chapter 2

Chapter 2Multiplying and Dividing Decimals

2-1 Multiplication PropertiesIWBAT use multiplication properties to solve problems mentally.

Multiplication Properties

• Order does not matter•

Commutative Property

• Grouping does not matter•

Associative Property

• The product of any number times 1 is itself•

IdentityProperty

• The product of any number times 0 is 0•Property of Zero

• Multiplying a factor with a group is the same as multiplying the group individually and then adding

DistributiveProperty

ExamplesFind mentally

1) Choose a property Distributive

2) Use the property 3×(10+7)

(3×10 )+(3×7)30 + 213) Order of operations

51

Find

1) Choose a property Commutative

2) Use the property

(2×5)×3863) Order of operations 10×386=

3860

ExamplesFind mentally

1) Choose a property Distributive

2) Use the property 4×(600−2)

3) Order of operations

(4×600 )−(4×2)

2400 - 8

2392

Find mentally

1) Choose a property Zero Property

2) Use the property

1,026×64×00

Practice

Identify and use the multiplication property to solve the problems mentally.

1. 1

2-2 Multiplying Whole Numbers and DecimalsIWBAT multiply large whole numbers and decimals

Multiplying Whole Numbers

26,328×15

1) Write vertically, lining up the digits in the ones place

26,328

15______

2) Multiply by the ones 26,328

15______

131640

3) Use a placeholder and then multiply by the ten

26,328 15______

13164026328X

Continued . . . 4) Add 26,328

15______131640

26328X_______

394,920

Examples

1) 209 36____

1254327X+ ______

3524

2) 1,650 412 ______

33001650X

+ ______

19800

3) 399 705______

1995000X

2793XX+ ______

281,295

Multiplying Decimals

Find 1.0894.2

1) Multiply just like whole numbers 1.0894.2 ______216

432X

972XX+ ______

101736

2) Count the number of places after a decimal in the problem

3 digits

3) Start right and move the number of places

101.736

Examples

1) 42.7 2.1

42.7 2.1 ______

427

854X+ ______8967

89.67

2) 0.38 86

0.38 86______

228304X

+ _______

3268

32.86

Practice

1) 399 2) 52.7 3) 417 705 3.9 26

4) 2.637 5) 5.034.36 0.07

6) 5.76 4.08 7) 0.08 0.007

__________ __________ __________

__________ __________

2-3 Interpret the RemainderIWBAT interpret quotients and remainders in division problems

Example #1

You and your 10 friends are going on a field trip to an amusement park. You can only enter the ride in groups of four. You decide that your friends need to find 5 more classmates to be able to all get in at one time.

1) If you don’t find 5 more people, how many people cannot go in with you? How do you know?

3 people. 11 4 = 2 R3

2) Explain how you decided that you needed 5 more people.11 + 5 = 16. 16 is divisible by 4.

3) What is the fewest number of people who need to join your group so that you all can go in? How do you know?

One person. 11 + 1 = 12. 12 is divisible by 4.

Example #2

Your class is going to see a movie. There are 27 students and your teacher wants one parent for every group of 4 students. Your teacher will go with the remaining students.

1) How many parents will your teacher need? How did you figure it out?

27 4 = 6 R36 Parents

2) What does the remainder represent?The number of students in the teacher’s group

3) How many groups will see the show? Explain.7 groups. There are 6 parent-led groups and one teacher-led group.

Practice

Your class of 37 students are taking a boat ride around a lake. Each boat holds 6 people. There are groups of 5 students for each parent. The teacher will be with the remaining students.

1) How many boats are needed? How did you find out?

2) How many students are in the teacher’s group?

2-4 Dividing by Whole NumbersIWBAT divide whole numbers by whole number divisors

Vocabulary

3124

Quotient

Divisor

Dividend

Vocabulary

12÷4=3

Dividend

Divisor

Quotient

Two-Digit Divisor and Whole Number Dividend

=?

1) Rewrite as long division and divide the hundreds

1622,223

2 3- ____3 2

2) Divide the tens11622,223

2 3- ____

3223

*Divide*Multiply*Subtract*Compare*Bring Down

- ____

92

*Compare*Divide*Multiply*Subtract*Bring Down

3) Divide the ones 114622,223

2 3- _____3223- ____

9292- ____

0

*Divide*Multiply*Subtract*Compare*Write remainder, if any

2-5 Dividing a Decimal by a DecimalIWBAT divide decimals by decimals

Dividing decimals by decimals is just like dividing any other number but you have to move the decimals if there is a decimal in the divisor.

2-6 Work Backwards

IWBAT solve problems by working backwards

ExampleVegetable or Fruit Price

Berries $2.00 per quart

Corn 5 for $1.00

Broccoli $0.80 per lb

Tomatoes $1.20 per lb

Kim bought 10 ears of corn, one quart of berries, and some tomatoes. Use the data given above. If Kim, gave the cashier $10.00 and received $1.80 in change, how many pounds of tomatoes did Kim buy?

1) Start with what is given and work your way backwards

$10.00 - $1.80

$8.20

2) Find amounts that are given to you

Corn: 5 for $1.0010 for $2.00

Money spent on corn and berries:

$2.00 + $2.00

$4.00

3) Continue to work backwards

$8.20 – $4.00

$4.20 = price of tomatoes

4) Find last part of problem

Tomatoes: $1.20 per lb

$4.20 $1.20

3.5 lbs of tomatoes

2-7 Solving Multiplication and Division EquationsIWBAT solve multiplication and division equations

2-8 Using a Pictograph

IWBAT use pictographs to solve problems

Remember

Always look at the key first!

Examples1) How many hours does Bob study each week?

9 hours

2) How many more hours did Roberto study than Maria?

Roberto: 8 hours

Maria: 1 hour

8 – 1

7 hours

Examples Continued

1) Which year did Middlebury’s population double from it’s original population in 1941?

1971 and 2001

2) Which year did Middlebury see the biggest increase in population?

1961