2When 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 = 3You could watch 3 episodes.
3General 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 divisor(start) (what groups look like)How many groups of 6 items are there?So, 18 ÷ 6 =3
4Dividing 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 = 1½ ÷ ¾ = 2/3Ok. Let’s look at how we can solve these problems…
5Dividing 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?”
6Dividing a Whole Number by a Fraction 123456711101298If 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?
7Dividing 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?
8Dividing 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
9Dividing 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.
10Dividing a Fraction by a Fraction Basically, in order to divide fractions we will have to multiply.1114x÷=2421
11Dividing a Fraction by a Fraction From this point, the problem can be solved in the way that you did for multiplying fractions.2214x2==2111
12How to Divide Fractions Step 1 – Convert whole numbers and mixed numbers to improper fractions.This example is from a prior slide.1313=÷÷414
13How to Divide Fractions Step 2 – Keep your first fraction.313=÷141
14How to Divide Fractions Step 3 – Change the operation to multiplication.313=x÷141
15How to Divide Fractions Step 4 – Flip the second fraction.3134=x÷1411
16How to Divide Fractions Step 5 – Multiply the numerators, then multiple the denominators.3412=x111
17How to Divide Fractions Step 6 – Simplify (if possible).3412==12x111
18Dividing Fractions – An Example 32=÷49Since both are fractions, now you can Keep (1st fraction), Change (the operation to multiplication), and Flip (2nd Fraction)…
26REVIEW: 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 = 1½ ÷ ¾ = 2/3