Multiplication and Division of Fractions Fractions and Whole Numbers Models to Process……..

Before we start . . .review what you know. Warm Up Multiply. 1. 2. 3. 4. 1 2 1 2 __ 3 • 1 6 __ • 4 5 __ 3 8 3 10 __ 3 11 __ 6 11 __ 3 8 __ 5 8 __ 15 64 __ • 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? 7 8 __

Do you remember the rules? We do NOT need a common denominator. We DO have to have all fractions in form.

Multiply. Write the answer in simplest form. 1 2 __ 4 5 __ 3 • 2 1 7 2 __ 4 5 • Write 3 as an improper fraction. 3 = 7 2 __ 1 14 5 __ 4 5 __ = 2 Write the answer in simplest form. You can write the answer as a mixed number.

Cooking Disaster! What is ¾ of 3 ½? n = ¾ (3 ½) Sam decided to make lasagna. He had just enough ingredients to 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 did Sam drop? What is ¾ of 3 ½? n = ¾ (3 ½)

Garden Time Jamie needs 5 ¼ yards of ground to plant his vegetable garden. If you need only ½ that much space, how much space do you need?

Challenge!! 2 x 2 = ? 2 1 1 1 2 1 2 1 What’s left? 70 ??

Cooking Dilemma!!!! Not in your notes. Darla is making meatloaf for a dinner party. She needs 1 ¾ pounds of ground 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? 3 How many more can she make?? 6 x 7 = 21 or 10 ½ 1 4 2 2 = 12 - 10 ½ 13 -10 ½ 2 ½ ÷ 1 ¾ = She can only make 1 more! 2 ½ lbs. are left………. ÷ = The question was . . . . How many more can she make? 20 14 ∙ =

Now let’s move on to division……. We will divide with fractions and whole numbers. We will work with models and the fraction division algorithm.

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! 3 4 __ 4 3 __ 1 4 __ 24 ÷ 4 1 = 24 • = 6

Let’s Find Reciprocals Invert (flip) it. ___ 1 Start with a fraction. 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 that is three feet long. We’ll do the section in your notes that says “Division Problem” later in the lesson.

Fraction Division Algorithm-Memorize 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 = ? Cancelling can happen here. Our division process has definite steps to follow: Write all values in fraction form. We are now ready to convert this division problem into a multiplication problem. COPY the first value Change the division sign to multiplication. FLIP the divisor (2nd number)

Think about it! A car trip is 6 hours long. Every 2/3 of an hour, Brian changes the radio station. How many times does he change the station during the trip? 3 1 COPY CHANGE SIGN FLIP to reciprocal. Write in fraction form.

Apply the Skill A bowl of soup holds 7 ounces. If a spoonful holds 1/6 of an ounce, how many spoonfuls are in a bowl of soup? 7 ounces divided into 1/6 ounce portions = ? How many spoonfuls would we have in three bowls? 42 spoonfuls 42 x 3 =126

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

Apply the Skill Each health book is ¾ inches wide. If the classroom bookshelf is 2 feet long, how many books can fit on the shelf? We have a hidden question here…….. How do we find our total inches??? 8 1

Process, Process, Process!!! 7 10 __ 1 5 __ ÷ Rewrite as multiplication using the reciprocal of , . 7 10 __ 1 5 __ 7 10 __ 5 1 __ ÷ = • 1 5 __ 5 1 __ 1 7 • 5 10 • 1 ____ = Simplify before multiplying. 2 7 2 __ = Multiply. 1 2 __ You can write the answer as a mixed number. = 3

Challenge!! 1 3 2 2 1 3 1

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.