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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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Great job!

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MULTIPLY and DIVIDE RATIONAL NUMBERS. MULTPILYING MIXED NUMBERS 1)Change all Mixed numbers to improper fractions 2)Simplify A) Up and Down B) Diagonally.

MULTIPLY and DIVIDE RATIONAL NUMBERS. MULTPILYING MIXED NUMBERS 1)Change all Mixed numbers to improper fractions 2)Simplify A) Up and Down B) Diagonally.

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