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 12 18 1x12 1x18 2x6 2x9 3x4 3x6 GCF = 6

Prime Factorization Create factors trees. 12 18 1 x 12 1 x 18 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 large Small

IMPROPER FRACTIONS large small

MIXED NUMBERS fraction whole number

Mixed Numbers

Improper Fractions

2 2 x 2 + 1 = = 2 2 2

2 2 3 2 = 3 3 -6 2

Express the mixed number as an improper fraction. = = 5

Express the improper fraction as a mixed number. 6 = = -18 1

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 81, 90, 99 10, 20, 30, 40, 50, 60, 70, 80 90, 100, 110 If you don’t see a common multiple, make each list go further. The LCM of 9 and 10 is 90

What is the Least Common Multiple of 6 & 8 6 = 6, 12, 18, 24, 30, 36 8 = 8, 16, 24, 32, 40, 48

Draw a picture Use >, <, or =. <

Use >, <, or =. “Butterfly” method 9 < 10 <

“Butterfly” method Use >, <, or =. 12 10 > >

To order fractions you can draw a picture or use the Least Common Denominator (LCD) or (LCM).

Order : least to greatest Draw a picture

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

List the fractions in order from greatest to least. Use LCD List the fractions in order from greatest to least.

Step 1: Find the LCM of the denominators Use LCD Step 1: Find the LCM of the denominators

Find the LCD: 6: 6, 12, 18, 24, 30, 36, 42, 48… 12: 12, 24, 36, 48 … 9: 9, 18, 27, 36, 45 … 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 … LCD = 36

6 21 36 36 20 24 36 36 Step 2: Write equivalent fractions. x 6 x 3 x 6

Step 3: Compare the numerators G L 21 6 36 36 24 20 36 36

In order from greatest to least: Use LCD In order from greatest to least: