Title: Fractions
1Fractions
Nancy Hughes Olathe District Schools
2Standards
 Seventh Grade
 N M7.1.4.K2d The student adds, subtracts,
multiplies, and divides fractions and expresses
answers in simplest form.  Eighth Grade
 M8.1.4.A1bThe student models, performs, and
explains computation with rational numbers, the
irrational number pi, and algebraic expressions
in a variety of situations.
3Vocabulary
 Addend
 Common denominators
 Denominator
 Dividend
 Division
 Equivalent fraction
 Fraction
 Improper fraction
 Least common denominator
 Lowest terms
 Minuend
 Mixed number
 Numerator
 Proper fraction
 Quotient
 Simplify
 Subtrahend
 Unit fraction
4Objectives
 Develop concepts of fractions and mixed numbers
 Use models to add, subtract, multiply and divide
fractions  Add, subtract, multiply, divide fractions and
mixed numbers
5Adding Fractions Using Fraction Circles
Pull out your fraction circles and sort them by
colors. The clear circle is the number 1 or 1
whole.
6Do the same with the fraction tiles. Sort them
by color.
1
7Adding Fractions Using Fraction Circles or
Fraction Tiles
Lets add
 Which colored circle or tile will you need to add
these fractions? Explain.  Because the fraction has a denominator of 4, find
the fraction piece that has been divided into
fourths.  Take the ¼ piece and add to it the piece.
8Adding Fractions Using Fraction Circles or Tiles
Use either fraction circles or tiles to model
Again, look at the denominator and choose your
tiles accordingly.
9Adding Fractions Using Fraction Circles or Tiles
Use either fraction circles or tiles to model
 Notice we do not have like denominators. This
makes it more of a challenge. Begin by taking
the ½ and the 1/3 and find tiles or circles that
are exactly the same size.  Did you find like tiles? Explain.
 If you found tiles or parts of a circle that have
a denominator of 6, you were correct.  Notice the ½ matches up with 3/6 and the 1/3
matches up with 2/6.
Now we can add!
10Adding Fractions Using fraction circles or tiles
Use either fraction circles or tiles to model
11You Try
Use your fraction circles or fraction tiles to
find
12Quick Review
Quick Review
Use two double number cubes for this activity.
The small number cube will be the numerator and
the larger number cube will be the denominator.
You will roll both number cubes, record the two
fractions from each number cube as fractions, and
then add.
Roll 1st Fraction 2nd Fraction Sum
1
2
3
4
5
13How to use your calculator to check!
Change to a fraction
Simplify
Mixed Number and Improper Fraction
Change to a decimal
Fraction bar
14Subtracting Fractions
 Visual approach using fraction tiles or fraction
circles
15Subtracting Fractions using fraction circles or
fraction tiles
 What is ? Again we will have to find
like denominators. Which sets of tiles or
circles will work? Explain.  If you guessed the 10ths you were right, 6/10
3/5

16Subtracting Fractions using fraction circles or
fraction tiles
 What is ? If you used fraction
circles, your work should be identical to the
fraction tiles.

17You Try Use fraction tiles or fraction circles
to show your answer.

or ¼

18Quick Review
Quick Review
Use two double number cubes for this activity.
The small number cube will be the numerator and
the larger number cube will be the denominator.
You will roll both number cubes, record the two
fractions from each number cube as fractions and
then subtract.
Roll 1st Fraction 2nd Fraction Difference
1
2
3
4
5
19Multiplying fractions
 Multiplying fractions is like finding what one
fraction is of another.
20Multiplying fractions
 For example, to find , we begin
with an area model. 
3/4
1
7
2
3
2/3
5
6
8
4
10
9
12
11
21Multiplying Fractions
 To simplify ,find the prime
factorization of 6 and 12.  Composite Prime Composite
Prime  6 2 12 2
 3 6 2
 3
6 2 3 1 12 2 2 3
2
22Multiplying fractions
¼
23Multiplying Fractions
To find the answer to ½ x 3/5, we will use
another model.
Show 3 out of 5
Show 1 out of 2
Shade the answer
24You try!
To find the answer to . Model your
answer.
Show 2 out of 3
Show 1 out of 5
Shade the answer
25Quick Review
Quick Review
Use two double number cubes for this activity.
The small number cube will be the numerator and
the larger number cube will be the denominator.
You will roll both number cubes, record the two
fractions from each number cube as fractions and
then multiply.
Roll 1st Fraction 2nd Fraction Product
1
2
3
4
5
26Dividing Fractions Fraction Tiles
Visualize how many ¼s will go into 5/8. Using
fraction tiles, visualize how many ¼s you can
place upon 5/8.
27Dividing Fractions Fraction Tiles
28You try! Use your fraction circles or tiles.
29Quick Review
Quick Review
Use two double number cubes for this activity.
The small number cube will be the numerator and
the larger number cube will be the denominator.
You will roll both number cubes, record the two
fractions from each number cube as fractions and
then divide.
Roll 1st Fraction 2nd Fraction Quotient
1
2
3
4
5
30Adding Fractions Using Arithmetic
Method 2 3 x5 15 2 x4 8 23 4
x5 20 5 x4 20 20
 Method 1
 3 x5 15
 4 x5 20
 2 x4 8
 5 x4 20
 23
 20
Method 3
31You try!
 Use one of the three methods to find
If you do not know the common denominator, find
the LCM.
Composite Prime
8 4 2 2 2
Composite Prime
3
2 2 2
3
LCM 2x2x2x324
32Subtracting Fractions Using Arithmetic
Method 2 3 x5 15  2 x4 8 7 4
x5 20 5 x4 20 20
 Method 1
 3 x5 15
 4 x5 20
 2 x4 8
 5 x4 20
 7
 20
Method 3
33You try!
 Use one of the three methods to find
If you do not know the common denominator, find
the LCM.
Composite Prime
12 6 2 2 3
Composite Prime
4 2 2
2 2
3
LCM 2x2x312
34Multiplying Fractions Using Arithmetic
Method 2
1
¼
Composite Prime
10 2 5
Composite Prime
40 20 20 2 2 2 5
4
35You Try!
 Use one of the two methods to multiply fractions.
36Dividing Fractions Using Arithmetic
Before you begin, change the problem to a
multiplication problem by using the reciprocal of
the fraction after the division sign.
Multiply the fractions.
37You try!
Before you begin, change the problem to a
multiplication problem by using the reciprocal of
the fraction after the division sign.
Multiply the fractions.
38Journaling
 Answer two of the following questions in your
journal  Explain how to add fractions using either
fraction circles or fraction tiles. Give
examples. Did the manipulatives help you
understand this operation? Explain.  Explain how to subtract fractions using either
fraction circles or fraction tiles. Give
examples. Did the manipulatives help you
understand this operation? Explain.  Explain how to multiply fractions using either
fraction circles or fraction tiles. Give
examples. Did the manipulatives help you
understand this operation? Explain.  Explain how to divide fractions using either
fraction circles or fraction tiles. Give
examples. Did the manipulatives help you
understand this operation? Explain.
39Practice Operations with Fractions
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