Unit 7, Lesson 1: Translating Expressions

Standard: AF 1.1Objective: Translate verbal phrases

Vocabulary & Key Concepts Expression: numbers, variables, and operations.

Example: 3x – 6

Numerical Expression: numbers and operations only. Example: 4 + 7

Algebraic Expression: expression with variables. Example: x + 10

Term: numbers with variables separated by + or – signs. Example: 7x + 9y – 7

Objective - To translate variable expressions.

addplussum

increased bytotal

more than

added to

subtractminus

differencedecreased by

diminished by

less than

subtracted from

less

multiplytimes

product…of...twice 2

dividequotient

Backwards Words

Add 3 and 7 = 3 + 7

The sum of 3 and 7 = 3 + 7

3 increased by 7 = 3 + 7

The total of 3 and 7 = 3 + 7

3 more than 7 = 7 + 3

3 added to 7 = 7 + 3

Backwards Words

7 subtract 3 = 7 - 3

The difference of 7 and 3 = 7 - 3

7 decreased by 3 = 7 - 3

7 diminished by 3 = 7 - 3

7 less than 3 = 3 - 7

7 subtracted from 3 = 3 - 7

7 less 3 = 7 - 3

Translate the following phrases.1) Five plus x minus 3

2) Three times y less 4

3) Eight multiplied by y minus 7

4) The product of 10 and m decreased by 7

5) Four more than the quotient of x and 3

6) Six times m plus 8

5 + x - 3

8y - 7

10m - 7

6m + 8

3y 4

x 3 4 xor 43

Match each phrase with its variable expression.

1) Twice the sum of x and 3

2) Two less than the productof 3 and x

3) Three times the difference of x and 2

4) Twice a number x less 3

5) Two more than 3 times anumber x

a) 2x 3

b) 3 x 2

c) 3x 2

d) 2 x 3

e) 3x 2

a

b

e

c

d

Write a phrase that describes each variable expression below.

1)

2)

3)

4 x 5 2

7 2 x 3

m 9 4

Four times the sum of x and 5 minus 2

Seven minus twice the quotient of x and 3

The quotient of m and 9 minus 4

Define a variable to represent the unknown andwrite the phrase as a variable expression.1) 10 mph faster than the Honda

2) 7 inches shorter than Jill’s brother

3) 5 acres larger than twice the size of my lot

4) $7.50 times the number of people plus a$20 group registration

Let x = the speed of the Hondax + 10

Let b = the height of Jill’s brotherb - 7

Let k = the size of my lot2k + 5

Let y = the number of people$7.5y + $20

Problem Situation #1

A cab driver charges a surcharge of $4 plus$1.50 per mile. Write a variable expressionthat represents the total cost of the fare.

Let x = # of miles driven

4 + 1.5x

Problem Situation #2ATI Phone Services charges a monthly fee of$16 plus 18 cents a minute for local calls and40 cents a minute for long distance. Write a variable expression that describes the totalmonthly bill.

Let a = # of local minutes

16

Let b = # of long distance minutes

+ 0.18a + 0.40b

Review

1) What is the difference between a numerical expression and an algebraic expression?

2) What is a term?3) What is a word for add?4) What is a word for subtract?5) What is a word for multiply?6) What is a word for divide?