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Fractions

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Title: Fractions


1
Fractions
Nancy Hughes Olathe District Schools
2
Standards
  • 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.

3
Vocabulary
  • 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

4
Objectives
  • Develop concepts of fractions and mixed numbers
  • Use models to add, subtract, multiply and divide
    fractions
  • Add, subtract, multiply, divide fractions and
    mixed numbers

5
Adding Fractions Using Fraction Circles
Pull out your fraction circles and sort them by
colors. The clear circle is the number 1 or 1
whole.
6
Do the same with the fraction tiles. Sort them
by color.
1
7
Adding 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.





8
Adding Fractions Using Fraction Circles or Tiles
Use either fraction circles or tiles to model
Again, look at the denominator and choose your
tiles accordingly.




9
Adding 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!
10
Adding Fractions Using fraction circles or tiles
Use either fraction circles or tiles to model




11
You Try
Use your fraction circles or fraction tiles to
find




12
Quick 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
13
How to use your calculator to check!
Change to a fraction
Simplify
Mixed Number and Improper Fraction
Change to a decimal
Fraction bar
14
Subtracting Fractions
  • Visual approach using fraction tiles or fraction
    circles

15
Subtracting 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

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


-
17
You Try Use fraction tiles or fraction circles
to show your answer.
  • What is ?



-
or ¼
-

18
Quick 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
19
Multiplying fractions
  • Multiplying fractions is like finding what one
    fraction is of another.

20
Multiplying 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
21
Multiplying 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
22
Multiplying fractions
  • What is?

¼





23
Multiplying 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
24
You try!
To find the answer to . Model your
answer.





Show 2 out of 3
Show 1 out of 5
Shade the answer
25
Quick 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
26
Dividing Fractions Fraction Tiles
  • Find

Visualize how many ¼s will go into 5/8. Using
fraction tiles, visualize how many ¼s you can
place upon 5/8.
27
Dividing Fractions Fraction Tiles
  • Find

28
You try! Use your fraction circles or tiles.
  • Find

29
Quick 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
30
Adding 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
31
You 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
32
Subtracting 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
33
You 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
34
Multiplying Fractions Using Arithmetic
Method 2
  • Method 1

1
¼
Composite Prime
10 2 5
Composite Prime
40 20 20 2 2 2 5
4
35
You Try!
  • Use one of the two methods to multiply fractions.

36
Dividing Fractions Using Arithmetic
  • Divide the following

Before you begin, change the problem to a
multiplication problem by using the reciprocal of
the fraction after the division sign.
Multiply the fractions.
37
You try!
  • Divide the following

Before you begin, change the problem to a
multiplication problem by using the reciprocal of
the fraction after the division sign.
Multiply the fractions.
38
Journaling
  • 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.

39
Practice Operations with Fractions
40
  • What is the value of.. ?

41
  • What is the value of.. ?

42
  • What is the value of.. ?

43
  • What is the value of.. ?

44
  • What is the value of.. ?

45
  • What is the value of.. ?

46
  • What is the value of.. ?

47
  • What is the value of.. ?

48
  • What is the value of.. ?

49
  • What is the value of.. ?

50
  • What is the value of.. ?

51
  • What is the value of.. ?

52
  • What is the value of.. ?

53
  • What is the value of.. ?

54
  • What is the value of.. ?

55
  • What is the value of.. ?

56
  • What is the value of.. ?

57
  • What is the value of.. ?

58
  • What is the value of.. ?

59
  • What is the value of.. ?
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