#### Transcript Equivalent fractions and mixed numbers

**3-4 Equivalent Fractions and Mixed Numbers**

**Preview**

### Warm Up

### California Standards

### Lesson Presentation

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers**

**Warm Up**

**Name a common factor for each pair.**

### Possible answers:

**1. **5 and 10

### 5

**2. **9 and 12

### 3

**3. **20 and 24

### 4

**4. **10 and 14

### 2

**5. **6 and 8

### 2

**6. **8 and 15

### 1

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers**

**California Standards**

**NS2.4 Determine **

the least common multiple and

**the greatest common divisor of whole numbers; use them to solve problems with fractions**

(

**e.g.**

to find a common denominator to add two fractions or

**to find the reduced form of a fraction**

).

*Also covered:*

**NS1.1**

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers**

**Vocabulary**

### equivalent fractions improper fraction mixed number

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers**

Different fractions can name the same number.

**Holt CA Course 1 3 5 = 6 10 = 15 25**

**3-4 Equivalent Fractions and Mixed Numbers**

In the diagram = 6 10 = 15 25 . These are called **equivalent fractions **because they are different expressions for the same nonzero number.

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

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers**

8 5 is an **improper** **fraction**. Its numerator is greater than its denominator.

**8 5 = 1 3 5**

1 3 5 is a **mixed** **number**. It contains both a whole number and a fraction.

**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 Additional Example 1: Finding Equivalent Fractions**

5 7 2 2

*Multiply the numerator and denominator by 2.*

5 7 3 3

*Multiply the numerator and denominator by 3.*

Remember!

A fraction with the same numerator and denominator, such as is equal to 1.

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers**

5 7 simplest form when the greatest common divisor of its numerator and denominator is 1.

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers Additional Example 3A: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent.**

**4 6**

4 6 Simplify both fractions and compare.

4 6 = 4 ÷ 6 ÷ 2 2 28 42 and 28 42 14 14

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers Additional Example 3B: Determining Whether Fractions are Equivalent Determine whether the fractions in each pair are equivalent.**

**6 10**

Simplify both fractions and compare.

6 10 2 2 6 10 20 25 5 5 are *not *equivalent because their simplest forms are not equal.

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers Additional Example 4: Converting Between Improper Fractions and Mixed Numbers A. Write 13 5 as a mixed number.**

First divide the numerator by the denominator.

13 5 = 2 3 5

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

**B. Write 7 2 3 as an improper fraction.**

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

+ 2 3 = 3 7 + 2 3

*Use the result to write the improper fraction.*

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers Check It Out!**

**Example 1**

6 12 2 2 6 ÷ 12 ÷ 2 2

**Holt CA Course 1**

*Multiply the numerator and denominator by 2.*

*Divide the numerator and denominator by 2.*

**3-4 Equivalent Fractions and Mixed Numbers Check It Out!**

**Example 2**

Find the GCD of 15 and 45.

15 = 3 • 5

*The GCD is 15 = 3 • 5.*

45 = 3 • 3 • 5 15 45 = 15 ÷ 45 ÷ 15 15

*Divide the numerator and denominator by 15.*

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers Check It Out!**

**Example 3A Determine whether the fractions in each pair are equivalent.**

**3 9 and 6 18**

Simplify both fractions and compare.

3 9 = 6 18 3 ÷ 9 ÷ 3 3 6 6 3 9 and 6 18

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers Check It Out!**

**Example 4 A. Write 15 6 as a mixed number.**

First divide the numerator by the denominator.

15 6 = 2 3 6 = 2 1 2

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

**B. Write 8 1 3 as an improper fraction.**

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

+

**8**

1 3 = 3 8 + 1 3

*Use the result to write the improper fraction.*

**Holt CA Course 1**

**3-4 Equivalent Fractions and Mixed Numbers Lesson Quiz**

1 2 , 3 6 no 1 3 2 1 8 31 7

**Holt CA Course 1**