1. Page 169 #12-33 ANSWERS

2. Student Progress Learning Chart
Lesson Reflection for
Chapter 4 Section 5

3. Math Learning Goal Students will understand number theory and fractions.

4. Learn to write equivalent fractions (4-5)
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)

5. Today’s Learning Goal Assignment
Course 1
4-5
Equivalent Fractions
Today’s Learning Goal Assignment
Learn to write equivalent fractions.

6. Course 1
4-5
Equivalent Fractions
6th Grade Math HW
Page 174
#1-11

7. 4-5 Equivalent Fractions Warm Up Problem of the Day
Course 1
Warm Up
Problem of the Day
Lesson Presentation

8. 4-5 Equivalent Fractions Warm Up List the factors of each number. 1. 8
Course 1
4-5
Equivalent Fractions
Warm Up
List 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
1, 2, 4, 5, 10, 20
1, 2, 3, 5, 6, 10, 15, 30

9. 4-5 Equivalent Fractions Problem of the Day
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

10. Today’s Learning Goal Assignment
Course 1
4-5
Equivalent Fractions
Today’s Learning Goal Assignment
Learn to write equivalent fractions.

11. Insert Lesson Title Here
Course 1
4-5
Equivalent Fractions
Insert Lesson Title Here
Vocabulary
equivalent fractions
simplest form

12. 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 = =

13. Additional Example 1: Finding Equivalent Fractions
Course 1
4-5
Equivalent Fractions
Additional Example 1: Finding Equivalent Fractions
Find two equivalent fractions for . 10
___ 12 10 12
___ 15 18
___ 5 6 __ = = 10 12
___ 15 18
___ 5 6 __
So , , and are all equivalent fractions.

14. 4-5 Equivalent Fractions Try This: Example 1
Course 1
4-5
Equivalent Fractions
Try This: Example 1
Find two equivalent fractions for . 4 __ 6 4 6 __ 8 12
___ 2 3 __ = = 4 6 __ 8 12
___ 2 3 __
So , , and are all equivalent fractions.

15. 4-5 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. 3 5 __ A.
___
In the denominator, 5 is multiplied by 4 to get 20. = 20 3 5
______
• 4 12
____
Multiply the numerator, 3, by the same number, 4. =
• 4 20 3 5 __ 12 20
___
So is equivalent to 3 5 __ 12 20
___ =

16. 4-5 Equivalent Fractions
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. 4 5 __ 80 B.
___ =
In the numerator, 4 is multiplied by 20 to get 80. 4 5
______
• 20 80
____
Multiply the denominator by the same number, 20. =
• 20
100 4 5 __ 80
100
___
So is equivalent to 4 5 __ 80
100
___ =

17. 4-5 Equivalent Fractions Try This: Example 2A
Course 1
4-5
Equivalent Fractions
Try This: Example 2A
Find the missing number that makes the fraction equivalent. 3 9 __ A.
___
In the denominator, 9 is multiplied by 3 to get 27. = 27 3 9
______
• 3 9
____
Multiply the numerator, 3, by the same number, 3. =
• 3 27 3 9 __ 9 27
___
So is equivalent to 3 9 __ 9 27
___ =

18. 4-5 Equivalent Fractions Try This: Example 2B
Course 1
4-5
Equivalent Fractions
Try This: Example 2B
Find the missing number that makes the fraction equivalent. 2 4 __
___ 40 B.
In the numerator, 2 is multiplied by 20 to get 40. = 2 4
______
• 20 40
____
Multiply the denominator by the same number, 20. =
• 20 80 2 4 __ 40 80
___
So is equivalent to 2 4 __ 40 80
___ =

19. 4-5 Equivalent Fractions
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.

20. Additional Example 3A: Writing Fractions 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 48
___
The GCF of 20 and 48 is 4, so is not in simplest form.
Method 1: Use the GCF. 20 48
_______
÷ 4 5 12 __ =
Divide 20 and 48 by their GCF, 4.
÷ 4

21. Method 2: Use a ladder diagram. So written in simplest form is .
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. 2
20/48
Use a ladder. Divide 20 and 48 by any common factor (except 1) until you cannot divide anymore 2
10/24
5/12 20 48
___ 5 12
___
So written in simplest form is
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.

22. Additional Example 3B: Writing Fractions in Simplest Form
Course 1
4-5
Equivalent Fractions
Additional Example 3B: Writing Fractions in Simplest Form
Write the fraction in simplest form. 7 10
___ B. 7 10
___
The GCF of 7 and 10 is 1 so is already in simplest form.

23. 4-5 Equivalent Fractions Try This: Example 3A
Course 1
4-5
Equivalent Fractions
Try This: Example 3A
Write the fraction in simplest form. 12
___ A. 16 12 16
___
The GCF of 12 and 16 is 4, so is not in simplest form.
Method 1: Use the GCF. 12 16
_______
÷ 4 3 4 __
Divide 12 and 16 by their GCF, 4. =
÷ 4

24. Method 2: Use a ladder diagram.
Course 1
4-5
Equivalent Fractions
Try This: Example 3A
Write the fraction in simplest form.
Method 2: Use a ladder diagram. 2
12/16
Use a ladder. Divide 20 and 48 by any common factor (except 1) until you cannot divide anymore 2
6/8
3/4 12 16
___ 3 4
So written in simplest form is

25. 4-5 Equivalent Fractions Try This: Example 3B
Course 1
4-5
Equivalent Fractions
Try This: Example 3B
Write the fraction in simplest form. 3 10
___ B. 3 10
___
The GCF of 3 and 10 is 1, so is already in simplest form.

26. Insert Lesson Title Here
Course 1
4-5
Equivalent Fractions
Insert Lesson Title Here
Lesson Quiz
Write two equivalent fractions for each given fraction.
Find the missing number that makes the fractions equivalent.
Write each fraction in simplest form.
Possible answers 4 10
___ 8 20
___ 2 5 , 7 14
___ 1 2
___ 14 28 , 2 7 __ 4 15 __ 20
___
___ = 6 = 75 21 4 8 __ 1 2 __ 7 49
___ 1 7
___