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ROD: Lowest Common Multiple ______________ A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, .... The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. It can be used to find the lowest common denominator when adding, subtracting or comparing fractions Eg.1: Find the LCM of 3 and 4: Don't let the "least" in the name fool you - the LCM is no smaller than the largest of the numbers. HINTS: LEAST - lowest or smallest. COMMON - something shared or in common. MULTIPLE - what you get when you multiply. Eg.2: Find the Least Common Multiple (L.C.M.) of 4 and 6. Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32.... 1*4, 2*4, 3*4, 4*4, 5*4, 6*4, and so on Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48.... 1*6, 2*6, 3*6, 4*6, 5*6, 6*6, and so on Since 12, 24, 36, 48.... can be all divided by BOTH 4 and 6, each of them is a common multiple. The lowest common multiple is 12, therefore it is the Least Common Multiple (L.C.M.) of 4 and 6. Math Model Book: Comparing Fractions ____________ How can we compare fractions with the same numerator? e.g. ½ , ¼ The larger the denominator, the smaller the fraction. How can we compare fractions with the same denominator? The larger the numerator, the larger the fraction. 2 5 is 1 larger than 5 . How can we compare fractions when the numerators and denominators are different? Change them to equivalent fractions with the same denominator. Then, compare the numerators. Example 8. Which is larger, 1 2 or 3 8? Answer. Make a common denominator. Choose the LCM of 2 and 8 -- which is 8 itself. We will change 1 2 = 4 8 1 2 to an equivalent fraction with denominator 8: . The denominators are now the same, and we can compare We see: 4 8 is larger than 8 . 3 1 2 is larger than That is, 3 8 4 3 with . 8 8 Proper and Improper Fractions _______ Proper and Improper fractions 2 ½ is read two and one-half This means 2 + ½ or 4 + ½ or 2 5 2 2½ Whole # And a fraction mixed number 5/2 improper fraction e.g 1 Convert 5/4 to a proper fraction: e.g 2 Convert 2 ¾ to an improper fraction numerator greater than denominator Math Model Book: Reducing Fractions ___________________ To reduce fractions to its lowest terms, we divide the numerator and the denominator by their GCF e.g. Reduce 20/25 divide top and bottom by 5 to get ____________________ In other words, we find an equivalent fraction by dividing by a form of one 12 12 4 3 = ÷ = 16 16 4 4 A form of 1 = 4/4