Transcript MultiplyingandDividingFractions - Math GR. 6-8

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.
1
8
2

What do you think happens
when you multiply a number
by a fraction?
Symbols
Words
3
Solve  12
4

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
3
4
3

3
3
12
3
3
 12  9
4
3
 35
5
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
5
Joel bought 24 markers, and of them have gel ink.
8
How many gel ink markers are there?
What information do you
 the problem?
need to solve
3
3
3
3
 24
5
 24  15
8
3
5
 24
8
3
3
3
2
Solve  6
5
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
2
62
5
5
2
Solve  6
5
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.
2
5
2
2
5
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
What information do you
5
need to solve the problem?
4
5

1
4
1  1 1 1 OR
 5 4 1
4
4
1
4
2 4
Solve 
3 5
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.

4
5

2
3
2 4 8
 
3 5 15
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.
3
5
About of an orchestra is made up of string instruments.
5
If of the string instruments are cellos, what fraction of the
8
orchestra is made up of cellos?

What information do you
need to solve the problem?
5
8


3
5

3 5

5 8
3 5 15
 
5 8 40
3

8
2
Solve 1  3
5
2
5
Step 1: Model 1 x 3

+
+
Step 2: Move the shaded
pieces around to fill as

many columns as
possible.
2
1
1 34
5
5
2
Solve 1  2
3
2
3
Step 1: Model 1 x 2

2
1
1 23
3
3
+

Step 2: Move the shaded
pieces around to fill as

many columns as
possible.
1
Solve 4  2
3
Step 1: Shade a rectangle that is 4 units high
1
and units
2 wide.
3
1
2
3


Step 2: Combine the 1/3 pieces to make as many
wholes as possible.

1
1
42 9
3
3
4

3
1
4
40
7
7
3
Solve 2 
4
Step 1: Draw a bar to represent the whole number.
Step 2: Divide each whole into fourths.

Step 3: Determine how many groups of
1st group
2
of circled group
3
2nd group




2
3
4
are in 2.
3
2
2 2
4
3
2
5
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.
Melissa made taco dip for a party and used 5 cups of
5
cheese. The recipe for one serving calls for 6 cup of
cheese. How many servings of taco dip did Melissa
make?

What information do you need to solve the problem?

5
5
5
6
5
5 6
6
4 2
Solve

5 5
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 2
 2
5 5
4/5
5 2
Solve 
6 3
5 4
Solve 
6 6
Step 1: Rename the second fraction so that both fractions have
a common denominator.
Step 2: Draw a bar and represent 5/6.
 Step 3: Determine how many equal groups
 of 4/6 are in 5/6.
1st group
1/4 group
5 2
1
 1
6 3
4
5/6
1 1

2 4
1st group
1 1

2 4
2nd group


2/4

2 1

4 4
1 1
 2
2 4