Equivalent fractions and mixed numbers

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Transcript Equivalent fractions and mixed numbers

3-4 Equivalent Fractions and Mixed Numbers

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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

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3-4 Equivalent Fractions and Mixed Numbers

Vocabulary

equivalent fractions improper fraction mixed number

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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.

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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.

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3-4 Equivalent Fractions and Mixed Numbers

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

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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.

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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

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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.

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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.

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

Example 1

6  12  2 2 6 ÷ 12 ÷ 2 2

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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.

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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

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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.

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3-4 Equivalent Fractions and Mixed Numbers Lesson Quiz

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

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