Transcript Dividing Fractions…

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:
Or this one:
3 ¾ ÷ 2 1/3
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?
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