All About Fractions Adding - PowerPoint Presentation

Slide1

All About Fractions

Adding

Equivalent Fractions

Mixed Numbers

Simplify

Subtract

Slide2

PARTS OF A FRACTION

The top number of a fraction is the

The bottom number of a fraction is the

3

4

Numerator

Denominator

Slide3

MIXED NUMBERS

AND IMPROPER FRACTIONS

To change an improper fraction into a mixed number divide the numerator by the denominator; whatever is left over is the new numerator…keep the same denominator. For Example:

11 divided 4 equals 2; there is 3 left over.

2

3

4

11

4

Slide4

MIXED NUMBERS

AND IMPROPER FRACTIONS

To change a mixed number into an improper fraction get MAD…Multiply – Add – Put over Denominator 4 x 2 = 8

8 + 1 = 9

9

2

4

1

2

=

Slide5

Least Common Multiple

Least Common Denominator

Slide6

Multiples

A multiple is formed by multiplying a given number by the counting numbers.The counting numbers are 1, 2, 3, 4, 5, 6, etc.

Slide7

Least Common Multiple (LCM)

The least common multiple is the smallest number that is common between two lists of multiples.

Slide8

Example: List the multiples of 4:

4 x 1 = 44 x 2 = 84 x 3 = 124 x 4 = 164 x 5 = 20

4 x 6 = 24

Counting Numbers

So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc.

Slide9

EXAMPLE:

Find the LCM of 12 and 18

The multiples of 12:12 x 1 = 1212 x 2 =24

12 x 3 = 3612 x 4 = 4812 x 5 =60

The multiples of 18:

18 x 1 = 18

18 x 2 = 36

18 x 3 = 54

18 x 4 = 72

18 x 5 = 90

Slide10

12, 24, 36, 48, 60

18, 36, 54, 72, 90

The first number you see in both lists is

36

The least common multiple of 12 and 18 is

36

EXAMPLE:

Find the LCM of 12 and 18

Slide11

Equivalent Fractions

Slide12

Equivalent fractions

A fraction can have many different appearances, these are called

equivalen

t fractions

In the following picture we have ½ of a cake because the whole cake is divided into two equal parts and we have only one of those parts.

But if we cut the cake into smaller equal pieces, we can see that

=

Or we can cut the original cake into 6 equal pieces,

Slide13

Equivalent fractions

A fraction can have many different appearances, these are called

equivalen

t fractions

Now we have 3 pieces out of 6 equal pieces, but the total amount we have is still the same.

Therefore

,

=

=

If you don’t like this, we can cut the original cake into 8 equal pieces,

Slide14

Equivalent fractions

A fraction can have many different appearances, they are called

equivalen

t fractions

Then we have 4 pieces out of 8 equal pieces, but the total amount we have is still the same.

=

=

=

Therefore

,

Wow, that’s confusing!

Slide15

Equivalent Fractions

One Whole

or1

Slide16

Cut them in half

Equivalent Fractions

1

1

2

2

Slide17

Equivalent Fractions

This shape shows one half shaded.

1 2How many pieces shaded

How many pieces it’s cut into

NUMERATOR

DENOMINATOR

Slide18

Equivalent Fractions

I cut my shape again

I still show 1 2But I also show 2 4

1

1

1

1

4

4

4

4

Slide19

Fractions

Adding

Slide20

+

We need a common

denominator to add

these fractions.

Slide21

7, 14, 21, 28, 35…

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

Count by 2's

Count by 7's

+

We need a common

denominator to add

these fractions.

Slide22

7, 14, 21, 28, 35…

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

Count by 2's

Count by 7's

The first number

IN COMMON

that appears on both lists

becomes the common denominator

Slide23

+

=

x 2

x 2

=

X 7

x 7

7

6

7 + 6 =

13

Add the numerators

13

Make equivalent

fractions.

14

14

14

Never add the denominators

Just use the common denominator

Slide24

Fractions

Subtracting

Slide25

-

We need a common

denominator to add

these fractions.

3, 6, 9, 12, 15, 18, 21, 24, 27

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

Count by 3's

Count by 5's

Slide26

X 5

=

x 3

x 3

=

x 5

10

9

-

10 – 9 =

1

Subtract the numerators

1

15

15

15

Keep the same denominator

Slide27

Simplify FRACTIONS

Greatest Common Factor

Slide28

Factors

The numbers you multiply

together to get a product

Slide29

Greatest Common Factor

THINK . . .

Greatest . . . The biggest possible Common . . . They both have it

Factor . . . A factor of both numbers

Slide30

Factors

List the factors of 8

List the factors of 16What is the biggest number

In both lists?

This is the GCF.

Slide31

GREATEST COMMON FACTOR

Helps Simplify fractions

GREATEST COMMON FACTOR (GCF)

Slide32

This fraction is not in simplest form.

As long as there is a number that

you can divide the numerator and

denominator by (other than 1)

The fraction is not in simplest form.

6

12

Slide33

Simplifying Fractions

What’

s the GCF??What factors do they share?Which of those factors is the largest?GREATEST COMMON FACTOR= ?

6

12

6

12

Slide34

6

12

Now divide both theNumerator and denominator

By the GCF

÷

÷

6

6

1

2

=

Slide35

Greatest Common Factor

HINT

The GCF will ALWAYS beEQUAL toOrSMALLER thanthe smallest of the numbers

Slide36

Simplifying a Fraction

4

8=

To simplify a fraction you must divide the numerator and the denominator by the Greatest Common Factor.

The Greatest Common Factor is the biggest number you can divide both the numerator and denominator by.

=

÷

÷

4

4

1

2

Greatest Common Factor is 4