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Fourth Grade

Fraction Decimal Concepts

2015-11-23 www.njctl.org

Slide 3 / 162 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

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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?

1 2 3 4 5

Positive WHOLE Numbers

Click for Answer

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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 Numbers

Click 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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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:

• ne

half

• ne

quarter two thirds three fourths four fifths three eighths five tenths

• ne

sixths

Proper Fractions in Standard Form:

3 8 2 3 5 10 1 4 4 5 1 2 3 4 1 6

Slide to the right to reveal fractions in standard form.

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3 8 2 3 5 10 1 4 4 5 1 2 3 4 1 6

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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3 8 2 3 5 10 1 4 4 5 1 2 3 4 1 6

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Let's review what we know so far about fractions. 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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1 2 3 4 5 6 7 8 9 10 12 11

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.

• f the balls are

needed for practice.

Slide 17 / 162 Naming Fractions 2 3

top number = numerator bottom number = denominator

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1 Which number is the numerator in the fraction?

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2 Which number is the denominator in the fraction?

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3 Which fraction has a 5 in the denominator? A B C

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4 Which fraction has a 3 in the numerator? A B C

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5 What fraction of this set is blue?

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6 What fraction of this set is purple?

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7 What fraction of this set is red?

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Mixed Numbers

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Take out the following number of pattern blocks hexagon 1 trapezoid 9 rhombus 8 triangle 11

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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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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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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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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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14 If the triangle is , what is a trapezoid worth?

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15 If the triangle is , what is the hexagon worth?

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Fractions that are greater than one are

• ften 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

5 6 31

• 30

1

Quotient Divisor Remainder Then write in the form: quotient remainder divisor

click for mixed number

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To convert an improper fraction to a mixed number. First divide 30 by 4

7 4 30

• 28

2

Quotient Divisor Remainder Then write in the form: quotient remainder 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.

numerators denominators

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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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23 Which of the following is ordered greatest to least? A B C

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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

• f 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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25 Which of the following is ordered greatest to least? A B 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. 1 2 1

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26 Which fraction is closest to zero? A B C D

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27 Which fraction is closest to one? A B C D

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28 Which fraction is closest to a half? A B C D

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29 Which fraction is closest to one? A B C D

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30 Which fraction is closest to a half? A B C D

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31 Which fraction is closest to zero? A B C D

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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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33 Which of the following is ordered least to greatest? A B C

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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

Slide 73 / 162 Fraction Stick Chart Slide 74 / 162

34 Find an equivalent fraction for

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35 Find an equivalent fraction for

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36 Find an equivalent fraction for

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37 Find an equivalent fraction for

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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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39 Which number is larger? A B

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40 Which number is larger? A B

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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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42 What fraction of the whole is shaded?

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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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44 Is the shaded region the same in each of these? Yes No

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1 9 1 9 1 9

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?

Slide 90 / 162 Multiplication Rule

To find an equivalent fraction, multiply both the numerator and the denominator of the fraction by the same number.

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2 5 = ? ? Use the multiplication table to make equivalent fractions.

Pull

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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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46 What fractions are equivalent to ? A B C 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?

Slide 99 / 162 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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51 What is in simplified form?

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52 What is in simplified form?

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53 What is in simplified form?

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54 What is in simplified form?

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Converting Decimals to Fractions

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Slide 113 / 162 Converting a Decimal to a Fraction

• 1. 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 = Slide 116 / 162

62 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)

0.44 = Slide 117 / 162

63 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)

0.2 = Slide 118 / 162

64 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)

0.05 = Slide 119 / 162

65 What fraction is equivalent to the decimal below? (Be sure answer is in simplified form.)

0.33 = Slide 120 / 162

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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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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75 What is the fraction in decimal form?

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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 2 3 4 9 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. 0.42 0.45 0.48

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6.45 6.46 On the following number line, draw a line and move the decimals to their correct location. 6.452 6.458

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Label the numbers on the number line. 2 3

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Label the numbers on the number line.

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79

Where would the following number be correctly placed

• n the number line?

A B C D 9 10 9.5

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80

Where would the following number be correctly placed

• n the number line?

A B C D 5 6 5.5

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81

Where would the following number be correctly placed

• n the number line?

A B C D 2 3 2.5

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82

Where would the following number be correctly placed

• n the number line?

A B C D 1 0.5

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83

Where would the following number be correctly placed

• n the number line?

A B C D 1 0.5

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84

Where would the following number be correctly placed

• n the number line?

A B C D 1 0.5

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85

Where would the following number be correctly placed

• n the number line?

A B C D 2 1

Be careful of the scale of the number line!

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86

Where would the following number be correctly placed

• n the number line?

A B C D 2 1

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87

Where would the following number be correctly placed

• n the number line?

A B C D 2 1 3

Slide 157 / 162 Steps to Create Your Own Number Line

• 1. 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.

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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 1 2 1 2

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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.

1 2 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