UNIT 1.1 PATTERNS AND EXPRESSIONS

1.1

Perform the indicated operation.

1. 12 1.5 2. 3.3 7

ANSWER 8 ANSWER 23.1

3. 11.6 – 5.9

ANSWER 5.7

4. Julia ran 10 2miles last week and 8 5

miles this week.

How many more miles did she run last week?3 6

ANSWER 1 5 mi6

1.1 Vocabulary

Variable – a letter that is used to replace a

number

Algebraic expression – an expression that

contains numbers, varailbes, and operations.

Evaluate and algabreic expression – to find the

value of an algabreic expression by substituting a

number for each variable.

Power – an expression that represents reapeated

multiplication of the same factor.

1.1 VocabularyExponent – the number or variable that represents

the number of times the base of a power is used as

a factor.

Base of a power – the number or expression that is

used as a factor in repeated multiplication.

Example

9³Base Exponent

1.1

Evaluate the expression when n = 3.

Substitute 3 for n.

Multiply.

Substitute 3 for n.

Subtract.

c. n – 1 = 3 – 1

= 2

Substitute 3 for n.

= 3 Divide.

93

b.9n

=

Substitute 3 for n.

Add.

d. n + 8 = 3 + 8

= 11

a. 13 n = 13 3

= 39

1.1

1. 12

3. 6

2. 4

Evaluate the expression when y = 2.

1. 6y

2.8y

3. y + 4

4. 94. 11 – y

ANSWERS

1.1

Movies

The total cost of seeing a movie at a theater can be

represented by the expression a + r where a is the

cost (in dollars) of admission and r is the cost (in

dollars) of refreshments. Suppose you pay $7.50 for

admission and $7.25 for refreshments. Find the total

cost.

1.1

Add.

The total cost is $14.75

ANSWER

Write expression.

Substitute 7.50 for a and

7.25 for r.= 7.50 + 7.25

= 14.75

Total cost =

SOLUTION

a + r

1.1

WHAT IF? In Example 2, suppose you go back to the theater with a friend to see an afternoon movie.You pay for both admissions. Your total cost (indollars) can be represented by the expression 2a. Ifeach admission costs $4.75, what is your total cost?

The total cost is $9.50.

ANSWER

1.1

Product

Write the power in words and as a product.

Power Words

seven to the first powera. 71 7

five to the second power,

or five squared

b. 52 5 5

c. 12

3one half to the third power,

or one half cubed

1 1 12 2 2

z to the fifth powerd. z5 z z z z z

1.1

Write the power in words and as a product.

Power Words Product

Nine to the fifth power6. 95

Two to the eighth power7. 28

n to the fourth power

9 9 9 9 9

2 2 2 2 2 2 2 2

8. n4 n n n n

1.1

a. x4 = 24

= 2 2 2 2

= 16

Evaluate the expression.

a. x4 when x = 2

b. n3 = 1.53

= (1.5)(1.5)(1.5)

= 3.375

b. n3 when n = 1.5

SOLUTION

1.1

Evaluate the expression.

9. x3 when x = 8 9. 512

10. 6.2510. k3 when k = 2.5

ANSWERS

11. d4 when d = 1

311.

1

81

1.1

SOLUTION

Storage cubes

Write formula for volume.

Substitute 14 for s.

Evaluate power.

V = s3

= 143

= 2744

Each edge of the medium-sized

pop-up storage cube shown is 14

inches long. The storage cube is

made so that it can be folded flat

when not in use. Find the

volume of the storage cube.

The volume of the storage cube is 2744 cubic inches.

1.1

WHAT IF? In Example 5, suppose

the storage cube is folded flat to

form a square. Find the area of the

square.

The area of square is 196 in2.

ANSWER

1.1

3. 54

ANSWER 0.9

ANSWER 625

Evaluate the expression or power.

1. 13g when g = 7 2. 1.65 – a when a = 0.75

ANSWER 9113

3

4.

ANSWER 127

5. Emily is saving for a $300 bicycle. She has saved

$128.25. The amount she still needs to save is given

by the expression c – s, where c is the cost of the

bicycle and s is the amount she has saved. How

much does she have left to save?

$171.75ANSWER

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