fractions. index what is a fraction? equivalent fractions making equivalent fractions by multiplying...

$: Fractions. Index What is a fraction? Equivalent Fractions Making Equivalent Fractions by multiplying Making Equivalent Fractions by dividing Simplest$
Fractions

Index• What is a fraction?• Equivalent Fractions• Making Equivalent Fractions by multiplying • Making Equivalent Fractions by dividing• Simplest Form • Uses of Fractions • Fractions Written as a Whole• Improper Fraction• Mixed Number• How to change from Improper Fraction to Mixed Number• How to change from Mixed Number to Improper Fraction • Comparing Fractions• Ordering Fractions • Ordering Fractions with Number Line• Adding Fractions

What is a Fraction?

3

2

I’m the NUMERATOR. I tell you the number of

equal parts you are looking at or have.

I’m the DENOMINATOR. I tell you the number of equal parts into which the whole is

divided.

A fraction is formed by dividing a whole into a number of parts

Uses of Fractions

• A fraction may represent division.

• Fractions can express probability.

• Fractions are used to compare two quantities as a ratio.

Student Reference Book p. 57-58

Equivalent Fractions

2

1

12

6

Equivalent fraction: fractions that have the same value

12

6

1 WHOLE 1 WHOLE4

26

3

• Multiply the numerator and denominator by the same number.

• You will get a new fraction with the same value as the original fraction.

• We are not changing the value of the fraction, because we are simply multiplying by a fraction that is equivalent to ONE.

To Make Equivalent Fractions

What do you get when you multiply a fraction by 1?

You get

AN EQUIVALENT FRACTION

that makes

adding & subtracting fractions

possible.

Make An Equivalent FractionFind the Missing Numerator!

Given the newdenominator, can you

find the missing numerator?

x 3

x 3

Make An Equivalent FractionFind the Missing Numerator!

Given the newdenominator, can you

find the missing numerator?

x 4

x 4

Make An Equivalent FractionIf you have larger numbers, you can make equivalent fractions using division. Divide by a common factor.

In this example,

we can divide both

numbers by 7.

÷ 7

÷ 7

2835

45

Fractions in Simplest FormFractions are in simplest form when the numerator and denominator do not have any common factors besides 1.

Examples of fractions that are in simplest form:

45

211

38

Writing Fractions in Simplest Form

• Find the greatest common factor (GCF) of the numerator and denominator.

• Divide both numbers by the GCF.

Example:

2028

201 x 20

2 x 10

4 x 5

281 x 28

2 x 14

4 x 7

20: 1, 2, 4, 5, 10, 20

28: 1, 2, 4, 7, 14, 28

Common Factors: 1, 2, 4

GCF: 4

We will divide by 4.

÷ 4÷ 4

= 57

Simplest Form

Fractions Written as a Whole

2

213

31

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

1 Whole

Trapezoid Trapezoid

TrapezoidTrapezoid

Trapezoid

2 Trapezoids = 1 Hexagon 1 Whole 1 Whole

½

We can report this as 2 ½ or 5/2 Trapezoid

Improper Fractionfractions that are equal to or greater than 1

5/2

is read as – five halves

Mixed Numbera whole number and a fraction written together

2 ½

is read as - two and one half

If a triangle is 1/3,what shape is ONE whole?

1/3

Remember: Numerator is what you have- 1.

Denominator is how many pieces your whole is cut into - 3.

How many more triangles do you need to make a whole?

1/31/3

What shape can we make?

1/3 + 1/3 + 1/3 = 3/3 or 1 Whole

Trapezoid1 Whole

If the triangle is 1/3, what is the rhombus?

If the rhombus is 1/3, what shape is the WHOLE?

Turn to MJ p. 124

If the rhombus is 1/3, what is the triangle?

If the triangle is ½, what shape is the WHOLE?

If the triangle is ½, what is the trapezoid?

Mixed Number

• A mixed number has a part that is a whole number and a part that is a fraction.

= 1 34

What is the mixed number?

= 3 34


= 4 34


= 5 12

Improper Fraction

• A fraction in which the numerator is greater than the denominator.

=84

What is the improper fraction?

= 154


= 194


= 112

How is the mixed number below related to the

improper fraction?

=112

=125

How to change an improper fraction to a mixed number

= 52

Divide the numerator by the denominator.

Put your remainder over the denominator.


= 52

2 ) 5 numerator

denominator


= 52

2 ) 5 numerator

denominator

2 r 1


= 52

2 ) 5 numeratordenominator 2

1

Put your remainder over the Denominator.

2

Change this improper fraction to a mixed number.

7

3= 3 ) 7

2 r 1


= 213


8

3= 3 ) 8

2 r 2


= 223


9

2= 2 ) 9

4 r 1


= 412


11

5= 5 ) 11

2 r 1


= 215


10

5= 5 ) 10

2

If there is no remainderyour answer is a wholenumber.

= 2


16

4= 4 ) 16

4

If there is no remainderyour answer is a wholenumber.

= 4

How to change a mixed number to an improper fraction

• Multiply the whole number times the denominator.

• Add your answer to the numerator.

• Put your new number over the denominator.

412x

+=

92

Change this mixed number to an improper fraction




623x

+=203





3 25x

+=175





4 34x

+=194





6 23x

+=203





8 35x

+=435

Use >, <, or =.

5

33

29 10<

<

Cross Multiply or “Butterfly Method”

Comparing Fractions

Use >, <, or =.

10

34

112 10>

>

Cross Multiply or “Butterfly Method”

To order fractions you can draw a picture or

use the Least Common Denominator (LCD).

Ordering Fractions

One way to compare or order fractions is to

express them with the same denominator.

Any common denominator could be used. But the

Least Common Denominator (LCD)

makes the computation easier.

Use LCD

List the fractions in order from greatest to least.

3

2,9

5,

12

7,6

1

Use LCD

Step 1: Find a common denominator

3

2,9

5,

12

7,6

1

6, 12, 18, 24, 30, 36 ….

LCD = 36

Find the LCD:

12, 24, 36, 48, 60 …9, 18, 27, 36 …

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 …

Put the largest denominator first and write down the first 5 multiples

Then continue with the next denominator until you find a common digit…

Step 2: Write equivalent fractions.

6

1

36x 6

x 6 6 12

736x 3

x 321

9

536x 4

x 420 3

236x 12

x 1224

Step 3: Compare the numerators

6

136 6

12

73621

9

53620

3

23624

In order from greatest to least:

6

1,9

5,

12

7,3

2

PRACTICE: Use LCD

In order from greatest to least:

6

1,9

5,

12

7,3

2

Finding Fractions on a Number Line

• We can use number lines to help us order fractions.


• This number line breaks one whole into fourths.

• Where would ¼ be on the number line?

• What about 4/4?

4

1

4

4


• How many sections does this number line break one whole into?

• Can you locate where 1/8 would be?

• Name a fraction in eighths that is between ½ and ¾.

8

1

4

1

4

2 4

3


• What does this number line show?

• Where would 7/9 be?

• What fraction is between 1/9 and 2/9?


• How would you explain this number line using words?

• Can you find 3/5?

• Can you mark a fraction larger than 4/5 on the number line?


• What type of number line is this?

• Can you order 5/8, 1/4, 2/3, and 3/16 on this number line?

Adding Fractions with common denominators

8

4

8

3

8

7

Add these fractions

1/5

1/51/5

1/5

35

15

+ =45

1/5

Add these fractions

1/4

1/4

1/424

14

+ =3

4

Adding Fractions with different denominators

Problem:

You can’t add fractions with different denominators without getting them ready first. They will be ready to add when they have common denominators

Solution: Turn fractions into equivalent fractions with a

common denominator that is find the Lowest Common Multiple (LCM) of the two denominators

7, 14, 21, 28, 35…

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

2

1

7

3We need a common denominator to add

these fractions.

7, 14, 21, 28, 35…

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

REMEMBER the first number IN COMMONthat appears on both lists

becomes the common denominator

x 2

x 2

X 7

x 7 7

6

7 + 6 = 1313

2

1

7

3

14

14

14

5

17

3

We need a common denominator to add

these fractions.

5, 10, 15, 20, 25, 30, 35, 40, 45

7, 14, 21, 28, 35, 42, 49, 56, 63

x 7

x 7

X 5

x 5 15

7

15 + 7 = 22

22

35

35

35

7

3

5

1

Try These

A

F

EB

C

D

Answers On Next Slide

• Each click on the next slide reveals an answer.

• Check your papers.

• If you discover an incorrect answer, be able to explain your mistake.

Try These

A

F

EB

C

D1727

1920

109

4128

2621

1312

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