Dividing of Fractions When would you divide fractions

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. 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 ÷ dividend (start) 6 = divisor (what groups look like) So, 18 ÷ 6 = 3 How many groups of 6 items are there?

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 2 ½ ÷ ¾ = /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 9 10 7 8 11 12 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 2 ÷ 1 4 = 1 x 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 1 x 4 =2 = 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 3÷ 4 = 1 ÷ 1 4

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

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

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

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

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

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

Now, Multiply and Simplify 3 38 3 x 9 = 27 4 2 8 8)27 24 3

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

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

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

Now, Multiply and Simplify 2 96 7 x 8 = 56 3 2 6 6)56 54 2 ÷ 2 = 1 9 6 ÷ 2 9 3 2

Dividing Fractions So, 1 2 3 ÷ 2 = 1 9 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 2 ½ ÷ ¾ = /3

Great job!