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Fraction Notes Vocabulary common factor – a number that is a factor of two or more numbers common multiple – a whole number that is a multiple of two or more numbers. fraction - number that represents part of a whole or part of a set denominator – the bottom number in a fraction. It represents the number of parts in the whole. numerator – the top number in a fraction; the part of the fraction that tells the number of parts you have. Least Common Multiple (LCM) – the smallest whole number greater than 0 that is a common multiple of each of two or more numbers. least common denominator – the least common multiple of the denominators of two or more fractions Greatest Common Factor (GCF) – the greatest of the common factors of two or more numbers. mixed number - a fraction that has a whole number part and a fraction part improper fraction – a fraction with a numerator that is greater than or equal to the denominator. simplest form - a fraction in which the GCF of the numerator and the denominator is 1. Notes: Reducing or Simplifying Fractions: ~When reducing a fraction first find the Greatest Common Factor (GCF) between the numerator and the denominator Example: Simplify 15 21 15 The factors of 15 are 1, 3, 5, and 15 21 The factors of 21 are 1, 3, 7, and 21 The Greatest Common Factor (GCF) between 15 and 21 is 3, so take the numerator and denominator and divide both of them by 3. (What you do to the bottom you have to do to the top) 15 ÷ 3 = 5 21 ÷ 3 = 7 5 7 is in simplest form, because the only common factor between 5 and 7 is 1. Reducing or Simplifying and Improper Fraction When you have an improper fraction you can divide the numerator by the denominator. You will end up with a whole number. If you have a remainder, it becomes your numerator. The divisor will be your denominator. (You have now created a mixed number (a whole number with a fraction). Example: 8 5 Take 8 ÷ 5 = 1 R 3, so your new number will be 1 3 5 *You may have to simply once you make your mixed number. In this case 3 5 is already in simplest form. Adding Fractions with LIKE Denominators: When the denominators are the same you simply add or subtract the numerators. DO NOT add the denominators). Then simplify if needed. 2 1 4 4 Examples: + = 3 4 4 5 3 2 5 1 4 4 4 4 3 +1 =4 =5 3 1 5 5 − = Adding Fractions with UNLIKE Denominators: When adding and subtracting fractions with unlike denominators first you have to find the least common denominator (use the Least Common Multiple (LCM) to find the least common denominator). Once you have found a common denominator you carry out the function. Finally, simplify if needed. Adding: 1 2 1 1𝑥3 3 2𝑥3 + = + 1𝑥2 3𝑥2 = Subtracting without barrowing: 3 6 7 8 + 2 6 = 5 6 1 7𝑥2 2 8𝑥2 − = − 1𝑥8 2𝑥8 = 14 16 − 8 16 = 6 ÷2 16÷2 = 3 8 Subtracting with barrowing: There are two ways you can barrow when subtracting: 1) You can change the fractions back into improper fractions by multiplying the whole number and the denominator and then add the numerator. 1 1 21 5 21 5𝑥2 21 10 11 3 5 −2 = − = − = − = =2 4 2 4 2 4 2𝑥2 4 4 4 4 2) Or you can first find a common denominator if needed and then barrow from the whole number. When you are barrowing from the whole number your numerator and denominator should be the same. Add that fraction to the fraction that is already there (if there is one). Then carry out the function. 1 1 1 1𝑥2 1 2 4 1 2 5 2 3 5 −2 =5 −2 =5 −2 =4 ( + )−2 =4 −2 = 2 4 2 4 2𝑥2 4 4 4 4 4 4 4 4