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Multiplying Fractions &amp; Mixed Numbers

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Multiplying Fractions &amp; Mixed Numbers. EQ: How is the process to multiply mixed numbers related to multiplying fractions?. MACC.6.EE.2.7 MA.6.A.3.1, MA.6.A.3.2, MA.6.A.3.3. Multiplying Fractions by Whole Numbers using a Number Line. 6 x

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### Multiplying Fractions & Mixed Numbers

EQ: How is the process to multiply mixed numbers related to multiplying fractions?

MACC.6.EE.2.7

MA.6.A.3.1, MA.6.A.3.2,

MA.6.A.3.3

Multiplying Fractions using an Array (Model)

You are choosing 18 CDs to take to a party.

You want two-thirds of the CDs to have dance music. How many dance music CDs should you choose?

Estimating a Product

You have 15 CDs. Each CD case is three-eighths inch wide. Estimate how wide a space you need on a CD rack to fit all 15 CDs.

Space = x 15

Space = x 16

Space = 6 Think: of 16 is 2, so multiply 2 by 3 for 6.

Multiplying Fractions by Whole Numbers
• Step 1 – Make all factors fractions
• Change whole numbers into fractions by placing a “1” as the denominator
• For example:

6 ∙

∙ ·

Changing Improper Fractions to Mixed Numbers

The fraction bar means divide

• Divide the numerator by the denominator

- 8

1

Step 3 – Simplify

• Put the fractions in simplest form
• Change improper fractions into mixed numbers

= =

You Try It!
• Evaluate 4x, where x =
Real World
• There are 25 students in the music club,

are also in the band. How many music club students are also in the band?

Multiplying Fractions by Fractions
• Step 1 – Multiply the numerators and multiply the denominators

·

Step 2 – Simplify

• Put the fractions in simplest form
• Change improper fractions into mixed numbers

÷ =

Multiplying Fractions by Fractionswith Cross Simplification
• Step 1 – Multiply the numerators and multiply the denominators or cross simplify

1

·

3

• Step 2 – Simplify
• Put the fractions in simplest form
• Change improper fractions into mixed numbers
Changing Mixed Numbers to Improper Fractions

6

• Multiply the whole number by the denominator
• Add the numerator to the product
• The sum becomes the numerator and the denominator stays the same
Multiplying Fractions by Mixed Numbers
• Step 1 – Change all factors into fractions

· format

· = ·

• Step 3 – Simplify
• Put the fractions in simplest form
• Change improper fractions into mixed numbers

5-2

Multiplying Mixed Numbers

1

__

Write 1 as an improper fraction. 1 =

4

1

1

1

1

4

1 • 4

4

1

_____

__

__

__

__

__

__

__

__

3

12

3

3

4

3

3

4

3

4 • 3

Course 1

Additional Example 1A: Multiplying Fractions and Mixed Numbers

Multiply. Write the answer in simplest form.

A. • 1

Multiply numerators. Multiply denominators.

Write the answer in simplest form.

5-2

Multiplying Mixed Numbers

Write the mixed numbers as improper

fractions. 1 = 2 =

3

3

1

1

13

7

13

7 • 13

91

19

7

__

__

__

__

__

__

__

______

__

__

__

24

6

4

6

4

6

24

4 • 6

6

4

4

Course 1

Try This: Example 2A

Find each product. Write the answer in simplest form.

A. 1 • 2

Multiply numerators. Multiply denominators.

You can write the improper fraction as a mixed number.

3

5-2

Multiplying Mixed Numbers

7

3

1

3

5

1

1

5

1

7

__

__

__

__

__

__

__

__

__

__

__

__

1

5

20

10

4

40

5

2

8

5

14

4

7

2

grain

Course 1

Insert Lesson Title Here

Lesson Quiz

Multiply. Write each answer in simplest form.

1. 3 2. 1

Find each product. Write the answer in simplest form.

3. 2•1 4. 5 • 3

5. A nurse gave a patient 3 tablets of a medication. If each

tablet contained grain of the medication, how much

medication did the patient receive?

2

16

1

1