Dividing of Fractions by Carol Edelstein

Warm Up

Warm up What does it mean to divide?

Essential Question How can you divide a fraction by a fraction?

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 Fractions – Conceptual Understanding Like when we divided decimals, 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 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 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 Basically, in order 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 – 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

Great job!