Multiplication and Division of Fractions

Fractions and Whole Numbers

Models to Process……..

Warm UpMultiply.

1. 2.

3. 4. 38__ 5

8__• 2

•45__ 3

8__

311__

12__1

3__ •

•

16__ 3

10__

611__ 15

64__

Before we start . . .review what you know.

1

2

Problem of the Day

Tracy and Zachary are sharing a large pizza. Tracy cuts the pizza in half. Zachary says he cannot eat that much. Zachary cuts his half into fourths and eats one piece. What fraction of the whole pizza does Zachary not eat? 78__

Do you remember the rules?

• We do NOT need a common denominator.

• We DO have to have all fractions in

form. b

a

Multiply. Write the answer in simplest form.

3 • 12__ 4

5__

Write 3 as an improper fraction. 3 =

72__1

2__1

2__7

2__ 4

5__•

145__

Write the answer in simplest form. You can write the answer as a mixed number.

45__= 2

2

1

5

42

10

82

10

28

Cooking Disaster!Sam decided to make lasagna. He had just enough ingredientsto make the dish!

The recipe called for 3 ½ cups of tomato sauce. Just as he was finishing, he dropped ¾ of his sauce! How much of the sauce didSam drop?

What is ¾ of 3 ½?

n = ¾ (3 ½)

2

7

4

3n

8

52

8

21n

Garden TimeJamie needs 5 ¼ yards of ground to plant hisvegetable garden. If you need only ½ that much space,how much space do you need?

4

15

2

1

4

21

2

1

yardsor8

52

8

21

Challenge!!

2

12

5

336

4

31

3

2

9

11

2

5

5

18

1

6

4

7

3

2

9

102

1

1

1

2

1

2

1

2 x 2 = ? 1

1

What’s left?

70 ??

Cooking Dilemma!!!!Darla is making meatloaf for a dinner party. She needs 1 ¾ pounds ofground beef for each meatloaf.

She bought 13 pounds of beef to make these meatloaves……She has already made 6 meatloaves. How many more will Darla be able to make?

What has she already used?

6 x 71 4

2

3= 21 or 10 ½

2

How many more can she make??

13-10 ½

= 12 - 10 ½

2

2

2 ½ lbs. are left……….

The question was . . . . How manymore can she make?

2 ½ ÷ 1 ¾ =

2

5 ÷4

7=

2

5

7

4∙ =2014

She can only make 1 more!

Not in your

notes.

We will divide with fractions and whole numbers.

We will work with models and the fraction division algorithm.

Now let’s move on to division…….

Vocabulary

Reciprocal: The reciprocal is the inverted

form (flipped form) of a fraction.

Reciprocals can help you divide by fractions. Two numbers are reciprocals if their product is 1.

Look at the relationship between the

fractions and . When you multiply any number by its reciprocal, the product is ONE.

WHY do we need reciprocals? To divide by a fraction, we MULTIPLY by its reciprocal!

34__ 4

3__

24 ÷ = 24 • = 614__

3

4

4

3

Let’s Find Reciprocals

3

2 5

17

3

22

9

5

2

31

5___ 1 7

1

3

8

8

3

5

9

Start with a fraction.

Invert (flip) it.

STOP…create an improper fraction first!

Let’s apply this to a word problem……

In this example, we will take a 3 ft. board and split it into sections that are just ¾ of a foot. You need to draw 3 lines to create fourths!

“How many shelves, ¾ ft. long, can we cut from a 3’ board? “We are trying to find how many sections that are ¾ of a foot are found in a board that is 3’

1 2 3

We can make 4 shelves that are ¾ ft. long from a board thatis three feet long.

We’ll do the section in your notes that says “Division Problem” later in the lesson.

Fraction Division Algorithm-Memorize!!!To divide a fraction, multiply by the

reciprocal of the divisor.

• Write the problem in its original form!• If needed rewrite the problem with all

fractions in a/b form.• Keep the first term.• CHANGE the division sign to a

multiplication sign• FLIP (INVERT) the divisor (this is the

fraction behind the sign.)

Back to the board example….

Our first example asked us to divide a 3 ft. board into sections that are just ¾ of a foot. Think about it like this….Three feet split in ¾ sections would be ?

3 ÷ ¾ = ?

Our division process has definite steps to follow: Write all values in

fractionform.

4

3

1

3

We are now ready to convert this division problem into a multiplication problem.

3

4

1

3

COPY the first valueChange the division signto multiplication.

FLIP the divisor (2nd

number)

43

12

Cancelling can happen here.

Think about it!A car trip is 6 hours long. Every 2/3 of an hour, Brian changesthe radio station. How many times does he change the stationduring the trip?

3

26

3

2

1

6

2

3

1

6

Write infraction form.

COPYCHANGE SIGNFLIP to reciprocal.

3

1

times9

Apply the Skill A bowl of soup holds 7 ounces. If a spoonful holds 1/6 of an ounce, howmany spoonfuls are in a bowl of soup?

6

1

1

7

How many spoonfuls would we have in three bowls?

1

6

1

7spoonfuls42

42 spoonfuls42 x 3 =126

7 ounces divided into 1/6 ounce portions = ?

Apply the Skill How many ¼ pound burgers can Danny make with 12 pounds of ground turkey????

4

1

1

12 1

4

1

12burgersturkey48

Apply the Skill Each health book is ¾ inches wide. If the classroom bookshelf is 2 feetlong, how many books can fit on the shelf?

4

3

1

24

3

4

1

24 books32

We have a hidden question here……..

How do we find our total inches???

8

1

Challenge!!

2

12

5

336

4

31

3

2

9

11

2

5

5

18

1

6

4

7

3

2

9

10

5

2

5

18

6

1

4

7

2

3

9

10 1

3

3

1

2

1 10

7

2

Fractions Make You Strong

Did we accomplish our goal?

We have reviewed the basics of multiplying and dividing fractions. We will continue working with these concepts this week.