1. – ALGEBRA I – Unit 1 – Section 2
Translating Words into Expressions and Equations
The process of translating written statements into mathematical expressions can by tricky…but the key is knowing which words mean which mathematical operations.
Let’s start by looking at the words for the basic arithmetic…

2. IMPORTANT GENERAL WORDS TO KNOW
What does the word NUMBER always translate into in math?
The word number always implies your variable.
X…Y…t…m…etc.
What does the word IS translate into in math?
The word IS (when used by itself) means equals (=).

3. WORDS THAT MEAN ADDITION
What are some words that mean addition?
SUM
INCREASE
A few words might include:
PLUS
ADD
MORE THAN
MORE
GREATER THAN
GREATER

4. WORDS THAT MEAN ADDITION
Translate the following statements into mathematical expressions:
A number is increased by twelve.
X + 12
Eight more than a number.
X + 8
The sum of a number and fifteen.
X + 15

5. WORDS THAT MEAN ADDITION
Is it okay to switch the order of the variable and the number when you add?
X + 12
12 + X
YES!
X + 8
8 + X
X + 15
15 + X

6. WORDS THAT MEAN SUBTRACTION
What are some words that mean subtraction?
DIFFERENCE
DECREASE
A few words might include:
SUBTRACT
TAKE AWAY
MINUS
**LESS THAN
LESS
**SUBTRACTED FROM

7. WORDS THAT MEAN SUBTRACTION
What is the difference between “less than” and “subtracted from” as compared to the others?
When you are writing the expression, you need to switch the order of the terms so that they are in the opposite order in the expression as compared to how they were written in words.

8. WORDS THAT MEAN SUBTRACTION
Translate the following statements into mathematical expressions:
A number is decreased by five.
X – 5
Sixteen less than a number.
X – 16
The difference between eight and a number.
8 – X

9. NO! WORDS THAT MEAN SUBTRACTION X – 5 5 – X X – 16 16 – X 8 – X X – 8
Is it okay to switch the order of the variable and the number when you subtract?
NO!
X – 5
5 – X
X – 16
16 – X
You cannot switch the order when you subtract.
8 – X
X – 8

10. WORDS THAT MEAN MULTIPLICATION
What are some words that mean multiplication?
PRODUCT
MULTIPLY
A few words might include: OF
(when used by itself)
TIMES
**TWICE
**DOUBLE
**TRIPLE

11. WORDS THAT MEAN MULTIPLICATION
Translate the following statements into mathematical expressions:
Nine times a number. 9x
The product of a number and two. 2x
A number multiplied by four. 4x

12. WORDS THAT MEAN MULTIPLICATION
Is it okay to switch the order of the variable and the number when you multiply? 9x
x · 9
YES! 2x
x · 2 4x
x · 4

13. WORDS THAT MEAN DIVISION
What are some words that mean division?
DIVIDED BY
QUOTIENT
A few words might include:
DIVIDE
**HALF
**THIRD
**FOURTH

14. WORDS THAT MEAN DIVISION
Translate the following statements into mathematical expressions:
A number divided by 8.
X  8
Nineteen divided by a number.
19  X
The quotient of a number and three.
X  3

15. WORDS THAT MEAN DIVISION You cannot switch the order when you divide.
Is it okay to switch the order of the variable and the number when you divide?
NO!
X  8
8  X
19  X
X  19
You cannot switch the order when you divide.
X  3
3  X

16. EXPRESSIONS AND EQUATIONS What is a mathematical expression?
An expression is a mathematical statement that contains numbers, variables, and symbols.
What is an equation?
An equation contains an two expressions separated by an equal sign (=).

17. WRITING EQUATIONS
When translating an equation from words into mathematical symbols, follow these steps:
Look for the word “is”. This is your equals sign and literally splits the sentence into the two parts.
Work on each part of the equation separately.
Look for the word number and begin translating the phrase closest to that word.

18. WRITING EQUATIONS X – 6 = 12 Final equation  X – 6 = 12
Translate the following equation:
The difference between a number and six is twelve.
X – 6 = 12
Final equation 
X – 6 = 12

19. WRITING EQUATIONS Three times a number is fifteen. 3x = 15
Try translating these equations. Look out for ones that have two or more steps!
Three times a number is fifteen.
3x = 15
Four more than twice a number is twenty-six.
2x + 4 = 26
The sum of a number and five is tripled. The result is sixty.
3(x + 5) = 60

20. Try These Problems… 1. Five more than a number is twelve.
Try translating these equations. Although there is no “work” to show, check your answer to see if makes sense.
1. Five more than a number is twelve.
2. The product of a number and three is twenty-seven.
3. Eight more than a number is the same as five times the number.
4. Twice the difference of a number and three is five less than the number.
**The answers can be found at the end of the PowerPoint.

21. ALGEBRA IS FUN AND EASY!
**Answers: 1) x + 5 = 12 2) 3x = 27 3) x + 8 = 5x 4) 2(x – 3) = x – 5