Transcript Dividing Fractions - Pacoima Charter School

Today we will compute
simple division of
fractions.
Compute= calculate or work out
But First let’s review what we’ve
already learned!
Remember that when multiplying
fractions
• When multiplying fractions, they do NOT need to
have a common denominator.
• To multiply two (or more) fractions, multiply across,
numerator by numerator and denominator by
denominator.
• If the answer can be simplified, then simplify it.
• Example: 2  9  2  9  18 2  9
5 2
52
10 2
• Example: 3  5  3 5  15
4 2
4 2
8
5
Equivalent Fractions
• Name the same amount but have
different numerators and
denominators.
1
2
1 = 2
2
4
1
4
1
4
Equivalent Fractions
•
Are sometimes called equal
fractions: two or more fractions that
name the same number.
1
2
1 = 2
2
4
1
4
1
4
Equivalent Fraction Models
1
2
=
2
4
=
3
6
40
Simplifying
10
4  10
=
1  10
Reduce
=
4
1
=
4
10 = Greatest Common Factor
Write the numerator and denominator as a product of factors, then
cancel common factors and obtain the result.
16
Simplifying
72
44
=
4  18
=
4
18
22
=
29
=
2
9
Write the numerator and denominator as a product of common factors
then cancel the common factors and obtain the result.
Repeat the simplification process until all common factors are removed.
Converting Mixed Numbers
1
5
3

+
=
16
3
Multiply the whole number by the denominator
Add the numerator to the result
Place over the initial denominator
Compute the final result
Converting Mixed Numbers
2
6
9

+
=
56
9
Multiply the whole number by the denominator
Add the numerator to the result
Place over the initial denominator
Compute the final result
Let’s think about what dividing fractions means.
3
4
:
1
8
=
?
In this expression it means
“How many one eighths are in three
fourths?”
For example, how many
one eighth slices of pizza
are in three fourths of a
pizza?
3
:
4
1
=
?
8
How many one eighths are in three fourths?
To find this we must first
find 3/4 of the pizza.
We then cut each fourth into
halves to make eighths.
We can see there are 6
eighths in three fourths.
3
4
:
1
8
=
6
EXAMPLE 1: How many one eighths are in one half?
1
2
:
1
8
=
?
Using a fraction
manipulative, we show
one half of a circle.
To find how many one eighths are in one half, we cover
the one half with eighths and count how many we use.
We find there are 4. There are four one eighths in one half.
1
2
:
1
8
=
4
Dividing Fractions
• When dividing fractions, they do NOT need to have a
common denominator.
• To divide two fractions, change the operation to
multiply and take the reciprocal of the second fraction
(flip the second fraction). Keep-Change-Change.
Change Operation.
2 9 2 2
  
5 2 5 9
Flip 2nd Fraction.
Dividing Fractions
• Finish the problem by following the rules for
multiplying fractions.
2 9 2 2
4
   
5 2 5 9 45
Ex) Divide.
Dividing Fractions
15 5

22 6
Ex) Divide.
Dividing Fractions
15 5

22 6
15 6


22 5
Ex) Divide.
Dividing Fractions
15 5

22 6
15 6


22 5
Invert and Multiply !
Ex) Divide.
Dividing Fractions
15 5

22 6
15 6


22 5
15 and 5 have a common factor.
Ex) Divide.
Dividing Fractions
15 5

22 6
15 6


22 5
Divide them both by 5.
Ex) Divide.
Dividing Fractions
15 5

22 6
15 6


22 5
3 6


22 1
Ex) Divide.
Dividing Fractions
15 5

22 6
15 6


22 5
3 6


22 1
22 and 6 have a common factor.
Ex) Divide.
Dividing Fractions
15 5

22 6
15 6


22 5
3 6


22 1
Divide them both by 2.
Ex) Divide.
Dividing Fractions
15 5

22 6
15 6


22 5
3 6


22 1
3 3
 
11 1
Divide them both by 2.
Ex) Divide.
Dividing Fractions
15 5

22 6
15 6


22 5
3 6


22 1
3 3
 
11 1
Ex) Divide.
Dividing Fractions
15 5

22 6
15 6


22 5
3 6


22 1
3 3 9
  
11 1 11
It is important to know how to
compute simple division of
fractions because...
• You will need to know it for 7th grade math!
• You will need it for the CST’s!
• Why else is it important?
What we’ve learned!
• How do you reduced fractions? Do you use
the LCM or the GCF?
• What does compute mean?
• What happens if you need to multiply or
divide fractions and the number is mixed?