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**Fractions and Decimals**

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**Greatest Common Factor**

The largest factor shared by two or more numbers.

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**Rainbow Method Find the factors of 12 and 18.**

12: 1, 2, 3, 4, 6, GCF:6 18: 1, 2, 3, 6, 9, 18

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**House Method Find the GCF of 12 and 18. 12 18 1x12 1x18 2x6 2x9**

1x x18 2x x9 3x x6 GCF = 6

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**Prime Factorization Create factors trees. 12 18 1 x 12 1 x 18**

1 x x 18 2 x x 9 2 x x 3 GCF= 2 X 3= 6

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**Simplifying Fractions**

Step 1: Find the GCF Step 2: Divide the numerator and the denominator by the GCF 12 /6 = 2 18 /6= 3

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**Mixed Numbers and Improper Fractions**

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

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PROPER FRACTIONS large Small

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IMPROPER FRACTIONS large small

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MIXED NUMBERS fraction whole number

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Mixed Numbers

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Improper Fractions

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2 2 x 2 + 1 = = 2 2 2

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2 2 3 2 = 3 3 -6 2

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**Express the mixed number as an improper fraction.**

= = 5

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**Express the improper fraction as a mixed number.**

6 = = -18 1

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**Least Common Multiples**

LCM OR LCD

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**Least Common Multiple (LCM)**

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

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**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

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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.

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**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

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**What is the Least Common Multiple of 6 & 8**

6 = 6, 12, 18, 24, 30, 36 8 = 8, 16, 24, 32, 40, 48

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

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

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

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

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Order : least to greatest Draw a picture

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**Order the fractions from least to greatest.**

, ,

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**One way to compare or order fractions is to express them with the same denominator.**

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**The Least Common Denominator is the Least Common Multiple of the denominators.**

LCD = LCM

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**List the fractions in order from greatest to least.**

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

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**Step 1: Find the LCM of the denominators**

Use LCD Step 1: Find the LCM of the denominators

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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

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

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**Step 3: Compare the numerators**

G L 21 6 36 36 24 20 36 36

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**In order from greatest to least:**

Use LCD In order from greatest to least:

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