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Fourth Grade
Fraction Decimal Concepts
2015-11-23
www.njctl.org
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Table of Contents
- Number Line Location
- Convert Decimals to Fractions- Convert Fractions to Decimals
Click on the topic to go to that section
- Understanding Fractions- Mixed Numbers- Compare and Order Fractions- Equivalent Fractions
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Understanding Fractions
click to return to table of contents
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1 02345678910 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
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Mr. Number Line is taking a short nap. He's a little tired from a long day of problem solving!
What type of numbers is he using to count sheep?
12 3
4 5
Positive WHOLE NumbersClick for Answer
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1 02345678910 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
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While napping, Mr. Number Line is dreaming of pepperoni pizza! What type of numbers would you
use to help Mr. Number Line count the total number of pizzas in his dream?
Fractions and/or Mixed NumbersClick for Answer
Talk to an elbow partner and share how you would count the pizzas.
How are fractions different from whole numbers?
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1 02345678910 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
##
While napping, Mr. Number Line is dreaming of pepperoni pizza! What type of numbers would you
use to help Mr. Number Line count the total number of pizzas in his dream?
Fractions and/or Mixed NumbersClick for Answer
Talk to an elbow partner and share how you would count the pizzas.
How are fractions different from whole numbers?
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Students could use one of the following strategies to count the halves.
Using only fractions: 1/2 2/2 3/2 4/2 5/2 6/2 7/2one half...two halves...three halves...
Using fractions and whole numbers: 1/2 1 3/2 2 5/2 3 7/2one half.... one....three halves....two....
Using fractions, whole numbers and mixed numbers:
1 1 2 2 3 3
one half....one....one and one half....two.....
Great way to go over difference between whole numbers, fractions and mixed numbers.
12
12
12
12
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Fractions represent what is BETWEEN whole numbers. A fraction is a PART of a WHOLE.
The first fractions we will learn about are PROPER FRACTIONS. Examples of proper fractions are shown below in word form:
one
half
one
quarter
two
thirds
three
fourths
four
fifths
three
eighths
five
tenths
one
sixths
Proper Fractions in Standard Form: 38
23
510
14
45
12
34
16
Slide to the right to reveal fractions in standard form.
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Fractions represent what is BETWEEN whole numbers. A fraction is a PART of a WHOLE.
The first fractions we will learn about are PROPER FRACTIONS. Examples of proper fractions are shown below in word form:
one
half
one
quarter
two
thirds
three
fourths
four
fifths
three
eighths
five
tenths
one
sixths
Proper Fractions in Standard Form: 38
23
510
14
45
12
34
16
Slide to the right to reveal fractions in standard form.
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Students may need to review standard form. Practice with the 8 fractions on this slide. Have students explain how a fraction is written in standard form. If important
vocabulary (numerator and denominator) does not come easily, the slides that follow will go over these terms. The most important thing is that students know that standard
form is the typical way we see fractions. A number on top and a number on the bottom and a line segment in
between. By the way this line segment is called the vinculum or fraction bar.
IMPORTANT: The word document "Proper Fraction - Flash Cards" contains the 8 fractions on this slide plus eight additional proper fractions. Students can work in groups to write the standard form on each flash card.
Once students cut out these flash cards, they can write "Proper Fraction" on the blank side.
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38
23
510
14
45
12
34
16
Let's look at the 8 proper fractions we discussed on the previous slide.
Talk to an elbow partner and share what you know about these proper fractions. Write down any important ideas you discuss with
your partner so that you can share these ideas with the whole class.
We will organize our ideas on the next slide.
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38
23
510
14
45
12
34
16
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Let's review what we know so far about fractions.
0 1 2
{1. All Proper Fractions can be found between 0 and 1 on a number line.
Proper Fractions
2. Whole numbers are the first types of numbers we learn about. Whole numbers are found in the real world, but fractions are used much more frequently.
Brainstorm with a partner where we can find fractions in the real world.
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123
4567
8910
1211
1/4c
1/2c
3/4c
1c
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Let's review some important vocabulary to help us better understand fractions. Noomy the Numerator and Deeno the
Denominator are here to help us.
Noomy the numerator represents the top part of a fraction.
He shows the PART of the fraction that we are looking at.
PART and Purple both start with P.
Deeno the denominator represents the bottom of a fraction.
He shows the WHOLE (or ONE) that we are looking at.
ONE and Orange both start with O.
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Every fraction is division and every division problem can be shown as a fraction. Even the division sign looks like a fraction.
Click on the top part of the division sign.
Click on the bottom part of the division sign.
NUMERATOR
DENOMINATOR
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Fractions can be used to name a part of a whole object.
You ate of the pie.
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Fractions can also be used to name a part of a collection of objects.
of the balls are
needed for practice.
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Naming Fractions
23
top number = numeratorbottom number = denominator
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1 Which number is the numerator in the fraction?
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1 Which number is the numerator in the fraction?
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2
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2 Which number is the denominator in the fraction?
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2 Which number is the denominator in the fraction?
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7
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3 Which fraction has a 5 in the denominator?
A
B
C
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3 Which fraction has a 5 in the denominator?
A
B
C
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C
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4 Which fraction has a 3 in the numerator?
A
B
C
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4 Which fraction has a 3 in the numerator?
A
B
C
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Ans
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A
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5 What fraction of this set is blue?
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5 What fraction of this set is blue?
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37
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6 What fraction of this set is purple?
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6 What fraction of this set is purple?
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25
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7 What fraction of this set is red?
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7 What fraction of this set is red?
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36
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Mixed Numbers
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Take out the following number of pattern blocks
hexagon1
trapezoid9
rhombus
8
triangle11
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If a hexagon is worth 1, what are 3 trapezoids worth?
click for answer
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If a hexagon is worth 1, what are 4 rhombi worth?click for answer
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8 If a hexagon is worth 1, what are 5 triangles worth?
click for answer
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8 If a hexagon is worth 1, what are 5 triangles worth?
click for answer
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9 If a hexagon is worth 1, what are 5 trapezoids worth?
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9 If a hexagon is worth 1, what are 5 trapezoids worth?
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10 If a hexagon is worth 1, what are 8 rhombi worth?
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10 If a hexagon is worth 1, what are 8 rhombi worth?
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11 If a hexagon is worth 1, what are 11 triangles worth?
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11 If a hexagon is worth 1, what are 11 triangles worth?
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12 If a hexagon is worth 1, what are 9 trapezoids worth?
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12 If a hexagon is worth 1, what are 9 trapezoids worth?
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Sometimes the hexagon is not worth one.
What do we do if a unit other than one is given?
First figure out what one is worth, then solve the problem.click
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13 If the triangle is , what shape is ONE?
A hexagon B rhombus C trapezoid
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13 If the triangle is , what shape is ONE?
A hexagon B rhombus C trapezoid
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B
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14 If the triangle is , what is a trapezoid worth?
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14 If the triangle is , what is a trapezoid worth?
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34
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15 If the triangle is , what is the hexagon worth?
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15 If the triangle is , what is the hexagon worth?
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64
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Fractions that are greater than one are often called improper fractions, even
though there is nothing improper about them.
Improper Fraction Mixed Number
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A mixed number is a number that has a whole part and a fractional part.
For example: 6 is the whole part is the fractional part
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To convert an improper fraction to a mixed number.
First divide 31 by 6
56 31 -30 1
QuotientDivisor
Remainder
Then write in the form:
quotient remainderdivisor
click for mixed number
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To convert an improper fraction to a mixed number.
First divide 30 by 4
74 30 -28 2
QuotientDivisor
Remainder
Then write in the form:
quotientremainder
divisor
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Match the Mixed Numbers and Improper Fractions.
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Compare and Order Fractions
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The first step when comparing fractions is to look at the numerators and denominators.
numeratorsdenominators
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When the denominators are the same:
- the unit fractions are the same size- only need to compare the number of pieces ###
(numerators) need to be compared
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Reorder the following fractions from least to greatest.
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22 Which of the following is ordered least to greatest?
A B C
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22 Which of the following is ordered least to greatest?
A B C
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B
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23 Which of the following is ordered greatest to least?
A B C
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23 Which of the following is ordered greatest to least?
A B C
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A
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When the numerators are the same:
- there are the same number of pieces- compare the size of the denominator
The smaller the denominator, the larger the size of
each piece.
The larger the denominator, the smaller the size of each piece.
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Reorder the following fractions from least to greatest.
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24 Which of the following is ordered least to greatest?
A B C
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24 Which of the following is ordered least to greatest?
A B C
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B
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25 Which of the following is ordered greatest to least?
A B C
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25 Which of the following is ordered greatest to least?
A B C
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C
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If numerators and denominators are not the same, we need to use other methods to compare fractions.
Use benchmarks to see if the fraction is close to 0, 1/2, or 1 and then order them.
012 1
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26 Which fraction is closest to zero?
A
B
C
D
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26 Which fraction is closest to zero?
A
B
C
D
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B
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27 Which fraction is closest to one?
A
B
C
D
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27 Which fraction is closest to one?
A
B
C
D
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A
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28 Which fraction is closest to a half?
A
B
C
D
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28 Which fraction is closest to a half?
A
B
C
D
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C
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29 Which fraction is closest to one?
A
B
C
D
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29 Which fraction is closest to one?
A
B
C
D
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D
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30 Which fraction is closest to a half?
A
B
C
D
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30 Which fraction is closest to a half?
A
B
C
D
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A
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31 Which fraction is closest to zero?
A
B
C
D
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31 Which fraction is closest to zero?
A
B
C
D
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C
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Use benchmarks of 0, 1/2 and 1 to order the fractions least to greatest.
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Use benchmarks of 0, 1/2 and 1 to order the fractions least to greatest.
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32 Which of the following is ordered least to greatest?
A B C
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32 Which of the following is ordered least to greatest?
A B C
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A
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33 Which of the following is ordered least to greatest?
A B C
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33 Which of the following is ordered least to greatest?
A B C
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B
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If the previous strategies don't work to compare fractions, we need to find
equivalent fractions in order to compare them.
Equivalent Fractions
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Click below to use this interactive number line.
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A fraction stick is a model for the whole, or ONE.
Use it to find equivalent fractions.
Find equivalent fractions for
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Fraction Stick Chart
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Fraction Stick Chart
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Teac
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fraction stick chart or use manipulatives as shown here to aide students in their understanding of equivalent fractions.
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34 Find an equivalent fraction for
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34 Find an equivalent fraction for
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6/8, 9/12, etc.
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35 Find an equivalent fraction for
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35 Find an equivalent fraction for
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16/32, 24/48, etc.
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36 Find an equivalent fraction for
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36 Find an equivalent fraction for
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1 2/6, 1 3/9, etc.
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37 Find an equivalent fraction for
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37 Find an equivalent fraction for
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14/12, 21/18, etc.
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A fraction stick is a model for the whole, or ONE.
Use it to compare fractions.
Which number is larger? or
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38 Which number is larger?
A B
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38 Which number is larger?
A B
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B
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39 Which number is larger?
A B
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39 Which number is larger?
A B
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B
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40 Which number is larger?
A B
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40 Which number is larger?
A B
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nsw
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A
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Splitting Fractions Sticks to Make Equivalent Fractions
What fraction of the whole is shaded?
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If a horizontal line is drawn to divide each part of the rectangle into 2 parts, what fraction of the whole is shaded?
Has the shaded amount of the rectangle changed?
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41 What fraction of the whole is shaded now?
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41 What fraction of the whole is shaded now?
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412
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42 What fraction of the whole is shaded?
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42 What fraction of the whole is shaded?
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14
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43 Use these two horizontal lines to divide the whole.
What fraction of the whole is shaded now?
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43 Use these two horizontal lines to divide the whole.
What fraction of the whole is shaded now?
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312
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44 Is the shaded region the same in each of these?
Yes No
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44 Is the shaded region the same in each of these?
Yes No
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Yes
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19
19
19
What do you notice about the denominators in each set of equivalent fractions?
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What patterns have you noticed in the previous examples about making equivalent fractions?
What important idea do we know about multiplying by 1?
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Multiplication RuleTo find an equivalent fraction, multiply both the
numerator and the denominator of the fraction by the same number.
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25
= ??
Use the multiplication table to make equivalent fractions.Pu
ll
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25
= ??
Use the multiplication table to make equivalent fractions.
Pull
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Teac
her N
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equivalent to 2/5, move the fraction
circle along the strips between 2 and 5.
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Find three equivalent fractions.
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45 Which two fractions are equivalent to ?
A B C D
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45 Which two fractions are equivalent to ?
A B C D
[This object is a pull tab]A
nsw
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B & D
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46 What fractions are equivalent to ?
A B C D
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46 What fractions are equivalent to ?
A B C D
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D
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48 What is a fraction equivalent to ?
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49 What is a fraction equivalent to ?
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What important idea to we know about dividing by 1?
How can we use division to find equivalent fractions?
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Steps to Simplifying Fractions
1. Find the GCF of both numbers.2. Divide the numerator and denominator by that number.
3. Answer will be the fraction in simplified form.
GCF = 2
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50 What is in simplified form?
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50 What is in simplified form?
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1/3
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51 What is in simplified form?
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51 What is in simplified form?
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1/2
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52 What is in simplified form?
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52 What is in simplified form?
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1/2
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53 What is in simplified form?
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53 What is in simplified form?
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1/5
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54 What is in simplified form?
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54 What is in simplified form?
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1/8
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Converting Decimals to Fractions
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Converting a Decimal to a Fraction1. Put the digits in the numerator.
2. The denominator represents the place value.3. Simplify fraction if you can.
Example:
0.9 =
0.25 =
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Match the following decimals with their fraction equivalents.
0.6 =
0.3 =
0.06 =
0.03 =
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61 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)
0.7 =
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62 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)
0.44 =
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63 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)
0.2 =
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64 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)
0.05 =
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65 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)
0.33 =
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Converting Fractions to Decimals
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Converting fractions to decimal form by changing the denominator.
Steps:1. Use mental math, the multiplication rule or the division rule to
change each fraction to an equivalent fraction having a denominator of 10 or 100.
2. Write the new fraction as a decimal.
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Examples:
x 4
x 4
x 5
x 5
6
6_
_
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68 What is the fraction in decimal form?
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68 What is the fraction in decimal form?
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0.2
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Convert the following fractions to decimals.
When you can not make an equivalent fraction with a denominator of 10 or 100, then you must divide to find the decimal equivalent.
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74 What is the fraction in decimal form?
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74 What is the fraction in decimal form?
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0.625
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75 What is the fraction in decimal form?
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75 What is the fraction in decimal form?
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0.125
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3 1
Notice what happens with this division.This is called a repeating decimal and it is written as
0.3 and is read as point three repeating.
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Use a calculator to convert these fractions to decimals to see the repeating pattern.
fraction calculator display decimal
23
49
5 12
4 11
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Number Line Location
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0.4 0.5
On the following number line, draw a line and move the decimals to their correct location.
0.420.45
0.48
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0.4 0.5
On the following number line, draw a line and move the decimals to their correct location.
0.420.45
0.48
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Steps:1. Divide the number line into smaller parts using tick marks.2. Compare the decimals and place them correctly.
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6.45 6.46
On the following number line, draw a line and move the decimals to their correct location.
6.4526.458
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6.45 6.46
On the following number line, draw a line and move the decimals to their correct location.
6.4526.458
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Steps:1. Divide the number line
into smaller parts using tick marks.
2. Compare the decimals and place them correctly.
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Label the numbers on the number line.
2 3
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Label the numbers on the number line.
2 3
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Steps:1. Convert numbers to same form. 2. Divide the number line into smaller parts using tick marks.2. Compare the numbers and place them correctly.
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Label the numbers on the number line.
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Label the numbers on the number line.
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Steps:1. Convert numbers to same
form. 2. Divide the number line into smaller parts using tick marks.2. Compare the numbers and
place them correctly.
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79 Where would the following number be correctly placed on the number line?
A B C D
9 109.5
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79 Where would the following number be correctly placed on the number line?
A B C D
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C
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80 Where would the following number be correctly placed on the number line?
A B C D
5 65.5
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80 Where would the following number be correctly placed on the number line?
A B C D
5 65.5
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A
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81 Where would the following number be correctly placed on the number line?
A B C D
2 32.5
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81 Where would the following number be correctly placed on the number line?
A B C D
2 32.5
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C
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82 Where would the following number be correctly placed on the number line?
A B C D
0 10.5
Slide 151 (Answer) / 162
82 Where would the following number be correctly placed on the number line?
A B C D
0 10.5
[This object is a pull tab]
Ans
wer
B
Slide 152 / 162
83 Where would the following number be correctly placed on the number line?
A B C D
0 10.5
Slide 152 (Answer) / 162
83 Where would the following number be correctly placed on the number line?
A B C D
0 10.5
[This object is a pull tab]
Ans
wer
C
Slide 153 / 162
84 Where would the following number be correctly placed on the number line?
A B C D
0 10.5
Slide 153 (Answer) / 162
84 Where would the following number be correctly placed on the number line?
A B C D
0 10.5
[This object is a pull tab]
Ans
wer
C
Slide 154 / 162
85 Where would the following number be correctly placed on the number line?
A B C D
0 21
Be careful of the scale of the number line!
Slide 154 (Answer) / 162
85 Where would the following number be correctly placed on the number line?
A B C D
0 21
Be careful of the scale of the number line!
[This object is a pull tab]
Ans
wer
C
Slide 155 / 162
86 Where would the following number be correctly placed on the number line?
A B C D
0 21
Slide 155 (Answer) / 162
86 Where would the following number be correctly placed on the number line?
A B C D
0 21
[This object is a pull tab]
Ans
wer
A
Slide 156 / 162
87 Where would the following number be correctly placed on the number line?
A B C D
0 21 3
Slide 156 (Answer) / 162
87 Where would the following number be correctly placed on the number line?
A B C D
0 21 3
[This object is a pull tab]
Ans
wer
C
Slide 157 / 162
Steps to Create Your Own Number Line1. Convert numbers all to the same form.
2. Order the numbers to determine the range of numbers you need to include.
3. Draw a number line and divide it into equal size pieces.
4. Put a dot and label each number.
Slide 158 / 162
Example:Plot and label the numbers in the box on a number line.
1. Convert numbers all to the same form. In this case, all to decimal will be the easiest.
1.5, 0.75, 0.2, 1.2, 0.45
2. Order the numbers to determine the range of numbers you need to include. 0.2, 0.45, 0.75, 1.2, 1.5
We need a number line from 0 to 2
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3. Draw a number line and divide it into equal size pieces. Label 0, 1 and 2 Divide in between the whole numbers into tenths.
4. Put a dot and label each number.
.2 .45 .75 1.2 1.5
0 1 2
0 1 2
Slide 160 / 162
Example:Plot and label the numbers in the box on a number line.
1. Convert numbers all to the same form. In this case, all to decimal will be the easiest.
1.2, 0.6, 0.4, 1.8, 1
2. Order the numbers to determine the range of numbers you need to include.
0.4, 0.6, 1, 1.2, 1.8 We need a number line from 0 to 2
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3. Draw a number line and divide it into equal size pieces. Label 0, 1 and 2 Divide in between the whole numbers into two-tenths.
4. Put a dot and label each number.
0 1 2
0 1 2.4 .6 1.2 1.8
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Plot and label the following sets of numbers on a number line. Make a separate number line for each set.
Set 1 Set 2 Set 3