Fractions and Decimals

Greatest Common Factor

• The largest factor shared by two or more numbers.

Rainbow Method

• Find the factors of 12 and 18.

12: 1, 2, 3, 4, 6, 12 GCF:6

18: 1, 2, 3, 6, 9, 18

House Method

• Find the GCF of 12 and 18.

12 18

1x12 1x18

2x6 2x9

3x4 3x6

GCF = 6

Prime Factorization

• Create factors trees.

12 18

1 x 12 1 x 18

2 x 6 2 x 9

2 x 3 3 x 3

GCF= 2 X 3= 6

Simplifying Fractions

• Step 1: Find the GCF

• Step 2: Divide the numerator and the denominator by the GCF

12 /6 = 2

18 /6= 3

Mixed Numbers and Improper Fractions

• A mixed number is the sum of a whole number and a fraction.

PROPER FRACTIONS

large3

2

4

3

9

6

IMPROPER FRACTIONS

large

small

4

5

3

6

5

9

10

MIXED NUMBERS

3

25

4

17 5

31

fraction

whole number

11

4

11

12

4

5

13

1= 2 x 2 + 1

2=

52

2 2

14

88=

2

-62

23 3

2

3

15

Express the mixed number as an improper fraction.

5

13 =

3 x 5 + 15

=5

16

16

Express the improper fraction as a mixed number.

3

19= 193

6

-181

=3

16

Least Common Multiples

LCM OR LCD

Least Common Multiple (LCM)

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

EXAMPLE: Find the LCM of 12 and 18

The multiples of 12:

•12 x 1 = 12

•12 x 2 =24

•12 x 3 = 36

•12 x 4 = 48

•12 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

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 2: Find the LCM of 9 and 10

9, 18, 27, 36, 45, 54, 63, 72

10, 20, 30, 40, 50, 60, 70, 80

If you don’t see a common multiple, make each list go further.

81, 90, 99

90, 100, 110

The LCM of 9 and 10 is 90

What is the Least Common Multiple of 6 & 8

8 = 8, 16, 24, 32, 40, 48

6 = 6, 12, 18, 24, 30, 36

4

3

6

5<

Draw a picture Use >, <, or =.

Use >, <, or =.

5

33

29 10<

<

“Butterfly” method

Use >, <, or =.

10

34

112 10>

>

“Butterfly” method

To order fractions you can draw a picture or

use the Least Common Denominator (LCD) or

(LCM).

4

3

6

5

Draw a pictureOrder :

least to greatest

2

1

4

32

1

6

5

Order the fractions from least to greatest.

, ,

One way to compare or order fractions is to

express them with the same denominator.

The Least Common Denominator is the

Least Common Multiple of the denominators.

LCD = LCM

Use LCD

List the fractions in order from greatest to least.

3

2,

9

5,

12

7,

6

1

Use LCD

Step 1: Find the LCM of the denominators

3

2,

9

5,

12

7,

6

1

6: 6, 12, 18, 24, 30, 36, 42, 48…

LCD = 36

Find the LCD:

12: 12, 24, 36, 48 …

9: 9, 18, 27, 36, 45 …

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

27, 30, 33, 36 …

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

G LStep 3: Compare the numerators

6

1

36 6

12

73621

9

53620

3

23624

Use LCD

In order from greatest to least:

6

1,

9

5,

12

7,

3

2