Page 190 #1-9 ANSWERS Student Progress Learning Chart Lesson Reflection for Chapter 4 Section 9.
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Transcript of Page 190 #1-9 ANSWERS Student Progress Learning Chart Lesson Reflection for Chapter 4 Section 9.
Students will understand number theory and fractions by being able
to do the following:• Learn to use divisibility rules (4-1)• Learn to write prime factorizations of composite numbers (4-
2)• Learn to find the greatest common factor (GCF) of a set of
numbers (4-3)• Learn to convert between decimals and fractions (4-4)• Learn to write equivalent fractions (4-5)• Learn to use pictures and number lines to compare and
order fractions (4-6)• Learn to convert between mixed numbers and improper
fractions (4-7)• Learn to add and subtract fractions with like denominators
(4-8)
•Learn to multiply fractions by whole numbers (4-9)
Today’s Learning Goal Assignment
Learn to multiply fractions by whole numbers.
Course 1
4-9 Multiplying Fractions by Whole Numbers
6th Grade Math HW
Page 194#1-13
& Finish Chop Chop Quiz!Course 1
4-9 Multiplying Fractions by Whole Numbers
4-9 Multiplying Fractions by Whole Numbers
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm UpMultiply.
30
96
144
Course 1
4-9 Multiplying Fractions by Whole Numbers
66
120
1. 15 2
2. 12 8
3. 9 16
4. 6 11
5. 8 15
Problem of the Day
The length of three dowels are 13 inches, 27 inches, and 19 inches. How can you use the three dowels to mark off a length of 5 inches?
13 + 19 – 27
Course 1
4-9 Multiplying Fractions by Whole Numbers
Today’s Learning Goal Assignment
Learn to multiply fractions by whole numbers.
Course 1
4-9 Multiplying Fractions by Whole Numbers
Course 1
4-9 Multiplying Fractions by Whole Numbers
Recall that multiplication by a whole number can be represented as repeated addition. For example, 4 • 5 = 5 + 5 + 5 + 5. You can multiply a whole number by a fraction using the same method.
++ =
3 • = 34__1
4__
Course 1
4-9 Multiplying Fractions by Whole Numbers
31
__ 14
__ 3 • 11 • 4
______ 34
__•
There is another way to multiply with fractions. Remember that a whole number can be written as an improper fraction with 1 in the denominator. So 3 = .3
1__
= =Multiply numeratorsMultiply denominators
Course 1
4-9 Multiplying Fractions by Whole Numbers
Additional Example 1A: Multiplying Fractions and Whole Numbers
Multiply. Write the answer in simplest form.
19
__
19
__71
__ 7 • 11 • 9
______
79
__
• =
=
Write 7 as a fraction. Multiply numerators and denominators.
A. 7 •
Course 1
4-9 Multiplying Fractions by Whole Numbers
Additional Example 1B: Multiplying Fractions and Whole Numbers
Multiply. Write the answer in simplest form.
18
__
18
__61
__ 6 • 11 • 8
______
68
__
• =
=
Write 6 as a fraction. Multiply numerators and denominators.
34
__= Write your answer in simplest form.
B. 6 •
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4-9 Multiplying Fractions by Whole Numbers
Additional Example 1C: Multiplying Fractions and Whole Numbers
Multiply. Write the answer in simplest form.
23
__
23
__81
__ 8 • 21 • 3
______
16 3
___
• =
=
Write 8 as a fraction. Multiply numerators and denominators.
13
__or 5
C. 8 •
Course 1
4-9 Multiplying Fractions by Whole Numbers
Try This: Example 1A
Multiply. Write the answer in simplest form.
15
__
15
__41
__ 4 • 11 • 5
______
45
__
• =
=
Write 4 as a fraction. Multiply numerators and denominators.
A. 4 •
Course 1
4-9 Multiplying Fractions by Whole Numbers
Try This: Example 1B
Multiply. Write the answer in simplest form.
16
__
16
__31
__ 3 • 11 • 6
______
36
__
• =
=
Write 3 as a fraction. Multiply numerators and denominators.
12
__= Write your answer in simplest form.
B. 3 •
Course 1
4-9 Multiplying Fractions by Whole Numbers
Try This: Example 1C
Multiply. Write the answer in simplest form.
34
__
34
__91
__ 9 • 31 • 4
______
27 4
___
• =
=
Write 9 as a fraction. Multiply numerators and denominators.
34
__or 6
C. 9 •
Course 1
4-9 Multiplying Fractions by Whole Numbers
Additional Example 2A: Evaluating Fraction Expression
Evaluate 4x for the value of x. Write the answer in simplest form.
110
___
41
__
110
___
410
___
•
=
Write the expression.4x
4
• 110
___
=25
__
Multiply.
Substitute for x. 110
___
Write your answer in simplest form.
A. x =
Course 1
4-9 Multiplying Fractions by Whole Numbers
Additional Example 2B: Evaluating Fraction Expression
Evaluate 4x for the value of x. Write the answer in simplest form.
38
__
41
__
38
__
12 8
___
•
=
Write the expression.4x
4
• 38
__
=32
__
Multiply.
Substitute for x.38
__
Write your answer in simplest form.12
__,or 1
B. x =
Course 1
4-9 Multiplying Fractions by Whole Numbers
Try This: Example 2A
Evaluate 3x for the value of x. Write the answer in simplest form.
19
__
31
__
19
__
39
__
•
=
Write the expression.3x
3
• 19
__
=13
__
Multiply.
Substitute for x.19
__
Write your answer in simplest form.
A. x =
Course 1
4-9 Multiplying Fractions by Whole Numbers
Try This: Example 2B
Evaluate 3x for the value of x. Write the answer in simplest form.
47
__
31
__
47
__
12 7
___
•
=
Write the expression.3x
3
• 47
__
=
Multiply.
Substitute for x.47
__
Write your answer in simplest form.57
__ 1
B. x =
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4-9 Multiplying Fractions by Whole Numbers
Sometimes the denominator of an improper fraction will divide evenly into the numerator. When this happens, the improper fraction is equivalent to a whole number, not a mixed number.
This makes sense if you remember that the fraction bar means “divided by”.
12 3
___ = 4
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4-9 Multiplying Fractions by Whole Numbers
Additional Example 3: Application
There are 25 students in the music club. Of those
students, are also in the band. How many music
club students are in the band?
3 5
__
53__To find of 25, multiply.
25 1
___35
__• 25 = •
35
__
75 5
___=
= 15
There are 15 music club students in the band.
Course 1
4-9 Multiplying Fractions by Whole Numbers
Try This: Example 3
There are 18 saltwater fish in the aquarium. Of those
fish, are blue. How many fish in the aquarium
are blue?
23
__
23
__
To find of 18, multiply.
18 1
___23
__• 18 = •
23
__
36 3
___=
= 12
There are 12 blue fish in the aquarium.
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4-9 Multiplying Fractions by Whole Numbers
Lesson Quiz
Multiply. Write each answer in simplest form.
1. 10 • 2. 6 •
Evaluate 6x for each value of x. Write your answer
in simplest form.
3. x = 4. x =
5. Alicia spent 15 minutes making a pizza. Of those
minutes were spent rolling out the crust. How many
minutes did Alicia spend rolling out the crust?
25
__ 110
__
14
__ 56
__
13
__
5 minutes
5
4 35
__
, or 112
__32
__