations and Inequalities
COPY THIS!

The words for equal are: is, are, was, were,
will be, gives, yields, sold for

The words for inequalities are as follows:
Less than
<
Less than or equal to, at most
≤
Greater than
>
Greater than or equal to, at least
≥
Example # 6
Nine less than the product of ten and a number d is
eleven
1.
2.
3.
4.
The variable is 10 and a number d, which is
written as 10d
Nine less means to subtract 9
“is” means equal
The total is 11
The algebraic expression is:
10d – 9 = 11
Comments

On the next couple of slides are some
practice problems…The answers are on the
last slide…

Do the practice and then check your
answers…If you do not get the same answer
you must question what you did…go back and
problem solve to find the error…
Your Turn
COPY THIS!
Translate the verbal phrase into an algebraic expression.
Use x for the variable in your expression
1.
Nine more than an number
2.
Three more than ½ a number
3.
The quotient of a number and two tenths
4.
The difference of ten and a number
5.
Five squared minus a number
Your Turn
COPY THIS!
Write each sentence as an algebraic equation or inequality
6.
Nine is greater than three times a number
7.
Twenty-five is the quotient of a number y and 3.5
8.
Three times the quantity two less than a number x is
ten
9.
The quotient of thirty-five and a number t is less than
or equal to seven
10.
A number q is equal to or greater than one hundred
Check your answers
Translate the verbal phrase into an algebraic expression.
Use x for the variable in your expression
1.
Nine more than an number
2.
Three more than ½ a number ½x + 3 or 3 + ½x
3.
The quotient of a number and two tenths
x  2/10
The difference of ten and a number 10 – x
4.
5.
9 + x or x + 9
Five squared minus a number 52 – x
Check your answers
Write each sentence as an algebraic equation or inequality
6.
Nine is greater than three times a number 9 > 3x
7.
Twenty-five is the quotient of a number y and 3.5
25 = y / 3.5
Three times the quantity two less than a number x is ten
3(x – 2) = 10
The quotient of thirty-five and a number t is less than or
8.
9.
equal to seven
10.
35 / t ≤ 7
A number q is equal to or greater than one hundred
q ≥ 100
SAT Word Problem example 1
If 4 less than x is 1 more than y, what is x in
terms of y?
A.
B.
C.
D.
E.
Y–3
Y+1
Y+3
Y+4
Y+5
SAT Word Problem example 2
A number x is 3 less than 4 times the number y. Two times
the sum of x and y is 9. Which of the following pairs of
equations could be used to find the values of x and y?
A.
x = 4y – 3
2(x+y) = 9
B.
y = 4x – 3
2(x+y) = 9
C.
x = 4(y – 3)
2(x+y) = 9
D.
y = 4(x – 3)
2x+y = 9
E.
x = 4y – 3
2 (xy) = 9
SAT Word Problem example 3
Arthur has 3 times as many marbles as Scott. If
Arthur gives Scott 6 marbles, Arthur will be left with
4 more marbles than Scott. What is the total
number of marbles that Arthur and Scott have?
A.
B.
C.
D.
E.
36
32
30
24
21
SAT Word Problem example 4
GRID IN
Half the difference of two positive numbers is
10. If the smaller of the two numbers is 3, what
is the sum of the two numbers?
SAT Word Problem example 5
GRID IN
If 11 is less than 7 times a certain number is 7
more than 4 times the number, what is the
number?