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Dividing Fractions…And what it means

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Rules for Multiplying Fractions:*Review*

1) Change mixed numbers into improper fractions.

2) Cancel if possible.

3) Multiply the numerators.

4) Multiply the denominators.

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What does it mean to multiply a fraction?

For example, we want to multiply:

3 x 2/7

That equals: 2/7 + 2/7 + 2/7

What’s the answer?6/7

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Word problem review with fraction multiplication:

How do you write the equation for the question…

What is ¾ of 20?

Try it on your paper and show me….¾ x 20 =

15

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Try this…

How do you write what ½ of 7/8ths is in

an equation?Write it on your paper and show me

when you’re done please.

½ x 7/8 =7/16

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It is important that you understand multiplying fractions,

before we begin dividing them….

Are you READY?

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Dividing Fractions:What are we really doing when we divide fractions?

Whole number example: How many 2-foot sections are there in

something that is 10 feet long?We write: 10 ÷ 2 = 5 feet

Fraction example:

How many ½-foot sections are there in something that is 1 ¾ feet long?

We write: 1 ¾ ÷ ½= hmmm…

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Stop and take a Look !

The answer is: 3 ½

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Here’s another way we divide fractions…

Whole number example:

If 2 jump ropes are 10 meters long, how long is one jump rope?

We write: 10 ÷ 2 = 5 meters

Fraction example:

If ½ of a jump rope is 1 ¾ meters, what is the length of the whole rope?We write: 1 ¾ ÷ ½ =hmm…

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Let’s take another Look!

The answer is: 3 ½

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Be aware…

We cannot visualize all division by fraction problems, therefore it is necessary to know how to use

the mathematical process.

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Your turn…

Can you think of some word problems that would require division by fractions?

Think about it, then using scrap paper,create a visual for your word problem.

You have 4 minutes.

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Dividing Fractions:The Process

1) Change mixed numbers into improper fractions.

2) Invert and multiply. (You may choose to cancel before multiplying.)

3) Reduce your answer (if possible).

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Teacher Example:

15/3 ÷ 2/9=

We can prove that it’s correct too!

Answer: 45/2

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Another Teacher Example:

3 1/5 ÷ 1 2/8 =

Then,We’ll prove that it’s correct!

Answer: 64/25

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Understanding the rules

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Rule #1: Change mixed numbers into improper fractions. Which problem would you prefer to solve?

This one:

3 ¾ ÷ 2 1/3

Or this one:

15/4 ÷ 7/3

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Rule #2: Invert and Multiply

Why invert and multiply? This is actually a short cut that helps us get to the answer more quickly.

Dividing by a number is equivalent to multiplying by its reciprocal. After all, dividing by 1 is much

easier than dividing by 3/8!

Example: 6/7 ÷ 3/8 = ______

Answer: 16/7

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Rule #3: Reduce Your Answer

Reducing before multiplying helps simplify the equation early on, so that

there is less work later.

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Let’s try a few together:

1) 5/8 ÷ 7/8 =

2) 3/5 ÷ 2 =

3) 15 ÷ 2 ½ =

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Now you are ready to try some problems on your

own!

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Closing

What are the 3 steps in dividing fractions?