Writing Expressions for Word Phrases Objectives: Translate verbal expressions into math 
expressions and vice versa. Translate verbal equations into equations 
and vice versa

What is the area of a rectangle? What is a variable? What is the area of a rectangle? Length times Width If the length is 3 meters and the width is 2 
meters, what is the area? A = L x W A = 3 x 2 = 6 meters2 A, L and W are the variables. Therefore a 
variable is any letter that represents an 
unknown number.

An algebraic expression contains: 1) one or more numbers or variables, and 2) one or more arithmetic operations (?). Examples: x - 3 3 • 2n

We are not going to use the multiplication symbol any more. Why? In expressions, there are many different 
ways to write multiplication. 1) ab 2) a • b  3) a(b) or (a)b 4) (a)(b)  5) a x b We are not going to use the 
multiplication symbol any more. Why?
 

Division, on the other hand, is written as: 1) 2) x ÷ 3

decreased by plus less than difference increased by more than minus ADDITION SUBTRACTION decreased by plus less than sum increased by difference more than minus MULTIPLICATION DIVISION product quotient times divided by multiplied by of Organize the words.

ADDITION + Words that mean Verbal Phrase Variable "Addition"  Expression 1) Plus A number y y + 5   plus 5.
  2) More than 8 more than y + 8 a number y. * Translate "more than" phrases backwards. 3) Sum The sum of 3 3 + y and a number y.

SUBTRACTION − Words that mean Verbal Phrase Variable "Subtraction" Expression 1) Difference  The difference y - 12 of a number y and 12. 2) Less Than 3 less than a y - 3 number y. * Translate "less than" phrases backwards. 3) Minus  8 minus a 8 - y

MULTIPLICATION x • ( ) Words that mean Verbal Phrase Variable "Multiplication" Expression 1) Product The product 2 • 8 , 2 x 8 ,   of 2 and 8. 2(8) 2) Times A number y 5y , 5 x y,   times 5. 5 • y, 5(y)   * When multiplying a number and a variable, the number is always written first. 3) Multiplied by A number y 3y, 3 x y,   multiplied by 3. 3 • y, 3(y)

DIVISION ÷ ∕ − Words that mean Verbal Phrase Variable "Division"  Expression 1) Quotient The quotient of 12 ÷ 4, 12 and 4. 12/4, 12   4 2) Divided By A number y y ÷ 2, divided by 2. y/2, y   2

Directions: Organize the "addition" words by 
dragging out the words from the word bank. more than times remainder add subtract plus decreased by quotient difference multiply total divide product sum minus less than increased by ADDITION

Directions: Organize the "subtraction" words by 
dragging out the words from the word bank. more than times remainder add subtract plus decreased by quotient difference multiply total divide product sum minus less than increased by SUBTRACTION

Directions: Organize the "multiplication" words 
by dragging out the words from the word bank. more than times remainder add subtract plus decreased by quotient difference multiply total divide product sum minus less than increased by MULTIPLICATION

Directions: Organize the "division" words by 
dragging out the words from the word bank. more than times remainder add subtract plus decreased by quotient difference multiply total divide product sum minus less than increased by DIVISION

Translate the verbal phrase into a variable expression. 1) The sum of a number y and 20. 2) Six more than twice a number y. 3) The difference of 8 and a number y. 4) 9 divided by a number y. 5) The product of a number y and 20. 6) Two less than a number y. y + 20 2y + 6 8 - y 9 ÷ y, 9∕y, 9 y 20y, 20(y), 20•y y - 2 (Click on the yellow box to reveal the answer.)

2(4y) 4y + 2 5(y+3w) 5(y + 3)•w 8(12 - 2) 8(12 + 2) Translate the phrase as a variable expression. Click on the speaker to reveal answer. 2(4y) 7) Two more than 4 times a number y 4y + 2 8) Five times the sum of a number y and 3 times another number w. 5(y+3w) 5(y + 3)•w 9) Eight times the difference of 12 and 2. 8(12 - 2) 8(12 + 2)

11) The quotient of 14 divided by a number y. Match the expression to the phrase by dragging 
the variable expression to the verbal phrase. 14 - y 14 ÷ (7 - y) 7(14 + y) 14y 7 + y 2(y + 7) y + 14 7 + 14y y - 14 14 ÷ y 10) A number y multiplied by 14. 11) The quotient of 14 divided by a number y. 12) 14 less than a number y. 13) 7 increased by a number y. 14) A number y subtracted from 14.

16) 7 more than the product of 14 and a number y. Match the expression to the phrase by dragging the 
variable expression to the verbal phrase. 14 - y 14 ÷ (7 - y) 7(14 + y) 14y 7 + y 2(y + 7) y + 14 7 + 14y y - 14 14 ÷ y 15) 14 more than a number y. 16) 7 more than the product of 14 and a number y. 17) Twice the sum of a number y and 7. 18) Product of 7 and the sum of 14 and a number y. 19) 14 divided by the difference when a number y is subtracted from 7.

21) The number of yards in y feet. Match the expression to the phrase by dragging the 
variable expression to the verbal phrase. 24y 3y 60y y ÷ 60 y ÷ 24 y ÷ 3 20) The number of hours in y days. 21) The number of yards in y feet. 22) The number of minutes in y seconds. 23) The number of seconds in y minutes. 24) The number of days in y hours. 25) The number of feet in y yards.

What are some verbal expressions that suggest the equal sign? What is the difference between an 
algebraic expression and an equation? What are some verbal expressions that suggest 
the equal sign?

Which of the following expressions represents 7 times a number decreased by 13? 1. 7x + 13 2. 7x - 13 3. 13 - 7x 4. 13 + 7x

Which one of the following expressions 
represents 28 less than three times a number?

Which of the following verbal expressions represents 2x + 9? a. 9 increased by twice a number b. a number increased by nine c. twice a number decreased by 9 d. 9 less than twice a number

Which of the following expressions represents 
the sum of 16 and five times a number? a. 5x - 16 b. 16x + 5 c. 16 + 5x d. 16 - 5x

When looking at the expression 103 10 is called the base and 3 is called the exponent or power. 103 means 10 • 10 • 10 103 = 1000

How is it said? 21 Two to the first power 22 23 2n7 Two to the second power or two squared 23 Two to the third power or two cubed 2n7 Two times n to the seventh power

Which of the following verbal expressions represents x2 + 2x? a. the sum of a number squared and twice a number b. the sum of a number and twice the number c. twice a number less than the number squared d. the sum of a number and twice the number squared

Which of the following expressions 
represents four less than the cube of a 
number? a. 4 – x3 b. 4 – 3x c. 3x – 4 d. x3 – 4


Evaluate. 21 2  22 2 • 2 = 4 23 2 • 2 • 2 = 8 2n7 We can’t evaluate because we   don’t know what n equals to!!

Evaluate each and find out! Is 35 the same as 53? Evaluate each and find out! 35 = 53 =

Complete Study Guide and Intervention p. 1 (odds) p. 2 (odds) p. 33 (1 - 4) p. 34 (odds) Due at end of class (no exceptions)