Transcript 4-5

Page 169 #12-33 ANSWERS
Student Progress
Learning Chart
Lesson Reflection for
Chapter 4 Section 5
Math Learning Goal
Students will
understand number
theory and fractions.
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)
4-5 Equivalent Fractions
Today’s Learning Goal Assignment
Learn to write
equivalent
fractions.
Course 1
4-5 Equivalent Fractions
th
6
Grade Math HW
Page 174
#1-11
Course 1
4-5 Equivalent Fractions
Warm Up
Problem of the Day
Lesson Presentation
Course 1
4-5 Equivalent Fractions
Warm Up
List the factors of each number.
1. 8
1, 2, 4, 8
2. 10
1, 2, 5, 10
3. 16
1, 2, 4, 8, 16
4. 20
1, 2, 4, 5, 10, 20
5. 30
1, 2, 3, 5, 6, 10, 15, 30
Course 1
4-5 Equivalent Fractions
Problem of the Day
John has 3 coins, 2 of which are the
same. Ellen has 1 fewer coin than John,
and Anna has 2 more coins than John.
Each girl has only 1 kind of coin. Who
has coins that could equal the value of a
half-dollar?
Ellen and Anna
Course 1
4-5 Equivalent Fractions
Today’s Learning Goal Assignment
Learn to write
equivalent
fractions.
Course 1
4-5 Equivalent
Insert Lesson
Title Here
Fractions
Vocabulary
equivalent fractions
simplest form
Course 1
4-5 Equivalent Fractions
Fractions that represent the same value are
1 , __
2 , and __
4 are
equivalent fractions. So __
2
4
8
equivalent fractions.
1
2
Course 1
=
2
4
=
4
8
4-5 Equivalent Fractions
Additional Example 1: Finding Equivalent
Fractions
10
___
Find two equivalent fractions for 12 .
10
___
12
10
___
15
___
=
5
__
15
___
18
=
5
__
6
So 12 , 18 , and 6 are all equivalent fractions.
Course 1
4-5 Equivalent Fractions
Try This: Example 1
Find two equivalent fractions for
4
__
6
=
8
___
12
=
4
__
6
.
2
__
3
4 , ___
8 , and __
2 are all equivalent fractions.
So __
6
12
3
Course 1
4-5 Equivalent Fractions
Additional Example 2A: Multiplying and
Dividing to Find Equivalent Fractions
Find the missing number that makes the
fractions equivalent.
A.
3
__
5
=
___
20
3•4
______
12
= ____
5• 4
20
3
__
In the denominator, 5 is multiplied
by 4 to get 20.
Multiply the numerator, 3, by
the same number, 4.
12
___
So 5 is equivalent to 20 .
3
__
5
Course 1
=
12
___
20
4-5 Equivalent Fractions
Additional Example 2B: Multiplying and
Dividing to Find Equivalent Fractions
Find the missing number that makes the
fractions equivalent.
B.
4
__
5
=
80
___
4
• 20 ____
80
______
=
5 • 20 100
4
__
In the numerator, 4 is multiplied by
20 to get 80.
Multiply the denominator by
the same number, 20.
80
___
So 5 is equivalent to 100 .
4
__
5
Course 1
=
80
___
100
4-5 Equivalent Fractions
Try This: Example 2A
Find the missing number that makes the
fraction equivalent.
A.
3
__
9
=
___
27
3•3
______
9
= ____
9• 3
27
3
__
In the denominator, 9 is multiplied
by 3 to get 27.
Multiply the numerator, 3, by
the same number, 3.
9
___
So 9 is equivalent to 27 .
3
__
9
Course 1
=
9
___
27
4-5 Equivalent Fractions
Try This: Example 2B
Find the missing number that makes the
fraction equivalent.
B.
2
__
4
=
40
___
2
• 20 ____
40
______
=
4 • 20
80
2
__
In the numerator, 2 is multiplied by
20 to get 40.
Multiply the denominator by
the same number, 20.
40
___
So 4 is equivalent to 80 .
2
__
4
Course 1
=
40
___
80
4-5 Equivalent Fractions
Every fraction has one equivalent fraction
that is called the simplest form of the
fraction. A fraction is in simplest form
when the GCF of the numerator and the
denominator is 1.
Example 3 shows two methods for writing
a fraction in simplest form.
Course 1
4-5 Equivalent Fractions
Additional Example 3A: Writing Fractions in
Simplest Form
Write the fraction in simplest form.
20
___
A. 48
20
___
The GCF of 20 and 48 is 4, so 48 is not
in simplest form.
Method 1: Use the GCF.
20 ÷ 4
_______
48 ÷ 4
Course 1
=
5
__
12
Divide 20 and 48 by their GCF, 4.
4-5 Equivalent Fractions
Additional Example 3A: Writing Fractions in
Simplest Form
Write the fraction in simplest form.
Method 2: Use a ladder diagram.
2 20/48
2
10/24
5/12
Use a ladder. Divide 20 and 48 by any
common factor (except 1) until you cannot
divide anymore
So
20
___
48
5
___
written in simplest form is 12 .
Helpful Hint
Method 2 is useful when you know that the numerator and
denominator have common factors, but you are not sure
what the GCF is.
Course 1
4-5 Equivalent Fractions
Additional Example 3B: Writing Fractions in
Simplest Form
Write the fraction in simplest form.
B.
7
___
10
7 is already
The GCF of 7 and 10 is 1 so ___
10
in simplest form.
Course 1
4-5 Equivalent Fractions
Try This: Example 3A
Write the fraction in simplest form.
12
___
A. 16
12
___
The GCF of 12 and 16 is 4, so 16 is not
in simplest form.
Method 1: Use the GCF.
12 ÷ 4
_______
16 ÷ 4
Course 1
=
3
__
4
Divide 12 and 16 by their GCF, 4.
4-5 Equivalent Fractions
Try This: Example 3A
Write the fraction in simplest form.
Method 2: Use a ladder diagram.
2 12/16
2
6/8
3/4
12
___
Use a ladder. Divide 20 and 48 by any
common factor (except 1) until you cannot
divide anymore
3
___
So 16 written in simplest form is
.
4
Course 1
4-5 Equivalent Fractions
Try This: Example 3B
Write the fraction in simplest form.
B.
3
___
10
3
The GCF of 3 and 10 is 1, so ___ is already in
10
simplest form.
Course 1
4-5 Equivalent
Insert Lesson
Fractions
Title Here
Lesson Quiz
Write two equivalent fractions for each
given fraction. Possible answers
8
2 , ___
___
4
1. ___
5
10
20
7
2. ___
14
1 , ___
14
___
2
28
Find the missing number that makes the
fractions equivalent.
2
=
3. __
7
___
21
6
4
20
4. __ = ___
15
75
Write each fraction in simplest form.
4
__
5. 8
Course 1
1
__
2
7
___
6. 49
1
___
7