holt algebra 1 1-1 variables and expressions 1-1 variables and expressions holt algebra 1 warm up...

Holt Algebra 1

1-1 Variables and Expressions1-1 Variables and Expressions

Holt Algebra 1

Warm Up

Lesson Quiz

Lesson Presentation

Holt Algebra 1

1-1 Variables and Expressions

Warm UpAdd or subtract.

1. 6 + 104 2. 12(9)

3. 23 – 8 4.

Multiply or divide.

5. 324 ÷ 18 6.

7. 13.5(10) 8. 18.2 ÷ 2

108110

15

18

135 9.1

6

Holt Algebra 1


Translate between words and algebra. Evaluate algebraic expressions.

Objectives

Holt Algebra 1


variableconstantnumerical expressionalgebraic expressionevaluate

Vocabulary

Holt Algebra 1


A variable is a letter or a symbol used to represent a value that can change.

A constant is a value that does not change.

A numerical expression contains only constants and operations.

An algebraic expression may contain variables, constants, and operations.

Holt Algebra 1


You will need to translate between algebraic expressions and words to be successful in math.

Plus, sum,increased by

+ –

Minus, difference, less than

Times, product, equal groups of

Divided by, quotient

Holt Algebra 1


These expressions all mean “2 times y”:2y 2(y)2•y (2)(y)2 x y (2)y

Writing Math

Holt Algebra 1


Give two ways to write each algebra expression in words.

A. 9 + r B. q – 3

the sum of 9 and r

9 increased by r

the product of m and 7

m times 7

the difference of q and 3

3 less than q

the quotient of j and 6

j divided by 6

Example 1: Translating from Algebra to Words

C. 7m D. j 6

Holt Algebra 1


1a. 4 - n 1b.

1c. 9 + q 1d. 3(h)

4 decreased by n

the sum of 9 and q

the quotient of t and 5

the product of 3 and h

Give two ways to write each algebra expression in words.

Check It Out! Example 1

n less than 4 t divided by 5

q added to 9 3 times h

Holt Algebra 1


To translate words into algebraic expressions, look for words that indicate the action that is taking place.

Put together, combine

Add Subtract

Multiply Divide

Find how much more or less

Put together equal groups

Separate into equal groups

Holt Algebra 1


John types 62 words per minute. Write an expression for the number of words he types in m minutes.

m represents the number of minutes that John types.

62 · m or 62m Think: m groups of 62 words

Example 2A: Translating from Words to Algebra

Holt Algebra 1


Roberto is 4 years older than Emily, who is y years old. Write an expression for Roberto’s age

y represents Emily’s age.

y + 4 Think: “older than” means “greater than.”

Example 2B: Translating from Words to Algebra

Holt Algebra 1


Joey earns $5 for each car he washes. Write an expression for the number of cars Joey must wash to earn d dollars.

d represents the total amount that Joey will earn.

Think: How many groups of $5 are in d?

Example 2C: Translating from Words to Algebra

Holt Algebra 1


Use the Commutative, Associative, and Distributive Properties to simplify expressions.

Combine like terms.

Objectives

Holt Algebra 1


The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms.

4x – 3x + 2

Like terms Constant

Holt Algebra 1


A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1.

1x2 + 3x

Coefficients

Holt Algebra 1


Holt Algebra 1


The Distributive Property is used with Addition to Simplify Expressions.

The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.

Holt Algebra 1


Example 2A: Using the Distributive Property with Mental Math

Write the product using the Distributive Property. Then simplify.

5(59)

5(50 + 9)

5(50) + 5(9)

250 + 45

295

Rewrite 59 as 50 + 9.

Use the Distributive Property.

Multiply.

Add.

Holt Algebra 1


8(33)

8(30 + 3)

8(30) + 8(3)

240 + 24

264

Rewrite 33 as 30 + 3.

Use the Distributive Property.

Multiply.

Add.

Example 2B: Using the Distributive Property with Mental Math

Write the product using the Distributive Property. Then simplify.

Holt Algebra 1



Simplify by combining like terms.

3a. 16p + 84p

16p + 84p

100p

16p + 84p are like terms.

Add the coefficients.

3b. –20t – 8.5t2

–20t – 8.5t2 20t and 8.5t2 are not like terms.

–20t – 8.5t2 Do not combine the terms.

3m2 + m3 3m2 and m3 are not like terms.

3c. 3m2 + m3

Do not combine the terms.3m2 + m3

Holt Algebra 1


Example 4: Simplifying Algebraic Expressions

Simplify 14x + 4(2 + x). Justify each step.

14x + 4(2) + 4(x) Distributive Property

Multiply.

Commutative Property

Associative Property

Combine like terms.

14x + 8 + 4x

(14x + 4x) + 8

14x + 4x + 8

18x + 8

14x + 4(2 + x)1. 2. 3. 4. 5. 6.

Procedure Justification

Holt Algebra 1


6(x) – 6(4) + 9 Distributive Property

Multiply.Combine like terms.

6x – 24 + 9

6x – 15

6(x – 4) + 91. 2. 3. 4.


Check It Out! Example 4a

Simplify 6(x – 4) + 9. Justify each step.

Holt Algebra 1


–12x – 5x + x + 3a Commutative Property

Combine like terms.–16x + 3a

–12x – 5x + 3a + x1. 2. 3.


Check It Out! Example 4b

Simplify −12x – 5x + 3a + x. Justify each step.

Holt Algebra 1


Lesson Quiz: Part I

Simplify each expression.

1. 165 +27 + 3 + 5

2.

Write each product using the Distributive Property. Then simplify.

3. 5($1.99)

4. 6(13)

200

8

5($2) – 5($0.01) = $9.95

6(10) + 6(3) = 78

Holt Algebra 1


Lesson Quiz: Part II

Simplify each expression by combining like terms. Justify each step with an operation or property.

7. 301x – x

8. 24a + b2 + 3a + 2b2

5.

300x

27a + 3b2

6. 14c2 – 9c 14c2 – 9c

Holt Algebra 1


Lou drives at 65 mi/h. Write an expression for the number of miles that Lou drives in t hours.


t represents the number of hours that Lou drives.

65t Think: number of hours times rate per hour.

Holt Algebra 1


Miriam is 5 cm taller than her sister, than her sister who is m centimeters tall. Write an expression for Miriam’s height in centimeters.

Check It Out! Example 2b

m represents Miriam’s sister's height in centimeters.

m + 5 Think: Miriam's height is 5 added to her sister's height.

Holt Algebra 1


Check It Out! Example 2c

d represents the amount of money Elaine will earn each day.

32d Think: The number of days times the amount Elaine would earn each day.

Elaine earns $32 per day. Write an expression for the amount she earns in d days.

Holt Algebra 1


To evaluate an expression is to find its value.

To evaluate an algebraic expression, substitute numbers for the variables in the expression and then simplify the expression.

Holt Algebra 1


Evaluate each expression for a = 4, b =7, andc = 2.

A. b – c

b – c = 7 – 2 Substitute 7 for b and 2 for c.= 5

B. acac = 4 ·2

= 8

Substitute 4 for a and 2 for c.

Simplify.

Simplify.

Example 3: Evaluating Algebraic Expression

Holt Algebra 1


Evaluate each expression for m = 3, n = 2, and p = 9.

a. mn

b. p – n

c. p ÷ m


mn = 3 · 2

p – n = 9 – 2 = 7

= 6

p ÷ m = 9 ÷ 3 = 3

Substitute 3 for m and 2 for n.Simplify.

Substitute 9 for p and 2 for n.Simplify.

Substitute 9 for p and 3 for m.Simplify.

Holt Algebra 1


Example 4a: Recycling Application

Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag.

Write an expression for the number of bottles needed to make s sleeping bags.

The expression 85s models the number ofbottles to make s sleeping bags.

Holt Algebra 1


Find the number of bottles needed to make20, 50, and 325 sleeping bags.

Evaluate 85s for s = 20, 50, and 325.

s 85s

20

50

325

85(20) = 1700

85(50) = 4250

85(325) = 27,625

Example 4b: Recycling Application Continued

Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag.

To make 20 sleeping bags 1700 bottles are needed.

To make 50 sleeping bags 4250 bottles are needed.

To make 325 sleeping bags 27,625 bottles are needed.

Holt Algebra 1


A replacement set is a set of numbers that canbe substituted for a variable. The replacementset in Example 4 is (20, 50, and 325).

Writing Math

Holt Algebra 1


To make one sweater, 63 twenty ounceplastic drink bottles must be recycled.

Write an expression for the number of bottles needed to make s sweaters.

The expression 63s models the number ofbottles to make s sweaters.


Holt Algebra 1


Find the number of bottles needed to make12, 25 and 50 sweaters.

Evaluate 63s for s = 12, 25, and 50.

s 63s

12

25

50

63(12) = 756

63(25) = 1575

63(50) = 3150

To make 12 sweaters 756 bottles are needed.



Check It Out! Example 4b Continued

To make one sweater, 63 twenty ounceplastic drink bottles must be recycled.

Holt Algebra 1


Give two ways to write each algebraicexpression in words.

1. j – 3

2. 4p

3. Mark is 5 years older than Juan, who is y years old. Write an expression for Mark’s age.

The difference of j and 3; 3 less than j.

4 times p; The product of 4 and p.

y + 5

Lesson Quiz: Part I

Holt Algebra 1


Evaluate each expression for c = 6, d = 5, and e = 10.

4. 5. c + d

Shemika practices basketball for 2 hours each day.

de

12

11

2d

10 hours; 24 hours; 40 hours

Lesson Quiz: Part II

6. Write an expression for the number of hours she practices in d days.

7. Find the number of hours she practices in 5, 12, and 20 days.

holt algebra 1 1-1 variables and expressions 1-1 variables and expressions holt algebra 1 warm up...

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