Page 169 #12-33 ANSWERS Student Progress Learning Chart Lesson Reflection for Chapter 4 Section 5.

Page 169 #12-33 ANSWERS

Student Progress Learning

ChartLesson 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)

Today’s Learning Goal Assignment

Learn to write equivalent fractions.

Course 1

4-5 Equivalent Fractions

6th Grade Math HW

Page 174#1-11

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