Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Warm UpWarm Up

California StandardsCalifornia Standards

Lesson PresentationLesson Presentation

PreviewPreview

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Warm UpName a common factor for each pair.

1. 5 and 10 2. 9 and 12

3. 20 and 24 4. 10 and 14

5. 6 and 8 6. 8 and 15

5 3

4 2

2 1

Possible answers:

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Number Sense (NS2.4) - Determine the least common multiple and the the greatest common divisor of whole greatest common divisor of whole numbers; use them to solve numbers; use them to solve problems with fractionsproblems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form to find the reduced form of a fractionof a fraction).Also covered: Number Sense (NS1.1)Number Sense (NS1.1)

California Standards

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Objective:Objective: You will learn You will learn how to identify, write, and how to identify, write, and convert between equivalent convert between equivalent fractions and mixed fractions and mixed numbers.numbers.

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Vocabulary

equivalent fractionsimproper fractionmixed number

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Different fractions can name the same number.

35 = = 15

256

10

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

=

To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.

In the diagram = . These are called

equivalent fractions because they are different expressions for the same nonzero number.

5

310

6

25

15

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Find two fractions equivalent to .

Example 1: Finding Equivalent Fractions

5 27 2 = 10

14

5 37 3 = 15

21

Remember!A fraction with the same numerator and

denominator, such as is equal to 1.2 2

57

Using “Cake”

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

5 7

The fractions , , and are equivalent,

but only is in simplest form. A fraction is in

simplest formsimplest form when the greatest common divisor

of its numerator and denominator is 1.

57

1014

1521

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Check It Out! Example 2

Find two fractions equivalent to .

6 212 2 = 12

24

6 ÷ 212 ÷ 2

= 36

612

Using “Cake”

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Write the fraction in simplest form.

Example 3: Writing Fractions in Simplest Form

1824

Using Factors Using “Cake”

SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Write the fraction in simplest form.

Check It Out! Example 4

1545

Using Factors Using “Cake”

SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

To determine if two fractions are equivalent, simplify the fractions.

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Determine whether the fractions in each pair are equivalent.

Example 5: Determining Whether Fractions are Equivalent

and 46

2842

Simplify both fractions and compare.4

6 = 4 ÷ 26 ÷ 2 = 2

3

2842

=28 ÷ 1442 ÷ 14 = 2

3

are equivalent because both are equal to .

and 46

2842 2

3

Using “Cake”

SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Determine whether the fractions in each pair are equivalent.

Example 5: Comparing Using Cross-Products

and 46

2842

Holt CA Course 1

3-4 Equivalent Fractions and Mixed NumbersExample 6: Determining Whether Fractions are

EquivalentDetermine whether the fractions in each pair are equivalent.

and 610

2025

Simplify both fractions and compare.

= 6 ÷ 210 ÷ 2 = 3

52025

= 20 ÷ 525 ÷ 5 = 4

5

610

are not equivalent because and 2025

610

their simplest forms are not equal.

Using “Cake”

SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Example 6: Comparing Using Cross-Products

Determine whether the fractions in each pair are equivalent.

and 610

2025

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Check It Out! Example 7

Simplify both fractions and compare.

39 = 3 ÷ 3

9 ÷ 3 = 13

= 6 ÷ 618 ÷ 6 = 1

3

and 39

618

618

Determine whether the fractions in each pair are equivalent.

are equivalent because both are equal to .

and 39

618 1

3

Using “Cake”

SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Example 7: Comparing Using Cross-Products

Determine whether the fractions in each pair are equivalent.

and 39

618

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Check It Out! Example 8

and 412

948

Simplify both fractions and compare.

= 4 ÷ 412 ÷ 4 = 1

3

948

= 9 ÷ 348 ÷ 3 = 3

16

412

Determine whether the fractions in each pair are equivalent.

are not equivalent becauseand 948

412

their simplest forms are not equal.

Using “Cake”

SMART Response QuestionTo set the properties right click and selectSMART Response Question Object->Properties...

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Example 8: Comparing Using Cross-Products

Determine whether the fractions in each pair are equivalent.

and 412

948

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

85 = 13

5

85is an improper

fraction. Its numerator is greater than itsdenominator.

135is a mixed

number. Itcontains both awhole numberand a fraction.

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

(A) Write

Example 9: Converting Between Improper Fractions and Mixed Numbers

135 as a mixed number.

First divide the numerator by the denominator.

135

= 2 35

Use the quotient and remainder to write the mixed number.

(B) Write 723 as an improper fraction.

First multiply the denominator and whole number,and then add the numerator.

2233

+

= 3 7 + 23 = 23

3Use the result to write the improper fraction.

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Check It Out! Example 10

(A) Write 156 as a mixed number.

First divide the numerator by the denominator.

156 = 2 3

6Use the quotient and remainder to write the mixed number.

(B) Write 813 as an improper fraction.

First multiply the denominator and whole number,and then add the numerator.

113388

+

= 3 8 + 13 = 25

3

Use the result to write the improperfraction.

12

= 2

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Home Home

LearningLearning

On-Line On-Line TutoringTutoring

Equivalent Equivalent Fractions?Fractions?

Melvin’s Melvin’s DilemmaDilemma

Holt CA Course 1

3-4 Equivalent Fractions and Mixed Numbers

Lesson Quiz

1. Write two fractions equivalent to .

2. Determine if and are equivalent.

3. Write the fraction in simplest form.

4. Write as a mixed number.

5. Write 4 as an improper fraction.

1224

1648

37

317

18217

8

13

no

12

36

,

5 12

4 10