2-9 Equivalent Fractions and Mixed Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes.

2-9 Equivalent Fractions and Mixed Numbers

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

2-9 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:

2-9 Equivalent Fractions and Mixed Numbers

Problem of the Day

Find a number less than 100 for which all three statements are true:• Divide by 3. Remainder of 2.• Divide by 4. Remainder of 3.• Divide by 5. Remainder of 4.

59

2-9 Equivalent Fractions and Mixed Numbers

Learn to identify, write, and convert between equivalent fractions and mixed numbers.

2-9 Equivalent Fractions and Mixed Numbers

Vocabulary

equivalent fractionsrelatively prime

2-9

2-9 Equivalent Fractions and Mixed Numbers

In some recipes the amounts of ingredients are given as fractions, and sometimes those fractions do not equal the fractions on a measuring cup. Knowing how fractions relate to each other can be very helpful.

Different fractions can name the same number.

35 = = 15

256

10

2-9 Equivalent Fractions and Mixed Numbers

=

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

In the diagram = . These are called

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

35

610

1525

2-9 Equivalent Fractions and Mixed Numbers

Find two fractions equivalent to .

Additional Example 1: Finding Equivalent Fractions

57

5 · 27 · 2

= 1014

Multiply numerator and denominator by 2.

5 · 37 · 3 = 15

21Multiply numerator and denominator by 3.

2-9 Equivalent Fractions and Mixed Numbers

Check It Out: Example 1

Find two fractions equivalent to .

6 · 212 · 2

= 1224

Multiply numerator and denominator by 2.

6 ÷ 212 ÷ 2

= 36

Divide numerator and denominator by 2.

612

2-9 Equivalent Fractions and Mixed Numbers

A fraction is in simplest form when the numerat or and denominator are relatively prime. Relatively prime numbers have no common factors other than 1.

2-9 Equivalent Fractions and Mixed Numbers

Write the fraction in simplest form.

Additional Example 2: Writing Fractions in Simplest Form

1824

Find the GCF of 18 and 24.

The GCF is 6 = 2 • 3.

=1824

Divide the numerator and denominator by 6.

18 = 2 • 3 • 3

24 = 2 • 2 • 2 • 3

18 ÷ 624 ÷ 6 = 3

4

2-9 Equivalent Fractions and Mixed Numbers

Write the fraction in simplest form.

Check It Out: Example 2

1545

Find the GCF of 15 and 45.

The GCF is 15 = 3 • 5.

=1545

Divide the numerator and denominator by 15.

15 = 3 • 5

45 = 3 • 3 • 5

15 ÷ 1545 ÷ 15 = 1

3

2-9 Equivalent Fractions and Mixed Numbers

Determine whether the fractions in each pair are equivalent.

Additional Example 3A: Determining Whether Fractions are Equivalent

and 46

2842

Both fractions can be written with a denominator of 3.

46 = 4 ÷ 2

6 ÷ 2 = 23

2842

= 28 ÷ 1442 ÷ 14 = 2

3

The numerators are equal, so the fractions are equivalent.

2-9 Equivalent Fractions and Mixed Numbers

Additional Example 3B: Determining Whether Fractions are Equivalent

Determine whether the fractions in each pair are equivalent.

and 610

2025

Both fractions can be written with a denominator of 50.

= 6 · 510 · 5 = 30

502025

= 20 · 225 · 2 = 40

50The numerators are not equal, so the fractions are not equivalent.

610

2-9 Equivalent Fractions and Mixed Numbers

85= 13

5

85 is an improper

fraction. Its numerator is greater than itsdenominator.

1 35

is a mixednumber. Itcontains both awhole numberand a fraction.

An improper fraction is a fraction where the numerator is than or equal to the denominator.

Remember!

2-9 Equivalent Fractions and Mixed Numbers

A. Write

Additional Example 4: 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 a mixed number.

B. Write 7 23 as an improper fraction.

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

2233

+

= 3 · 7 + 23 = 23

3

Use the result to write the improperfraction.

2-9 Equivalent Fractions and Mixed Numbers

Check It Out: Example 4

A. Write 156 as a mixed number.

First divide the numerator by the denominator.

156

= 2 36

Use the quotient and remainder to write a mixed number.

B. Write 8 13 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

2-9 Equivalent Fractions and Mixed Numbers

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

2-9 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

182

12,

36

178

5 12

4 10

13

no

2-9 Equivalent Fractions and Mixed Numbers

1. Identify two fractions equivalent to .

A. Possible answer: ,

B. Possible answer: ,

C. Possible answer: ,

D. Possible answer: ,

Lesson Quiz for Student Response Systems

12 60

1

5

3 15

1

5

3 5

1

6

3 18

1 10

3 30

2-9 Equivalent Fractions and Mixed Numbers

2. Identify the fractions that are not equivalent.

A. , C. ,

B. , D. ,

Lesson Quiz for Student Response Systems

3 16

6 32

3 16

7 10

7 10

14 20

3 7

15 35

2-9 Equivalent Fractions and Mixed Numbers

3. Which of the following represents the fraction in simplest form?

A. C.

B. D.

Lesson Quiz for Student Response Systems

1 5

1 4

1 3

1 2

15 30

2-9 Equivalent Fractions and Mixed Numbers

4. Which of the following represents as a mixed number?

A. 5 C. 3

B. 4 D. 2

Lesson Quiz for Student Response Systems

1 6

1 6

1 6

1 6

19 6

2-9 Equivalent Fractions and Mixed Numbers

5. Which of the following represents the

fraction 4 as an improper fraction?

A. C.

B. D.

Lesson Quiz for Student Response Systems

29 6

28 6

27 6

25 6

5 6