course 2 1-8 translate words into math do now evaluate each algebraic expression for the given value...

Course 2

1-8 Translate Words into Math

Do NowEvaluate each algebraic expression for the given value of the variables.

1. 7x + 4 for x = 6

2. 8y – 22 for y = 9

3. 12x + for x = 7 and y = 4

4. y + 3z for y = 5 and z = 6

46

50

868y

23

Hwk: p 6 & 8 due Wednesday, test on chap 1 sec1-5

Course 2


EQ: How do I translate words into numbers, variables, and operations and use properties to solve algebraic expressions?

M7A1a Translate verbal phrases to algebraic expression

M7P1c Adapt and apply a variety of appropriate strategies to solve problems

Course 2


Course 2


Operation Verbal ExpressionsAlgebraic

Expressions

• add 3 to a number• a number plus 3• the sum of a number and 3• 3 more than a number • a number increased by 3

• subtract 12 from a number

• a number minus 12

• the difference of a number and 12• 12 less than a number

• a number decreased by 12

• take away 12 from a number• a number less than 12

n + 3

x – 12

Course 2


Operation Verbal ExpressionsAlgebraic

Expressions

• 2 times a number

• 2 multiplied by a number

• the product of 2 and a number

• 6 divided into a number

• a number divided by 6

• the quotient of a number and 6

2m or 2 • m

÷÷a6

÷ 6 ora

Course 2


Additional Example 1: Translating Verbal Expressions into Algebraic Expressions

Write each phrase as an algebraic expression.

A. the quotient of a number and 4

quotient means “divide”

B. w increased by 5

increased by means “add”

w + 5

n4

Course 2



Additional Example 1: Translating Verbal Expressions into Algebraic Expressions

C. the difference of 3 times a number and 7

the difference of 3 times a number and 7

D. the quotient of 4 and a number, increased by 10

3 • x – 73x – 7

the quotient of 4 and a number, increased by 10

4n + 10

Course 2


Check It Out: Example 1

A. a number decreased by 10

decreased means “subtract”

B. r plus 20

plus means “add”

r + 20

n – 10


Course 2




C. the product of a number and 5

D. 4 times the difference of y and 8

y – 8

n • 5

the product of a number and 5

5n

4 times the difference of y and 8

4(y – 8)

4 •

Course 2


When solving real-world problems, you may need to determine the action to know which operation to use.

Action Operation

Put parts together

Put equal parts together

Find how much more

Separate into equal parts

Add

Multiply

Subtract

Divide

Course 2


Mr. Campbell drives at 55 mi/h. Write an algebraic expression for how far he can drive in h hours.

Additional Example 2A: Translating Real-World Problems into Algebraic Expressions

You need to put equal parts together. This involves multiplication.

55mi/h · h hours = 55h miles

Course 2


On a history test Maritza scored 50 points on the essay. Besides the essay, each short-answer question was worth 2 points. Write an expression for her total points if she answered q short-answer questions correctly.

Additional Example 2B: Translating Real-World Problems into Algebraic Expressions

The total points include 2 points for each short-answer question.

Multiply to put equal parts together.

In addition to the points for short-answer questions, the total points included 50 points on the essay.

Add to put the parts together: 50 + 2q

2q

Course 2


Check It Out: Example 2A

Julie Ann works on an assembly line building computers. She can assemble 8 units an hour. Write an expression for the number of units she can produce in h hours.

You need to put equal parts together. This involves multiplication.

8 units/h · h hours = 8h

Course 2


Check It Out: Example 2B

At her job Julie Ann is paid $8 per hour. In addition, she is paid $2 for each unit she produces. Write an expression for her total hourly income if she produces u units per hour.

Her total wage includes $2 for each unit produced.

Multiply to put equal parts together.

In addition the pay per unit, her total income includes $8 per hour.

Add to put the parts together: 2u + 8.

2u

Course 2


VocabularyCommutative PropertyAssociative PropertyIdentity PropertyDistributive Property

Course 2


Course 2


Additional Example 1: Identifying Properties of Addition and Multiplication

Tell which property is represented.

A. (2 6) 1 = 2 (6 1)

B. 3 + 0 = 3

C. 7 + 9 = 9 + 7

Associative Property

Identity Property

Commutative Property

Course 2



Tell which property is represented.

A. 7 1 = 7

B. 3 + 4 = 4 + 3

C. (5 1) 2 = 5 (1 2)

Identity Property



Course 2


Additional Example 2: Using Properties to Simplify Expressions

Simplify each expression. Justify each step.

A. 21 + 16 + 9

B. 20 9 5

21 + 16 + 9 = 16 + 9 + 21 Commutative Property.

= 16 + (9 + 21)

= 16 + 30

Associative Property.

= 46

Add.

20 9 5 = 20 5 9 Commutative Property.

= 20 (5 9)

= 20 45


= 900

Multiply.

Course 2


Check It Out: Example 2A & B


A. 17 + 14 + 3

B. 12 3 5

17 + 14 + 3 = 14 + 17 + 3 Commutative Property.

= 14 + (17 + 3)

= 14 + 20


= 34

Add.

12 3 5 = 3 5 12 Commutative Property.

= 3 (5 12)

= 3 60


= 180

Multiply.

Course 2


You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

Course 2


Additional Example 3: Using the Distributive Property to Multiply Mentally

Use the Distributive Property to find 6(54).

Method 1:

Method 2:

= (6 50) + (6 4)

Rewrite 54 as 50 + 4.

= 300 + 24

= 324

Use the Distributive Property.

Multiply.

6(54) = 6(60 – 6) Rewrite 54 as 60 – 6.

= (6 60) – (6 6)

= 360 - 36

Use the Distributive Property. Multiply.

= 324 Subtract.

Add.

6(54) = 6(50 + 4)

Course 2



Use the Distributive Property to find 8(19).

Method 1:

Method 2:

= (8 10) + (8 9)

Rewrite 19 as 10 + 9.

= 80 + 72

= 152

Use the Distributive Property.

Multiply.

8(19) = 8(20 – 1) Rewrite 19 as 20 – 1.

= (8 20) – (8 1)

= 160 – 8

Use the Distributive Property. Multiply.

= 152 Subtract.

Add.

8(19) = 8(10 + 9)

Course 2


TOTD


1. 18 less than an number

2. the quotient of a number and 21

3. 8 times the sum of x and 15

4. 7 less than the product of a number and 5

x21

x – 18

8(x + 15)

5n – 7

5. The county fair charges an admission of $6 and then charges $2 for each ride. Write an algebraic expression to represent the total cost after r rides at the fair. 6 + 2r

Course 2


TOTDTell which property is represented.

1. 17 1 = 17

2. (12 + 14) + 5 = 12 + (14 + 5)

3. 2 16 = 16 2


4. 4 12 25

5. 48 + (15 + 2)

Use the Distributive Property to find each product.

6. 6 (12 + 5)

7. (20 – 7) 9

Identity Property



1,200

65

102

117

Course 2


Problem of the Day

Daniel usually buys 6 bottles of water and 3 apples when he goes to the grocery store. Next time he goes, he will buy three times as many of each. How many items will Daniel buy?

27

course 2 1-8 translate words into math do now evaluate each algebraic expression for the given value...

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