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FRACTIONS

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Title: FRACTIONS Author: CITT Last modified by: Misty Butterfield Created Date: 9/13/2007 5:40:54 PM Document presentation format: On-screen Show (4:3) – PowerPoint PPT presentation

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Title: FRACTIONS


1
View Curriculum Standards
Im ready to learn about fractions!
2
FRACTIONS
Basic Fractions
Comparing Fractions
Adding Fractions
Subtracting Fractions
Fraction Fun!
What are fractions?
3
What are fractions?
  • Fractions are for counting PART of something
  • The denominator tells us how many pieces
    something is cut into.
  • The numerator tells how many fractional pieces
    there are

4
Basic Fractions
  • A fraction is part of an entire object.

1/4 is pink
1/2 is pink
3/4 is pink
4/4 or one whole is pink
5
Comparing Fractions
  • If the denominators of two fractions are the
    same, the fraction with the largest numerator is
    the larger fraction.
  • For example
  • 5/8 is larger than 3/8
  • all of the pieces are the same and
  • five pieces are more than three pieces.

Comparing, cont.
6
Comparing Fractions, cont.
  • If the numerators of two fractions are the same,
    the fraction with the smaller denominator is the
    larger fraction.
  • For example
  • 5/8 is larger than 5/16
  • Each fraction says there are five pieces. If an
    object is divided into 8 pieces, each piece will
    be larger than if the object were split into 16
    pieces. Therefore five larger pieces are more
    than five smaller pieces.

7
Adding Fractions
  • Adding fractions with COMMON
  • denominators is simple.
  • Just add the numerators together, and place the
    resulting answer in the top of a fraction and use
    the existing denominator for the bottom number.
    Then reduce the fraction, if possible
  • For example
  • 3/8  2/8  5/8

Adding, cont.
8
Adding Fractions
  • You can only add together fractions that have the
    same denominator, so you must first change one or
    both of the fractions so that you end up with two
    fractions having a common denominator.
  • The easiest way to do this, is to simply select
    the opposite fraction's denominator to use as a
    top and bottom multiplier.
  • Please look at the example on the next page

Adding, cont.
9
Adding Fractions
  • Example
  • You have the fractions 2/3 and 1/4
  • Select the denominator of the second fraction
    (4) and multiply the top and bottom of the first
    fraction (2/3) by that number
  • 4/4 x 2/3 8/12
  • Select the denominator of the first fraction (3)
    and multiply the top and bottom of the second
    fraction (1/4) by that number
  • 3/3 x 1/4 3/12
  • These two fractions (8/12 and 3/12) have common
    denominators - the number 12 on the bottom of the
    fraction.
  • Add these two new fractions together
  • 8/12 3/12 11/12

10
Subtracting Fractions
To subtract two fractions with the same
denominator, subtract the numerators and place
that difference over the common denominator.
Look at a pizza cut into 8 pieces. Each piece is
1/8 of the pizza. Here we have 7 pieces or 7/8
of the pizza. Now take away 3/8 or 3
pieces. Were left with 4 pieces!
We just subtracted the numerators!
Subtracting, cont.
11
Subtracting Fractions
  • To Subtract Fractions with different
    denominators
  • Find the Lowest Common Denominator (LCD) of
    the fractions
  • Rename the fractions to have the LCD
  • Subtract the numerators of the fractions
  • The difference will be the numerator and the LCD
    will be
  • the denominator of the answer.
  • Simplify the Fraction

Click here to learn more about the LCD
12
LCD
  • To find the least common denominator, list the
    multiples of each denominator (multiply by 2, 3,
    4, etc.) then look for the smallest number that
    appears in each list.
  • Example Suppose we wanted to add 1/5 1/6. We
    would find the least common denominator as
    follows...
  • First list the multiples of each denominator.
  • Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,...
  • Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...
  • Now, when you look at the list of multiples, you
    can see that 30 is the smallest number that
    appears in each list.
  • Therefore, the least common denominator of 1/5
    and 1/6 is 30.

LCD, cont.
13
LCD
For more LCD help click here!
14
Fraction Fun!
If you eat 2 pieces of this pizza and your friend
eats 1 how many 10ths did you eat altogether?
If you eat 1/4 of this pizza how much will be
left?
Answer
15
Fraction Fun!
All the children are going to share the pizza. We
will cut enough pieces so each child can have
one, and the pieces should all be the same
size. If 7 children shared the pizza equally,
what fraction of the pizza did each child get?
Answer
16
Fraction Fun!
1. What fraction of the circle is shaded green?
2. What fraction of the circle is shaded red?
  1. What fraction would you write for the color RED?
  2. What fraction would you write for the color
    green?

Answers
17
3/4 left
3/10 eaten
More Fun!
Back to Question
18
  • 1/7

More Fun!
Back to Question
19
  1. 4/6 or 2/3
  2. 2/3
  3. 3/8
  4. 1/8

Back to Question
20
Concept Map
21
2005 Connecticut Mathematics Curriculum Framework
  • Numerical and Proportional Reasoning
    Quantitative relationships can be expressed
    numerically in multiple ways in order to make
    connections and simplify calculations using a
    variety of strategies, tools and technologies.
  • How are quantitative relationships represented by
    numbers?

Standards 2.1 and 2.2
22
  • Grade 3
  • 2.1
  • Students should understand that a variety of
    numerical representations can be used to describe
    quantitative relationships.
  • a. Represent numbers in expanded and regrouped
    forms in the base ten place value system.
  • b. Recognize that a fraction with the same
    numerator and denominator represents the whole
    object or an entire set.
  • c. Use fractions to measure and to represent
    points on a ruler or number line.
  • 2.2
  • Students should use numbers and their properties
    to compute flexibly and fluently, and to
    reasonably estimate measures and quantities
  • a. Use strategies that involve place value
    patterns and algebraic properties to estimate,
    add and subtract.
  • b. Approximate solutions to problems involving
    computation through the use of efficient methods.
  • c. Solve multiplication and division problems
    using rectangular arrays, number patterns, skip
    counting and repeated addends.
  • d. Compare fractions, identify equivalent
    fractions, add and subtract fractions with like
    and unlike denominators using models and
    pictures.

23
Works Cited
  • http//www.mathleague.com/help/fractions/fractions
    .htmwhatisafraction
  • http//www.coolmath4kids.com/fractions/index.html
  • http//math.rice.edu/lanius/fractions/index.html
  • http//www.coolmath4kids.com/fractions/fractions-1
    0-adding-with-like-denominators-01.html
  • http//www.superkids.com/aweb/tools/math/fraction/
    commond/add.shtml
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