multiplying fractions using models

MA.6.A.1.2Multiply and divide fractions and decimals efficiently.

MA.6.A.1.3Solve real-world problems involving multiplication

and division of fractions and decimals.

MA.6.A.1.1Explain and justify procedures for multiplying

and dividing fractions and decimals.

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

€

1

2× 8

Symbols Words

Step 1: Draw a bar to represent the whole numberStep 2: Divide the bar into 4 equal partsStep 3: Determine the number that is in each section

3333

12

€

3

4×12 = 9

€

3

4×12Solve

Step 4: Shade

€

3

4

€

3

5× 35

Step 1: Draw a bar to represent the whole number

Step 2: Divide the bar into equal partsStep 3: Determine the number that is in each section

Step 4: Shade the fractional part

What information do you need to solve the problem?

€

5

8× 24

24

3 33 3 333 3

€

5

8Joel bought 24 markers, and of them have gel ink.

How many gel ink markers are there?

€

5

8× 24 =15

€

2

5× 6Solve

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.

€

2

5× 6 = 2

2

5

+++++

6

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

€

2

5

€

2

5× 6Solve

Step 2: Make the rectangle 6 units wide

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

€

=22

5

What information do you need to solve the problem?

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

€

1

4

€

1

4× 5

€

1

4

5

€

1

4× 5 =1

1

4

€

=11

4OR

€

2

3×4

5Solve

Step 1: Construct a rectangle that represents 1 whole.

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

€

2

3

€

4

5

€

2

3×4

5=8

15

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

€

2

5×5

6

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.

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?

€

58

€

35

What information do you need to solve the problem?

€

3

5×5

8

€

5

8

€

3

5

€

3

5×5

8=15

40

€

=3

8

€

12

5× 3Solve

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

€

12

5× 3 = 4

1

5

++

Step 1: Model x 3

€

12

5

€

12

3× 2Solve

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

€

12

3× 2 = 3

1

3+

Step 1: Model x 2

€

12

3

€

4 × 21

3Solve 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

€

21

3

€

4 × 21

3= 91

3

€

21

3

3

14 40

7

7

Step 1: Draw a bar to represent the whole number.Step 2: Divide each whole into fourths.

2

€

2 ÷3

4= 22

3

€

2 ÷3

4Solve

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

€

3

4

€

2

3of circled group

€

1st group

€

2nd group

€

5 ÷2

3

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.

What information do you need to solve the problem?

5

€

5 ÷5

6= 6

€

5

6

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?

€

5 ÷5

6

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

4/5

€

4

5÷2

5= 2

€

4

5÷2

5Solve

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

1st group 2nd group

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

5/6

€

5

6÷2

3=11

4

€

5

6÷2

3Solve

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

1st group 1/4 group

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

€

5

6÷4

6Solve

2/4

€

1

2÷1

4= 2

1st group 2nd group€

1

2÷1

4

€

2

4÷1

4

€

1

2÷1

4