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What Are Multiple Representations of Rational Numbers? • A rational number represents a value or a part of a value. • Rational numbers can be written as integers, fractions, decimals, and percents. • The different representations for any given rational number are all equivalent: 3/10 = .30 = 30% 4/5 = .80 = 80% • The purpose for which the ratio is being used will determine the form. o He ate 3/5 of the pizza. o The interest rate of .27 on a bank loan is very high. o Only 42% of the class passed the test. How to calculate and write multiple representations of rational numbers: • Fractions are numbers that represent parts of a region or a set. They are written as ratios. o 1/5 = 1 part of a set of 5 o 2/7 = 2 parts of a set of 7 • Decimals are fractions with a denominator of 100 and written with a decimal point. o 2/5 = 40/100 or .40 o 6/10 = 60/100 or .60 • Percents are the numerator of a fraction with a denominator of 100 and written with a percent % sign. o 44/100 = 44% o 87/100 = 87% • To calculate the different representations, think “equivalent fractions.” © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

• If ½ = 2/4 = 25/50 = 50/100, then ½ also equal .50 or 50% o 50% of the class passed the test. If there are 20 students, only 10 passed. o They painted 50% of the house today, in other words ½ of the painting is done. o 50 cents is written as $.50 which is the same as ½ of a dollar. • Some fractions cannot be changed into fractions with 100 as the denominator. For instance 1/3 cannot become n/100 because 3 does not divide evenly into 100. We can choose the number closest to 100 ÷ 3 in order to calculate a percent. Any fraction can be changed to a percent that is approximate by dividing the numerator by the denominator. For instance, 3/7 would be approximately 22%. o 1/3 is about 33% o 1/7 is about 14% o 5/9 is approximately 56% o 21/37 is approximately 57% • You will see fractions such as 1/2, 2/3, and ¾ in recipes. All references to money or coins use decimal representations: $.45 (45 cents), $.75 (75 cents). Percents are used in newspaper articles which discuss parts of groups. For instance, you might read: “After the hurricane, 90% of the city was without electricity.” Choose the representation that best suits the context. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Try This! 4/20 = n/100 n = _____ 15/25 = n/100 n= _____ 65/100 = _____% 76/100 = _____% The decimal representation for 51/100 is __________. The decimal representation for 43/50 is __________. The fraction 6/9 is approximately _____%. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.