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Multiplying Fractions Using Models. NGSSS Connection. MA.6.A.1.1 Explain and justify procedures for multiplying and dividing fractions and decimals. MA.6.A.1.2 Multiply and divide fractions and decimals efficiently. MA.6.A.1.3

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ngsss connection
NGSSS Connection

MA.6.A.1.1

Explain and justify procedures for multiplying and dividing fractions and decimals.

MA.6.A.1.2

Multiply and divide fractions and decimals efficiently.

MA.6.A.1.3

Solve real-world problems involving multiplication and division of fractions and decimals.

think about it
Think About It

What do you think happens when you multiply a number by a fraction?

multiplying fractions and whole numbers
Multiplying Fractions and Whole Numbers

3

3

3

3

Model 1

Solve

Step 1: Draw a bar to represent the whole number

Step 2: Divide the bar into 4 equal parts

Step 3: Determine the number that is in each section

Step 4: Shade

12

multiplying fractions and whole numbers1
Multiplying Fractions and Whole Numbers

Step 1: Draw a bar to represent the whole number

Step 2: Divide the bar into equal parts

Step 3: Determine the number that is in each section

Step 4: Shade the fractional part

multiplying fractions and whole numbers2
Multiplying Fractions and Whole Numbers

Joel bought 24 markers, and of them have gel ink. How many gel ink markers are there?

What information do you need to solve the problem?

3

3

3

3

3

3

3

3

24

multiplying fractions and whole numbers3
Multiplying Fractions and Whole Numbers

Model 2

Solve

Used in the “Personal Tutor”

Step 1: Model 2/5 x 6

Step 2: Move the shaded pieces around to fill as many columns as possible.

+

+

+

+

+

multiplying fractions and whole numbers4
Multiplying Fractions and Whole Numbers

Model 3

Solve

Step 1: Construct a rectangle that is 2/5 units high and shade the fractional part

Step 2: Make the rectangle 6 units wide

6

Step 3: Move the shaded pieces around to fill as many columns as possible.

multiplying fractions and whole numbers5
Multiplying Fractions and Whole Numbers

Jenny made five loaves of banana bread that had cup of butter in each loaf. How many cups of butter were used in all?

What information do you need to solve the problem?

5

OR

multiplying fractions
Multiplying Fractions

Solve

Step 1: Construct a rectangle that represents 1 whole.

Step 2: Make the rectangle 2/3 units high and shade the fractional part.

Step 3: Make the rectangle 4/5 units wide and shade the fractional part.

multiplying fractions and whole numbers6
Multiplying Fractions and Whole Numbers

Step 1: Construct a rectangle that is 2/5 units high and shade the fractional part.

Step 2: Make the rectangle 5/6 units wide and shade the fractional part.

multiplying fractions1
Multiplying Fractions

About of an orchestra is made up of string instruments. If of the string instruments are cellos, what fraction of the orchestra is made up of cellos?

What information do you need to solve the problem?

multiplying whole numbers and mixed numbers
Multiplying Whole Numbers and Mixed Numbers.

Model 2

Solve

Step 1: Model x 3

Step 2: Move the shaded pieces around to fill as many columns as possible.

+

+

multiplying whole numbers and mixed numbers1
Multiplying Whole Numbers and Mixed Numbers.

Model 2

Solve

Step 1: Model x 2

Step 2: Move the shaded pieces around to fill as many columns as possible.

+

multiplying whole numbers mixed numbers
Multiplying Whole Numbers & Mixed Numbers

Solve

Step 1: Shade a rectangle that is 4 units high and units wide.

Step 2: Combine the 1/3 pieces to make as many wholes as possible.

4

slide23

1

4

40

dividing fractions and whole numbers
Dividing Fractions and Whole Numbers

Solve

Step 1: Draw a bar to represent the whole number.

Step 2: Divide each whole into fourths.

of circled group

st group

Step 3: Determine how many groups of are in 2.

nd group

2

dividing fractions and whole numbers1
Dividing Fractions and Whole Numbers

Step 1: Draw a bar to represent the whole number.

Step 2: Divide each whole into thirds.

Step 3: Determine how many groups of 2/3 are in 3.

dividing fractions and whole numbers2
Dividing Fractions and Whole Numbers

Melissa made taco dip for a party and used 5 cups of cheese. The recipe for one serving calls for cup of cheese. How many servings of taco dip did Melissa make?

What information do you need to solve the problem?

5

dividing fractions by fractions
Dividing Fractions by Fractions

Solve

Step 1: Draw a bar and represent 4/5.

Step 2: Determine how many equal groups of 2/5 are in 4/5.

1st group

2nd group

4/5

dividing fractions by fractions1
Dividing Fractions by Fractions

Step 1: Rename the second fraction so that both fractions have a common denominator.

Solve

Solve

Step 2: Draw a bar and represent 5/6.

Step 3: Determine how many equal groups of 4/6 are in 5/6.

1/4 group

1st group

5/6

dividing fractions by fractions2
Dividing Fractions by Fractions

1st group

2nd group

2/4