multiplying fractions & mixed numbers

Multiplying Fractions & Mixed Numbers

MACC.6.EE.2.7MA.6.A.3.1, MA.6.A.3.2,

MA.6.A.3.3

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

6 x

0 1 2 3 4 5

Multiplying Fractions by Whole Numbers using a Number Line

43

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?

Multiplying Fractions using an Array (Model)

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.

Estimating a Product

83

83

81

Step 1 – Make all factors fractions◦ Change whole numbers into fractions by placing a

“1” as the denominator◦ For example:

6 ∙

∙ ·

Multiplying Fractions by Whole Numbers

83

16

83

DN

DN

Step 2 – Multiply the numerators and multiply the denominators

∙ 16

83

The fraction bar means divide

Divide the numerator by the denominator - 8 1

Changing Improper Fractions to Mixed Numbers

49

294

412

Step 3 – Simplify

◦ Put the fractions in simplest form◦ Change improper fractions into mixed

numbers

= =

818

49

412

Evaluate 4x, where x =

You Try It!

85

There are 25 students in the music club, are also in the band. How many music club

students are also in the band?

Real World

52

Step 1 – Multiply the numerators and multiply the denominators

·

Multiplying Fractions by Fractions

83

92

Step 2 – Simplify

◦ Put the fractions in simplest form◦ Change improper fractions into mixed

numbers

÷ = 72

666

121

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

Multiplying Fractions by Fractionswith Cross Simplification

83

92

Multiplying Mixed Numbers

Change the following mixed number into an

improper fraction:

736

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

Changing Mixed Numbers to Improper Fractions

736

73

745

Step 1 – Change all factors into fractions

· format

· = ·

Multiplying Fractions by Mixed Numbers

DN

DN

542

83

??

83

Step 2 – Multiply the numerators and multiply the denominators

Step 3 – Simplify

◦ Put the fractions in simplest form◦ Change improper fractions into mixed

numbers

Course 1

5-2 Multiplying Mixed NumbersAdditional Example 1A: Multiplying Fractions and

Mixed NumbersMultiply. Write the answer in simplest form.

A. • 114__ 1

3__

Write 1 as an improper fraction. 1 =

43__1

3__1

3__1

4__ 4

3__•

1 • 44 • 3_____ Multiply numerators. Multiply denominators.

412__

13__ Write the answer in simplest form.

Course 1

5-2 Multiplying Mixed NumbersTry This: Example 2A

Find each product. Write the answer in simplest form.

A. 1 • 234__ 1

6__

74__ 13

6__•

7 • 134 • 6______ Multiply numerators. Multiply denominators.

9124__

1924__ You can write the improper fraction as a

mixed number.

Write the mixed numbers as improper fractions. 1 = 2 = 7

4__ 13

6__3

4__ 1

6__

3

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

Insert Lesson Title Here

Course 1

5-2 Multiplying Mixed Numbers

58__1

5__ • 5

7__7

10__ •

14__1

5__ 1

5__ 16

12__

120__

1 314__

2 34__

grain740__