Slide 1 / 162 Slide 2 / 162

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

Slide 4 / 162

Understanding Fractions

click to return to table of contents

Slide 5 / 162

1 02345678910 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

##

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

Slide 6 / 162

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?

Slide 7 / 162

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.

Slide 8 / 162

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.

Slide 9 / 162

38

23

510

14

45

12

34

16

Slide 10 / 162

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.

Slide 11 / 162 Slide 12 / 162

123

4567

8910

1211

1/4c

1/2c

3/4c

1c

Slide 13 / 162

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.

Slide 14 / 162

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

Slide 15 / 162

Fractions can be used to name a part of a whole object.

You ate of the pie.

Slide 16 / 162

Fractions can also be used to name a part of a collection of objects.

of the balls are

needed for practice.

Slide 17 / 162

Naming Fractions

23

top number = numeratorbottom number = denominator

Slide 18 / 162

1 Which number is the numerator in the fraction?

Slide 19 / 162

2 Which number is the denominator in the fraction?

Slide 20 / 162

3 Which fraction has a 5 in the denominator?

A

B

C

Slide 21 / 162

4 Which fraction has a 3 in the numerator?

A

B

C

Slide 22 / 162

5 What fraction of this set is blue?

Slide 23 / 162

6 What fraction of this set is purple?

Slide 24 / 162

7 What fraction of this set is red?

Slide 25 / 162

Mixed Numbers

click to return to table of contents

Slide 26 / 162

Take out the following number of pattern blocks

hexagon1

trapezoid9

rhombus

8

triangle11

Slide 27 / 162

If a hexagon is worth 1, what are 3 trapezoids worth?

click for answer

Slide 28 / 162

If a hexagon is worth 1, what are 4 rhombi worth?click for answer

Slide 29 / 162

8 If a hexagon is worth 1, what are 5 triangles worth?

click for answer

Slide 30 / 162

9 If a hexagon is worth 1, what are 5 trapezoids worth?

Slide 31 / 162

10 If a hexagon is worth 1, what are 8 rhombi worth?

Slide 32 / 162

11 If a hexagon is worth 1, what are 11 triangles worth?

Slide 33 / 162

12 If a hexagon is worth 1, what are 9 trapezoids worth?

Slide 34 / 162

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

Slide 35 / 162

13 If the triangle is , what shape is ONE?

A hexagon B rhombus C trapezoid

Slide 36 / 162

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

Slide 37 / 162

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

Slide 38 / 162

Fractions that are greater than one are often called improper fractions, even

though there is nothing improper about them.

Improper Fraction Mixed Number

Slide 39 / 162

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

Slide 40 / 162

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

Slide 41 / 162

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

Slide 42 / 162

Match the Mixed Numbers and Improper Fractions.

Slide 43 / 162 Slide 44 / 162

Slide 45 / 162 Slide 46 / 162

Slide 47 / 162 Slide 48 / 162

Slide 49 / 162

Compare and Order Fractions

click to return to table of contents

Slide 50 / 162

The first step when comparing fractions is to look at the numerators and denominators.

numeratorsdenominators

Slide 51 / 162

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

Slide 52 / 162

Reorder the following fractions from least to greatest.

Slide 53 / 162

22 Which of the following is ordered least to greatest?

A B C

Slide 54 / 162

23 Which of the following is ordered greatest to least?

A B C

Slide 55 / 162

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.

Slide 56 / 162

Reorder the following fractions from least to greatest.

Slide 57 / 162

24 Which of the following is ordered least to greatest?

A B C

Slide 58 / 162

25 Which of the following is ordered greatest to least?

A B C

Slide 59 / 162

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

Slide 60 / 162

26 Which fraction is closest to zero?

A

B

C

D

Slide 61 / 162

27 Which fraction is closest to one?

A

B

C

D

Slide 62 / 162

28 Which fraction is closest to a half?

A

B

C

D

Slide 63 / 162

29 Which fraction is closest to one?

A

B

C

D

Slide 64 / 162

30 Which fraction is closest to a half?

A

B

C

D

Slide 65 / 162

31 Which fraction is closest to zero?

A

B

C

D

Slide 66 / 162

Use benchmarks of 0, 1/2 and 1 to order the fractions least to greatest.

Slide 67 / 162

Use benchmarks of 0, 1/2 and 1 to order the fractions least to greatest.

Slide 68 / 162

32 Which of the following is ordered least to greatest?

A B C

Slide 69 / 162

33 Which of the following is ordered least to greatest?

A B C

Slide 70 / 162

If the previous strategies don't work to compare fractions, we need to find

equivalent fractions in order to compare them.

Equivalent Fractions

click to return to table of contents

Slide 71 / 162

Click below to use this interactive number line.

Slide 72 / 162

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

Slide 75 / 162

35 Find an equivalent fraction for

Slide 76 / 162

36 Find an equivalent fraction for

Slide 77 / 162

37 Find an equivalent fraction for

Slide 78 / 162

A fraction stick is a model for the whole, or ONE.

Use it to compare fractions.

Which number is larger? or

Slide 79 / 162

38 Which number is larger?

A B

Slide 80 / 162

39 Which number is larger?

A B

Slide 81 / 162

40 Which number is larger?

A B

Slide 82 / 162

Splitting Fractions Sticks to Make Equivalent Fractions

What fraction of the whole is shaded?

Slide 83 / 162

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?

Slide 84 / 162

41 What fraction of the whole is shaded now?

Slide 85 / 162

42 What fraction of the whole is shaded?

Slide 86 / 162

43 Use these two horizontal lines to divide the whole.

What fraction of the whole is shaded now?

Slide 87 / 162

44 Is the shaded region the same in each of these?

Yes No

Slide 88 / 162

19

19

19

What do you notice about the denominators in each set of equivalent fractions?

Slide 89 / 162

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 RuleTo find an equivalent fraction, multiply both the

numerator and the denominator of the fraction by the same number.

Slide 91 / 162

25

= ??

Use the multiplication table to make equivalent fractions.

Pull

Slide 92 / 162

Find three equivalent fractions.

Slide 93 / 162

45 Which two fractions are equivalent to ?

A B C D

Slide 94 / 162

46 What fractions are equivalent to ?

A B C D

Slide 95 / 162 Slide 96 / 162

48 What is a fraction equivalent to ?

Slide 97 / 162

49 What is a fraction equivalent to ?

Slide 98 / 162

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

Slide 100 / 162

Slide 101 / 162

50 What is in simplified form?

Slide 102 / 162

51 What is in simplified form?

Slide 103 / 162

52 What is in simplified form?

Slide 104 / 162

53 What is in simplified form?

Slide 105 / 162

54 What is in simplified form?

Slide 106 / 162

Slide 107 / 162 Slide 108 / 162

Slide 109 / 162 Slide 110 / 162

Slide 111 / 162 Slide 112 / 162

Converting Decimals to Fractions

click to return to table of contents

Slide 113 / 162

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 =

Slide 114 / 162

Match the following decimals with their fraction equivalents.

0.6 =

0.3 =

0.06 =

0.03 =

Slide 115 / 162

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

click to return to table of contents

Slide 121 / 162

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.

Slide 122 / 162

Examples:

x 4

x 4

x 5

x 5

6

6_

_

Slide 123 / 162 Slide 124 / 162

Slide 125 / 162 Slide 126 / 162

Slide 127 / 162

68 What is the fraction in decimal form?

Slide 128 / 162

Slide 129 / 162 Slide 130 / 162

Slide 131 / 162 Slide 132 / 162

Slide 133 / 162

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.

Slide 134 / 162

Slide 135 / 162 Slide 136 / 162

74 What is the fraction in decimal form?

Slide 137 / 162

75 What is the fraction in decimal form?

Slide 138 / 162

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.

Slide 139 / 162

Use a calculator to convert these fractions to decimals to see the repeating pattern.

fraction calculator display decimal

23

49

5 12

4 11

Slide 140 / 162

Slide 141 / 162 Slide 142 / 162

Slide 143 / 162

Number Line Location

click to return to table of contents

Slide 144 / 162

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

Slide 145 / 162

6.45 6.46

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

6.4526.458

Slide 146 / 162

Label the numbers on the number line.

2 3

Slide 147 / 162

Label the numbers on the number line.

Slide 148 / 162

79 Where would the following number be correctly placed on the number line?

A B C D

9 109.5

Slide 149 / 162

80 Where would the following number be correctly placed on the number line?

A B C D

5 65.5

Slide 150 / 162

81 Where would the following number be correctly placed on the number line?

A B C D

2 32.5

Slide 151 / 162

82 Where would the following number be correctly placed on the number line?

A B C D

0 10.5

Slide 152 / 162

83 Where would the following number be correctly placed on the number line?

A B C D

0 10.5

Slide 153 / 162

84 Where would the following number be correctly placed on the number line?

A B C D

0 10.5

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 155 / 162

86 Where would the following number be correctly placed on the number line?

A B C D

0 21

Slide 156 / 162

87 Where would the following number be correctly placed on the number line?

A B C D

0 21 3

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

Slide 159 / 162

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

Slide 161 / 162

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

Slide 162 / 162

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