Dividing of Fractions by Carol Edelstein

Dividing Fractions: Homework Add to AVID FOLDER Pg

Fill in the blanks on your notes using the slides.

When would you divide fractions? One example is when you are trying to figure out how many episodes of your favorite ½ hour tv program you could watch in the 1 ½ hrs you have available. 1½ ÷ ½ = 3 You could watch 3 episodes.

General Division Practice When you are faced with the division problem 18 divided by 6, think “If I have 18 items and I make groups of 6, how many groups will I have?” 18 ÷ 6 = dividend divisor (start) (what groups look like) How many groups of 6 items are there? So, 18 ÷ 6 =3

Dividing a Whole Number by a Fraction What is 3 ÷ ¼ ? Use your prior knowledge and the illustration above to figure it out. Think, “If I start with 3, how many groups that look like ¼ will I have?”

So, 3 ÷ ¼ = 12. If you start with 3, you will have 12 groups of 1/ Dividing a Whole Number by a Fraction Can you see how you could manipulate the fractions to get an answer of 12?

Dividing Fractions – Conceptual Understanding When you divide two fractions that are between 0 and 1, the quotient is going to be larger than at least one of your fractions. ½ ÷ ½ = 1 ½ ÷ ¾ = 2 / 3 Ok. Let’s look at how we can solve these problems…

Dividing a Whole Number by a Fraction So, 5 ÷ 1 / 3 = 15. If you start with 5, you will have 15 groups of 1/3. What is 5 ÷ 1 / 3 ? Can you see how you could manipulate the fractions to get an answer of 15?

Dividing a Fraction by a Fraction What is 1 / 2 ÷ 1 / 4 ? How many groups of 1 / 4 could you fit in the half of the rectangle? 2

Dividing a Fraction by a Fraction For the problem 1 / 2 ÷ 1 / 4, how could you get an answer of 2 ? Can you see how you could manipulate the fractions to get an answer of 2? Isn’t ½ x 4 = 2? Remember that division is the opposite operation of multiplication, so we can do the following… MULTIPLY.

Dividing a Fraction by a Fraction x To divide fractions we will have to multiply ÷ =

Dividing a Fraction by a Fraction x From this point, the problem can be solved in the way that you did for multiplying fractions. 1 2 = 2 1 = 2

How to Divide Fractions Step 1 – Convert whole numbers and mixed numbers to improper fractions. ÷ ÷ 4 3 = 1 This example is from a prior slide.

How to Divide Fractions Step 2 – Keep your first fraction. ÷ = 3 1

How to Divide Fractions Step 3 – Change the operation to multiplication. ÷ = 3 1 x

How to Divide Fractions Step 4 – Flip the second fraction. ÷ = 3 1 x 1 4

How to Divide Fractions Step 5 – Multiply the numerators, then multiple the denominators. x = 12 1

How to Divide Fractions Step 6 – Simplify (if possible). x = 12 1 =

Dividing Fractions – An Example = ÷ Since both are fractions, now you can Keep ( 1st fraction ), Change ( the operation to multiplication ), and Flip ( 2 nd Fraction )…

Now, Multiply and Simplify = )8) 3 x

Dividing Fractions = ÷ So,

Dividing Fractions – Another Example = ÷ 2 Convert to improper fraction

= ÷ x Keep Change Flip Dividing Fractions

Now, Multiply and Simplify = )6) 9 x ÷ 2 2 = ÷

Dividing Fractions 2 8 = ÷ So, 1 3 2

Dividing Fractions Keep Change Flip

Dividing Fractions – More Examples

REVIEW: Dividing Fractions – Conceptual Understanding Remember, when you divide two fractions that are between 0 and 1, the quotient is going to be larger than at least one of your fractions. ½ ÷ ½ = 1 ½ ÷ ¾ = 2 / 3

Dividing Fractions Word Problem

Great job!