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Simplifying and Comparing Fractions 5.4 Simplifying Fractions • A fraction is “simplified” when its numerator and denominator have a GCF of 1 To Simplify Fractions • Divide the numerator and denominator by the GCF Example Simplify: 12 20 • What is the GCF of 12 and 20? • 4 12 4 20 4 3 5 Simplify 4 10 • What is the GCF between 4 and 10? • 2 42 10 2 2 5 Simplifying With Variables • Divide numbers by GCF • List the variables out • Cancel out the variables Simplify: 5x 3 15 x 15 x x x 15 x 3 xx x 3 3 2 2 Simplify: 28 m n 3 4 42 m n 28 m m n n n 42 m m m m n 2n 2 3m 2 Comparing Fractions Using a Number Line • Graph the fractions on the number line • The number to the left is the smaller number Graph and Order from Least to Greatest 15 18 , 3 7 , 7 3 , 8 9 Comparing Fractions • Get the same denominator (LCD) – Find the LCM of the denominators • Make an Equivalent fraction – Multiply each the fraction (numerator and denominator) by number to make the LCM • Once the denominators are the same compare the numerators Compare Using <, > or = 2 3 , 5 7 Compare Using <, > or = 4 2 , 9 6 Heart Method to Compare Fractions • Multiply the diagonals, bring down and compare the products Use the heart method to compare 1 1 , 4 5 Use the heart method to compare 11 16 , 5 8 Homework Page 236 (16-42) even