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Using Number
Properties to Multiply and Divide
Rational Numbers
Unit 1 LESSON 16: Essential
Question
How do multiplication and division of rational numbers relate to one another?
• Carnegie Learning Lesson 5.3
• Properties of Operations Foldable
• Associative Property• Commutative Property• Identity Property of
Multiplication (One)• Multiplicative Inverse
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For all real numbers n,
WORDS
Multiplicative Identity Property
The product of a number and 1, the multiplicative identity, is the original number.
NUMBERS
ALGEBRA n • 1 = 1 • n = n
Identity = Self (the original)
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For all real numbers n,
WORDS
Multiplicative Inverse Property
The product of a nonzero number and its reciprocal, or multiplicative inverse, is 1.
NUMBERS
ALGEBRA n • 1 = 1 • n = n
Inverse = Reciprocal
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PracticeUsing Number Properties to Multiply and Divide
I can . . .
Apply properties to multiply and divide rational numbers.
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PracticeUsing Number Properties to Multiply and Divide
I can . . .
Apply properties to multiply and divide rational numbers.
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PracticeUsing Number Properties to Multiply and Divide
I can . . .
Apply properties to multiply and divide rational numbers.
![Page 7: Unit 1 LESSON 16: Associative Property Question Using ...hopsonteam7d.weebly.com/uploads/2/3/4/9/23490824/unit_1...Using Number Properties to Multiply and Divide Rational Numbers Unit](https://reader035.vdocument.in/reader035/viewer/2022071414/610f18d9c3c29367ea045e72/html5/thumbnails/7.jpg)
PracticeUsing Number Properties to Multiply and Divide
I can . . .
Apply properties to multiply and divide rational numbers.
![Page 8: Unit 1 LESSON 16: Associative Property Question Using ...hopsonteam7d.weebly.com/uploads/2/3/4/9/23490824/unit_1...Using Number Properties to Multiply and Divide Rational Numbers Unit](https://reader035.vdocument.in/reader035/viewer/2022071414/610f18d9c3c29367ea045e72/html5/thumbnails/8.jpg)
Mental MathUsing
Number Properties
Bonus Lesson: Essential
Question
How do I use number properties to compute mentally?
Mental math means “doing math in your head.”
Many mental math strategies use number
properties that you already know to make
equivalent expressions that may be easier
to simplify.
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Mental MathUsing
Number Properties
Bonus Lesson:
Commutative Distributive Inverse Associative
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I can . . .
use number properties to compute mentally.
Find each sum or product mentally.
1. 17 + 15 =
2. 29 + 39 =
3. 8(24) =
4. 7(12) =
5. 3(91) =
6. 6(15) =
32
68
192
84
273
90
22 + 10 =
40 + 28 =
8(20) + 8(4) =
3(90) + 3(1) =
6(10 + 5) =
70 + 14 =
PracticeComputing Mentally
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Let’s Try Some Mental Math
Evaluate
17 + 5 + 3 + 15
17 + 5 + 3 + 15 Look for sums that are multiples of 10
40
Use the Commutative Property. 17 + 3 + 5 + 15
(17 + 3) + (5 + 15)
Use mental math to add.
20 + 20
Use the Associative Property to make groups of compatible numbers.
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4 × 13 × 5 Look for products that are multiples of 10
260
Use the Commutative Property.13 × 4 × 5
13 × (4 × 5)
Use mental math to multiply.13 × 20
Use the Associative Property to group compatible numbers.
Evaluate
4 × 13 × 5
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Evaluate
12 + 5 + 8 + 5
12 + 5 + 8 + 5 Look for sums that are multiples of 10
30
Use the Commutative Property.12 + 8 + 5 + 5
(12 + 8) + (5 + 5)
Use mental math to add.
20 + 10
Use the Associative Property to make groups of compatible numbers.
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Evaluate
6 × 35
6 × 35 = 6 × (30 + 5) “Break apart” 35 into 30 + 5.
210
Use the Distributive Property.(6 × 30) + (6 × 5)
Use mental math to add.
180 + 30 Use mental math to multiply.
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Evaluate
9 x 87
9 × 87 = 9 × (80 + 7) “Break apart” 87 into 80 + 7.
783
Use the Distributive Property.(9 × 80) + (9 × 7)
Use mental math to add.
720 + 63 Use mental math to multiply.
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Evaluate
4 x 27
4 × 27 = 4 × (20 + 7) “Break apart” 27 into 20 + 7.
108
Use the Distributive Property.(4 × 20) + (4 × 7)
Use mental math to add.
80 + 28 Use mental math to multiply.
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Evaluate
6 × 43
6 × 43 = 6 × (40 + 3) “Break apart” 43 into 40 + 3.
258
Use the Distributive Property.(6 × 40) + (6 × 3)
Use mental math to add.
240 + 18 Use mental math to multiply.
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Evaluate.
1. 18 + 24 + 2 + 6 2. 10 × 5 × 3
3. 13 + 42 + 7 + 8
Use the Distributive Property to find each product.
4. 8 × 12 5. 6 × 15
6. Angie wants to buy 3 new video games. How much
will she need to save if each game costs $27?
(Assoc.) 150(Comm. and Assoc.) 50
(Comm. and Assoc.) 70
96 90
3 (27) = 3 (20 +7) = $81
Practice:Mental Math
I can . . .
use number properties to compute mentally.
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Conclusion
At the bottom of today’s notes, complete this sentence:
� One thing I need to remember from today’s lesson is . . .
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Converting Fractions to Decimals (Repeating and Terminating Decimals)
7.NS.2d
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7.7777……
0.246246…..
0.7222……
0.8121212……
4.12123123…...
22.52010101……
Unit 1 LESSON 18:
Repeating Decimals
Essential
Question
What symbol indicates that a number repeats?
How is this symbol used correctly?
Repeating Decimal: includes a pattern of
digits that REPEAT FOREVER.
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Fraction Decimal
0.454
0.454
5
11
means 5 ÷ 11
0 4 5 4
... 5 4
5.00000 11
0.45
Repeating Decimals: Bar Notation
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0.33
1
3
means 1÷ 3
0 3 3 3 ...
1.000 3 0.3
Fraction Decimal
Repeating Decimals: Bar Notation
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0.833
0.83
5
6
means 5 ÷ 6
0 8 3 3 ...
5.000 6
0.83
Fraction Decimal
Repeating Decimals: Bar Notation
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5
12
means 5 ÷ 12
0 4 1 6
... 6
5.0000 12 0.416
Fraction Decimal
Repeating Decimals: Bar Notation
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Write each repeating decimal with bar notation.
a) 7.7777…… =
b) 0.246246….. =
c) 0.7222…… =
d) 0.8121212…… =
e) 4.12123123…... =
f) 22.52010101…… =
7.7
0.246
0.72
0.812
4.12123
22.5201
Essential
Question
What symbol indicates that a number repeats?
How is this symbol used correctly?
![Page 27: Unit 1 LESSON 16: Associative Property Question Using ...hopsonteam7d.weebly.com/uploads/2/3/4/9/23490824/unit_1...Using Number Properties to Multiply and Divide Rational Numbers Unit](https://reader035.vdocument.in/reader035/viewer/2022071414/610f18d9c3c29367ea045e72/html5/thumbnails/27.jpg)
Unit 1 LESSON 18:
Terminating Decimals
Essential
Question
How do I know if the decimal form of a number terminates or repeats?
2.5
3.25
4.3Terminating Decimal: decimal that ends with
a specific digit
2.6
5.3566
0.003
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3
8
means 3 ÷ 8
0 3 7 5
Say it correctly!
3.000 8 0.375
375
1000
3
8=
125÷
125÷0.375
Fraction Decimal
Terminating Decimals: Look at the Denominator
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4
5
0.03
7
20
8
10=
3
100
0.35
0.8
5
5
•
•
35
100=
Fraction Decimal
Terminating Decimals: Look at the Denominator
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Converting Fractions to
Decimals (Repeating and
Terminating Decimals)
Unit 1 LESSON 18: Essential
Question
What are the steps to converting a rational number (fraction) to a decimal using long division?
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Converting Fractions to
Decimals (Repeating and
Terminating Decimals)
Unit 1 LESSON 18: Essential
Question
What are the steps to converting a fraction to a decimal using long division?
![Page 32: Unit 1 LESSON 16: Associative Property Question Using ...hopsonteam7d.weebly.com/uploads/2/3/4/9/23490824/unit_1...Using Number Properties to Multiply and Divide Rational Numbers Unit](https://reader035.vdocument.in/reader035/viewer/2022071414/610f18d9c3c29367ea045e72/html5/thumbnails/32.jpg)
1
9 0.1 =
2
9 0.2 =
3
9 0.3 =
=
1
3
1
100.1 =
2
10
0.2 =
Terminating
Terminating
3
10
0.3 =
Terminating
Repeating
Repeating
Repeating
Repeating Decimals as FractionsWhat do you notice about the repeating decimals compared to the
terminating decimals?
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1
9 0.1 =
2
9 0.2 =
3
9 0.3 =
=
1
3
1
100.1 =
2
10
0.2 =
Terminating
Terminating
3
10
0.3 =
Terminating
Repeating
Repeating
Repeating
4
9 0.4 =
5
9 0.5 =
6
90.6 = =
2
3
Writing Repeating Decimals as fractions can be a challenge. But following a pattern really helps!
Repeating Decimals as Fractions
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13
99
0.13 =
24
99
0.24 =
36
99
0.36 =
13
100
0.13 =
24
100
0.24 =
Terminating
Terminating
36
100
0.36 =
Terminating
What do you notice about the repeating decimals compared to the terminating decimals?
Repeating
Repeating
Repeating
Repeating Decimals as Fractions
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123
9990.123 =
2154
99990.2154 =
5
6
0.83 =
123
1000
0.123 =
2154
10000
0.2154 =
Terminating
Terminating
83
100
0.83 =
Terminating
Try these challenging ones!
Repeating
Repeating
Repeating When one digit is terminating this can be a challenge!
Repeating Decimals as Fractions
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Converting Fractions to
Decimals (Repeating and
Terminating Decimals)
Unit 1 LESSON 18:
Divide the numerator by the denominator.
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To Change a Fractions To a Decimal:Divide the numerator by the denominator.
4
5
45 0
.8
4 0
0
40.8
5=
Converting Fractions to Decimals
.
Zero Remainder? YESTerminating Decimal
![Page 38: Unit 1 LESSON 16: Associative Property Question Using ...hopsonteam7d.weebly.com/uploads/2/3/4/9/23490824/unit_1...Using Number Properties to Multiply and Divide Rational Numbers Unit](https://reader035.vdocument.in/reader035/viewer/2022071414/610f18d9c3c29367ea045e72/html5/thumbnails/38.jpg)
3
4
34 0
.7
2 8
2
0
0
5
20
0
30.75
4=
To Change a Fractions To a Decimal:Divide the numerator by the denominator.
Converting Fractions to Decimals
Zero Remainder? YESTerminating Decimal
.
0
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1
3
13 0
.3
9
1
0
0
3
9
1
10.3
3=
To Change a Fractions To a Decimal:Divide the numerator by the denominator.
Converting Fractions to Decimals
Zero Remainder? NORepeating Decimal
![Page 40: Unit 1 LESSON 16: Associative Property Question Using ...hopsonteam7d.weebly.com/uploads/2/3/4/9/23490824/unit_1...Using Number Properties to Multiply and Divide Rational Numbers Unit](https://reader035.vdocument.in/reader035/viewer/2022071414/610f18d9c3c29367ea045e72/html5/thumbnails/40.jpg)
6.7
459100
7610
9.45
Fraction Decimal
Converting Mixed Numbers: Leave the Whole Number Alone
![Page 41: Unit 1 LESSON 16: Associative Property Question Using ...hopsonteam7d.weebly.com/uploads/2/3/4/9/23490824/unit_1...Using Number Properties to Multiply and Divide Rational Numbers Unit](https://reader035.vdocument.in/reader035/viewer/2022071414/610f18d9c3c29367ea045e72/html5/thumbnails/41.jpg)
I can . . .
convert
rational
numbers to
decimals.
Practice:Converting Fractions to Decimals
![Page 42: Unit 1 LESSON 16: Associative Property Question Using ...hopsonteam7d.weebly.com/uploads/2/3/4/9/23490824/unit_1...Using Number Properties to Multiply and Divide Rational Numbers Unit](https://reader035.vdocument.in/reader035/viewer/2022071414/610f18d9c3c29367ea045e72/html5/thumbnails/42.jpg)
I can . . .
convert
rational
numbers to
decimals.
Practice:Converting Fractions to Decimals
![Page 43: Unit 1 LESSON 16: Associative Property Question Using ...hopsonteam7d.weebly.com/uploads/2/3/4/9/23490824/unit_1...Using Number Properties to Multiply and Divide Rational Numbers Unit](https://reader035.vdocument.in/reader035/viewer/2022071414/610f18d9c3c29367ea045e72/html5/thumbnails/43.jpg)
Conclusion
At the bottom of today’s notes, complete this sentence:
� One thing I need to remember from today’s lesson is . . .