Page 158 #9-24 ANSWERS Student Progress Learning Chart Lesson Reflection for Chapter 4 Section 3.
Page 169 #12-33 ANSWERS Student Progress Learning Chart Lesson Reflection for Chapter 4 Section 5.
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Transcript of Page 169 #12-33 ANSWERS Student Progress Learning Chart Lesson Reflection for Chapter 4 Section 5.
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)
Today’s Learning Goal Assignment
Learn to write equivalent fractions.
Course 1
4-5 Equivalent Fractions
4-5 Equivalent Fractions
Course 1
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm UpList the factors of each number.
1. 8
2. 10
3. 16
4. 20
5. 30
1, 2, 4, 8
1, 2, 5, 10
1, 2, 4, 8, 16
Course 1
4-5 Equivalent Fractions
1, 2, 4, 5, 10, 20
1, 2, 3, 5, 6, 10, 15, 30
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 Fractions
Vocabulary
equivalent fractionssimplest form
Insert Lesson Title Here
Course 1
4-5 Equivalent Fractions
Course 1
4-5 Equivalent Fractions
Fractions that represent the same value are equivalent fractions. So , , and are equivalent fractions.
= =
1
2__ 2
4__ 4
8__
12
24
48
Course 1
4-5 Equivalent Fractions
Additional Example 1: Finding Equivalent Fractions
Find two equivalent fractions for .1012___
1012___ 5
6__15
18___
1012___ 15
18___ 5
6__
==
So , , and are all equivalent fractions.
Course 1
4-5 Equivalent Fractions
Try This: Example 1
Find two equivalent fractions for .4
6__
46
__ 23__8
12___
46
__ 812___ 2
3__
==
So , , and are all equivalent fractions.
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.
35__
20___=
35
______
In the denominator, 5 is multiplied by 4 to get 20.
• 4• 4
Multiply the numerator, 3, by the same number, 4.
=1220
____
So is equivalent to .
35
__ 12 20___
35
__ 1220___=
Course 1
4-5 Equivalent Fractions
Additional Example 2B: Multiplying and Dividing to Find Equivalent Fractions
Find the missing number that makes the fractions equivalent.
B.
45__ 80___=
4 5______
In the numerator, 4 is multiplied by 20 to get 80.
• 20• 20
Multiply the denominator by the same number, 20.
=80100____
So is equivalent to .
45
__ 80100___
45
__ 80100___=
Course 1
4-5 Equivalent Fractions
Try This: Example 2A
Find the missing number that makes the fraction equivalent.
A.
39__
27___=
39
______
In the denominator, 9 is multiplied by 3 to get 27.
• 3• 3
Multiply the numerator, 3, by the same number, 3.
=927
____
So is equivalent to .
39
__ 9 27___
39
__ 927___=
Course 1
4-5 Equivalent Fractions
Try This: Example 2B
Find the missing number that makes the fraction equivalent.
B.
24__ 40___=
24______
In the numerator, 2 is multiplied by 20 to get 40.
• 20• 20
Multiply the denominator by the same number, 20.
=4080
____
So is equivalent to .
24
__ 40 80___
24
__ 4080___=
Course 1
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.
A. 20
48___
The GCF of 20 and 48 is 4, so is not in simplest form.
2048___
Method 1: Use the GCF.
2048_______÷ 4
÷ 4
Divide 20 and 48 by their GCF, 4.=512__
Course 1
4-5 Equivalent Fractions
Additional Example 3A: Writing Fractions in Simplest Form
Write the fraction in simplest form.
Method 2: Use a ladder diagram.
Use a ladder. Divide 20 and 48 by any common factor (except 1) until you cannot divide anymore
2048___
2 20/48
2 10/245/12
512___
So written in simplest form is .
Method 2 is useful when you know that the numerator and denominator have common factors, but you are not sure what the GCF is.
Helpful Hint
Course 1
4-5 Equivalent Fractions
Additional Example 3B: Writing Fractions in Simplest Form
Write the fraction in simplest form.
B. 710___
The GCF of 7 and 10 is 1 so is already in simplest form.
710___
Course 1
4-5 Equivalent Fractions
Try This: Example 3A
Write the fraction in simplest form.
A. 1216___
The GCF of 12 and 16 is 4, so is not in simplest form.
1216___
Method 1: Use the GCF.
1216_______÷ 4
÷ 4
Divide 12 and 16 by their GCF, 4.=34
__
Course 1
4-5 Equivalent Fractions
Try This: Example 3A
Write the fraction in simplest form.
Method 2: Use a ladder diagram.
Use a ladder. Divide 20 and 48 by any common factor (except 1) until you cannot divide anymore
2 12/16
2 6/83/4
1216___ 3
4___
So written in simplest form is .
Course 1
4-5 Equivalent Fractions
Try This: Example 3B
Write the fraction in simplest form.
B. 310___
The GCF of 3 and 10 is 1, so is already in simplest form.
310___
Lesson QuizWrite two equivalent fractions for each given fraction.
1. 2.
Find the missing number that makes the
fractions equivalent.
3. 4.
Write each fraction in simplest form.
5. 6.
Insert Lesson Title Here
6
Course 1
4-5 Equivalent Fractions
410___ 7
14___
2
7__ ___
21=
4
15__ ___20
=
48
__ 749___ 1
7___1
2__
75
12
___ 1428___,8
20___2
5___,
Possible answers