Translating Expressions and Sentences
Objectives:
…to translate written expressions and sentences into algebraic expressions
and equations…to represent a given situation using equations and inequalities
Assessment Anchors:
–Sol A.1- Create and/or interpret expressions, equations or inequalities that model
problem situations
NOTES
Operator Table
+
–
×
÷
Add
Sum
More
More than
Higher than
Increase
Subtract
Difference
Less
Decrease
**Less than
**Fewer than
**Subtracted from
Multiply
Product
Times
Divide
Quotient
**Special note below for these phrases.
To translate:
Read the written expression left to right.
Translate written words into mathematical operators
SPECIAL NOTE! If the phrase “less than” or “fewer than” or “subtracted from” is used, you
must invert your translation
EXAMPLES
Written expression
Algebraic Expression
The sum of A and 9
A+9
The quotient of 7 and K
7÷K
8 multiplied by C
8 C
X added to Y
X+Y
10 less than T
T – 10
Translating Expressions and Sentences
To translate more complex expressions:
the phrase “the quantity of” signifies a grouping using parenthesis
commas in written expression signify a grouping using parenthesis
the words “sum”, “difference”, “product”, “quotient” signify a grouping using parenthesis
MORE EXAMPLES
Written expression
Algebraic Expression Alternate Version
The sum of K and 9, divided by 10
(K + 9) ÷ 10
A more than the product of X and 5
A + (5X)
Written expression
Algebraic Expression Alternate Version
R divided by T, minus 6
(R ÷ T) – 6
4 less than the product of 7 and P
(7P) – 4
16 divided by the difference of A and B
16 ÷ (A – B)
The sum of X and Y, subtracted from 11
11 – (X + Y)
The product of 2 and B, less 5
(2B) – 5
To translate into equations and inequalities:
Look for key words that represent the equals sign or any inequality sign.
Translate each member (side) of the equation or inequality.
=
<
>
≤
≥
≠
…..
…..
…..
…..
…..
…..
“is” , “is equal to”, “equals”, “the result is”, “is equivalent to”
“is less than”, “is under”
“is greater than”, “is more than”, “is higher than”
“is less than or equal to”, “is not more than”, “is at most”
“is greater than or equal to”, “is not less than”, “is at least”
“is not equal to”, “is anything except”, “cannot be”
EVEN MORE EXAMPLES
Written sentence
Four less than a number is 10.
The product of 10 and a number is greater than 260 .
12 more than a number, divided by 5, is 40.
Equation or Inequality
x – 4 = 10
10y > 260
(12 + k) ÷ 5 = 40
Translating Expressions and Sentences
If the difference of a number and 4 is
multiplied by 3, the result is 19.
3(x – 4) = 19
If 7 is subtracted from six times a number,
the result is 11.
6y – 7 = 11
The sum of 10 and a number is less than 17.
10 + x < 17
The quotient of a number and 4 is not more than 10
x ÷ 4 ≤ 10
When you add 8 to the product of a number and 5,
the result is at least 150.
5k + 8 ≥ 150
STILL MORE EXAMPLES!!
Situation
Equation/Inequality
Jim has 14 CDs, which is 5 more than 3 times
as many CDs as Anna has. Use “x” to represent
how many CDs Anna has.
14 = 5 + 3x
Johnny leaves his house with $250. He comes
back with only $45. Let “y” represent how much
money he spent.
250 – y = 45
Alex worked on his math homework for 25 minutes,
Which was 5 minutes less than twice as long as
Becky worked on hers. Use “h” to represent how
Many minutes Becky worked on homework.
Ben has $400. He gets paid $15 to mow a lawn.
He would like to get a new TV that costs $1250.
Use “m” to represent how many lawns Ben must
mow in order to have enough money.
Gwen has $50 to spend at the video store. She can
rent a game system for $15, and video games for
$4 each. Use “v” to represent how many video
games she can buy.
Tom’s son is 34 inches tall. To ride on the go-karts
he must be taller than the line posted on the sign.
25 = 2h – 5
400 + 15m ≥ 1250
15 + 4v ≤ 50
Translating Expressions and Sentences
(the line is at 4 feet) If Tom’s son grows 3 inches
each year, use “y” to represent how many years
until he can ride the go-karts.
Situation
Jessica ate 24 cookies as her afternoon snack,
which is 2 more than twice as many cookies as
Dana ate. Use “c” to represent how many cookies
Dana ate.
Jim earns $9 an hour cleaning houses. He wants
to save $900 for a new stereo system. So far,
he has saved $490. Use “h” to represent how
many hours he must clean to have enough money.
Susan makes $30,000 a year, which is $5,000
less than half of what Mary makes a year. Use
“k” to represent how much Mary makes a year.
34 + 3y > 48
Equation/Inequality