dividing of fractions by carol edelstein dividing fractions: homework add to avid folder pg. 167 1-8
TRANSCRIPT
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 PracticeWhen 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 1/4 .
1 2
3 4
5 6
7 11
10
12
9
8
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
x12
41
From this point, the problem can be solved in the way that you did for multiplying fractions.
12=
21
= 2
How to Divide Fractions
• Step 1 – Convert whole numbers and mixed numbers to improper fractions.
÷4
31
1÷43 =1
This example is from a prior slide.
How to Divide Fractions
• Step 5 – Multiply the numerators, then multiple the denominators.
x 131
4 = 121
Dividing Fractions – An Example
29
34 =÷
Since both are fractions, now you can Keep (1st fraction), Change (the operation to multiplication), and Flip (2nd Fraction)…
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