To compare and order fractions we must first convert all integers, mixed numbers (mixed fractions) and fractions into VALUES that we can compare. We do this by first converting all terms into fractions, FINDING the least common denominator (LCD), then rewriting each term as an equivalent fraction with the LCD. Then we compare the numerators of each fraction and put them in correct order from least to greatest or greatest to least. Convert integers and mixed numbers to improper fractions Find the least common denominator LCD of all the fractions Rewrite fractions as equivalent fractions using the LCD Order the new fractions by the NUMERATOR Match original inputs to the ordered fractions to see the final order Input: 2, 3/4, 9/12, 3 5/8, -12/16 and order from least to greatest Convert integers and mixed numbers to improper fractions • 3/4, 9/12 and -12/16 are PROPER fractions so we can use those as they are written • 2 in fraction form is 2/1 • Convert 3 5/8 to an improper fraction. Multiply the whole number 3 by the denominator 8 to get 24. ADD 24 to the numerator 5 to get 29/8. So 3 5/8 = 29/8. • All inputs as fractions: 2/1, 3/4, 9/12, 29/8, -12/16 Find the least common denominator: LCD of 1, 4, 8, 12, 16 is 48 Rewrite the input fractions as equivalent fractions using the LCD • 2, 3/4, 9/12, 3 5/8, -12/16 become: • 96/48, 36/48, 36/48, 174/48, -36/48 Order these fractions from least to greatest numerator • -36/48 < 36/48 = 36/48 < 96/48 < 174/48 Place the original fractions in the same order as their equivalents • -12/16 < 3/4 = 9/12 < 2 < 3 5/8