• Substitute in values and estimate …

Estimate 49ab + 531c for a = 259, b = 37, and c = 192

4925937 + 531192

S2: Round numbers5030040 + 500200

S3: Perform Operations= 15,00040 + 100,000

= 600,000 + 100,000

= 700,000

49ab + 531cS1: Substitute numbers

• Operations with Positive and Negative Numbers …

REVIEW

- 4 + - 9 = - 13

+

+

“Neutral Pairs”

+ + + +

-3 + 4 = 1

–8 10 =

Change

(sign)

-Keep

Change

(operation)

+

+ + + + + + + +

- 2Use “keep-change-change” ~ only to change subtraction to addition.

- 9 ( 4) + 2 =– -+

Keep

Change

(operation)

Change

(sign)

+

+ + + +

- 3

+ +

“Hey, have you ever heard of a double negative in English class?”

A football team made the following yardage on five plays: lost 4, gained 16, gained 9, lost 8, and lost 4. What was the net yardage on the 5 plays?

- 4 + 16 + 9 – 8 – 4 = - 4 + 16 + 9 + - 8 + - 4

If you like “keep change change”

= 12 + 9 + - 8 + - 4 = 21 + - 8 + - 4 = 13 + - 4 = + 9

Click here for visual tiles

- 4 + 16 + 9 – 8 – 4 = - 4 + 16 + 9 + - 8 + - 4

+ + + + + + + + +

+ + + + + + +

+ + + + + + + + +

Back to Slide Show

= 9

12 4(3) = means “4 groups of 3”

+ +

+

+ +

+

+ +

+

+ +

+Group 1 Group 2 Group 3 Group 4

5(-4) =

Group 1 Group 2 Group 3

Group 4 Group 5

-20 means “5 groups of -4”

Why is a negative # times a negative # equal to a positive #?

3(-4) = -12

2(-4) = - 8

1(-4) = - 4

0(-4) = 0

-1(-4) =

4

3(4) = 12

2(4) = 8

1(4) = 4

0(4) = 0

-1(4) =

-4

-2(4) = -8 -2(-4) = 8

? ?

5 (40) 3( 4)

( 4) ( 4)2 3(5 5)

EXAMPLE:

Evaluate 5 – 2xy + 3x if x = -4 and y = -5

5 ( 8)( 5) 3( 4)

5 (40) 12

5 ( 40) 12 35 12 47

• Word Problems With Percentages …

Example:A sporting goods store advertises a $35 football at a 33% discount. What will be the sale price?

ANSWER: $23.45

Example:A TV regularly sells for $255. It is advertised at a 20% discount. Find the total cost of the TV including a 7% sales tax.

A TV regularly sells for $255. It is advertised at a 20% discount. Find the total cost of the TV including a 7% sales tax.

ANSWER: $218.28

John is paid a weekly salary of $350 plus a commission of 12% of all is sales for the week. He sells $1,562 worth of TV’s this week. He works 5 days a week. What are his average daily earnings for the week?

Weekly salary + 12% commission

= 350 + .12(1,562)Written as decimal

12% “of” weekly sales

= 350 + 187.44 = $ 537.44

Ooops! This isn’t the final answer! This represents his whole week.

Average daily earnings = 537.44/5

= $107.49

Gina chose a shade of green paint called Spring Green. The directions to make any quantity of this shade calls for 3 parts blue paint to 5 parts yellow paint. If Gina makes 16 ounces of Spring Green paint, how many ounces of blue paint will she use?

Blank Slide

EXAMPLE:

ANSWER: 6 ounces