Simple Verbal Expressions to Algebraic Expressions Date: ___________________________ SOL 7.23 The student will write verbal expressions/sentences as algebraic expressions/equations.

Build Your Vocabulary In the __________________ expression, lw, the letters l and w are called

_____________________.

In Algebra, variables are symbols used to represent unspecified _______________ or

________________. Any _____________ can be used as a variable. The letters l and w are

used above because they are the first letters of the words _______________ and

___________.

In the expression lw, l and w are called ________________, and the result is called the

__________________.

An expression like _______ is called a power and is read ________________ power. In the

expression nx , x is the __________ and the n is the __________________. The exponent

indicates the number of times the ____________ is used as a _________________.

Symbols Words Meaning

13 3 to the first power 3

23

3 to the ____________ power or 3 ____________ 3 • 3

33

3 to the ____________ power or 3 ____________ 3 • 3 • 3

43 3 to the ____________ power 3 • 3 • 3 • 3

52x 2 times x to the __________ power

___ • ___ • ___ • ___ • ___ • ___

Example 1 Write Simple Algebraic Expressions of Sums

Write a verbal expression for each algebraic expression.

a. a number n more than four four more than a number n

______________________ ______________________

b. a number p added to eleven eleven added to a number p

______________________ ______________________

c. a number x increased by eight eight increased by a number x

______________________ ______________________

d. a number m plus seven seven plus a number m

______________________ ______________________

e. the sum of a number c and nine the sum of nine and a number c

______________________ ______________________

Example 2 Write Simple Algebraic Expressions of Differences

Write an algebraic expression for each verbal expression.

a. a number y less than seven seven less than a number y

______________________ ______________________

b. one subtracted from a number w a number w subtracted from one

______________________ ______________________

c. a number h decreased by three three decreased by a number h

______________________ ______________________

d. a number p minus four four minus a number p

______________________ ______________________

e. five less a number k a number k less five

______________________ ______________________

d. the difference of a number x and six the difference of six and number x

______________________ ______________________

Example 3 Write Algebraic Expressions of Products

Write an algebraic expression for each verbal expression.

a. two times a number x __________________

b. twice a number c __________________

c. the product of two and a number p __________________

d. two multiplied by a number h __________________

Example 4 Write Algebraic Expressions of Quotients

a. a number m divided by eight eight divided by a number m

______________________ ______________________

b. the quotient of a number r and eight the quotient of eight and a number r

______________________ ______________________

Example 5 Write Algebraic Expressions with Powers

Write each expression algebraically.

a. a number a squared __________________

the square of a number a __________________

a number a to the second power __________________

b. a number w cubed __________________

the cube of a number w __________________

a number w to the third power __________________

c. a number x to the fourth power __________________

Example 5 Write Algebraic Expressions Using All Operations

Translate each phrase into an algebraic expression. Define the variable first!

a. twice a number Mark’s salary plus a $200 bonus

Let ____ be Mark’s salary ___________________

b. three more than the number of people squared

Let ____ be the number of people ___________________

c. six feet shorter than three times the mountain’s height

Let ____ be the height of the mountain ___________________

d. two seconds faster than four times Sarah’s time

Let ____ be Sarah’s time ___________________

e. five times a number less four

Let ____ be a number ___________________

f. seven less than a number times eight

Let ____ be a number ___________________

g. nine more than a number divided by six

Let ____ be a number ___________________

h. the quotient of eight and twice a number

Let ____ be a number ___________________

i. six times a number minus eleven

Let ____ be a number ___________________

j. the product of eight hundred and the cube of a number

Let ____ be a number ___________________

k. half the distance to school

Let ____ be the distance to school ___________________

l. eleven more than the product of seven and a number

Let ____ be a number ___________________

m. thirteen less the quotient of a number and twenty

Let ____ be a number ___________________

n. one-third a number added to one-fifth

Let ____ be a number ___________________

o. a number added to fifteen

Let ____ be a number ___________________

p. one added to a twice a number

Let ____ be a number ___________________

q. the square of a number less one

Let ____ be a number ___________________

r. twice the cube of a number increased by four

Let ____ be a number ___________________

s. the sum of seven times a number and five

Let ____ be a number ___________________

t. the difference of two and a number cubed

Let ____ be a number ___________________

Assignment Look at the phrases from Example 5, write your own phrases and translate them into algebraic expressions on separate sheet(s) of paper. There are 20 phrases.