Download - Chapter 2
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Chapter 2Multiplying and Dividing Decimals
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2-1 Multiplication PropertiesIWBAT use multiplication properties to solve problems mentally.
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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
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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
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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
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Practice
Identify and use the multiplication property to solve the problems mentally.
1. 1
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2-2 Multiplying Whole Numbers and DecimalsIWBAT multiply large whole numbers and decimals
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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
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Continued . . . 4) Add 26,328
15______131640
26328X_______
394,920
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Examples
1) 209 36____
1254327X+ ______
3524
2) 1,650 412 ______
33001650X
+ ______
19800
3) 399 705______
1995000X
2793XX+ ______
281,295
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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
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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
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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
__________ __________ __________
__________ __________
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2-3 Interpret the RemainderIWBAT interpret quotients and remainders in division problems
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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.
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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.
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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?
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2-4 Dividing by Whole NumbersIWBAT divide whole numbers by whole number divisors
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Vocabulary
3124
Quotient
Divisor
Dividend
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Vocabulary
12÷4=3
Dividend
Divisor
Quotient
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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
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3) Divide the ones 114622,223
2 3- _____3223- ____
9292- ____
0
*Divide*Multiply*Subtract*Compare*Write remainder, if any
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2-5 Dividing a Decimal by a DecimalIWBAT divide decimals by decimals
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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.
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2-6 Work Backwards
IWBAT solve problems by working backwards
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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
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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
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2-7 Solving Multiplication and Division EquationsIWBAT solve multiplication and division equations
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2-8 Using a Pictograph
IWBAT use pictographs to solve problems
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Remember
Always look at the key first!
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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
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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