Dividing of Fractions

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. Think: How many halves are in 1 ½ ? 1½ ÷ ½ = 3 You could watch 3 episodes.

Baking Cookies You have 1 cups of sugar. It takes cup to make 1 batch of cookies. How many batches of cookies can you make? How many cups of sugar are left? How many batches of cookies could be made with the sugar that’s left? 3 3

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?”

Dividing a Whole Number by a Fraction 1 2 3 4 5 6 7 11 10 12 9 8 If you start with 3, you will have 12 groups of 1/4 . So, 3 ÷ ¼ = 12. Can you see how you could manipulate the fractions to get an answer of 12?

Dividing a Whole Number by a Fraction What is 5 ÷ 1/3? If you start with 5, you will have 15 groups of 1/3 . So, 5 ÷ 1/3 = 15. 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 Basically, in order to divide fractions we will have to multiply. 1 1 1 4 x ÷ = 2 4 2 1

Dividing a Fraction by a Fraction From this point, the problem can be solved in the way that you did for multiplying fractions. 2 2 1 4 x 2 = = 2 1 1 1

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

How to Divide Fractions Step 2 – Keep your first fraction. 3 1 3 = ÷ 1 4 1

How to Divide Fractions Step 3 – Change the operation to multiplication. 3 1 3 = x ÷ 1 4 1

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

How to Divide Fractions Step 5 – Multiply the numerators, then multiple the denominators. 3 4 12 = x 1 1 1

How to Divide Fractions Step 6 – Simplify (if possible). 3 4 12 = = 12 x 1 1 1

Dividing Fractions – An Example 3 2 = ÷ 4 9 Since both are fractions, now you can Keep (1st fraction), Change (the operation to multiplication), and Flip (2nd Fraction)…

Now, Multiply and Simplify 3 3 3 9 27 8 x = 8) 4 2 8 27 24 3

Dividing Fractions So, 3 2 3 8 = ÷ 4 9

Dividing Fractions – Another Example 1 2 = 2 ÷ 3 8 Convert to improper fraction

Dividing Fractions 7 2 7 3 8 = ÷ x 3 8 2 Keep Change Flip

Now, Multiply and Simplify 2 7 8 56 9 6 x = 6) 3 2 6 56 54 2 2 1 ÷ 9 = 9 2 6 ÷ 2 3

Dividing Fractions So, 1 2 9 1 3 = 2 ÷ 3 8

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!