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Dividing of Fractions by Carol Edelstein

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**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.

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

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**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…

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**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?”

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**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?

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**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?

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**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

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**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.

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**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

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**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

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**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

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**How to Divide Fractions**

Step 2 – Keep your first fraction. 3 1 3 = ÷ 1 4 1

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**How to Divide Fractions**

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

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**How to Divide Fractions**

Step 4 – Flip the second fraction. 3 1 3 4 = x ÷ 1 4 1 1

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**How to Divide Fractions**

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

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**How to Divide Fractions**

Step 6 – Simplify (if possible). 3 4 12 = = 12 x 1 1 1

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**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)…

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**Now, Multiply and Simplify**

3 3 3 9 27 8 x = 8) 4 2 8 27 24 3

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

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**Dividing Fractions – Another Example**

1 2 = 2 ÷ 3 8 Convert to improper fraction

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

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**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

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

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**Dividing Fractions – More Examples**

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**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

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