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# Proportions/Equivalent Fractions Topic

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EQUIVALENT FRACTIONS What Are Equivalent Fractions? • Equivalent fractions represent the same ratio between two values. • Fractions show a ratio between two values. The fraction ½ represents 1 out of 2. If there were 2 students sharing an assignment, each would do part of the work. The work would be divided into 2 equal parts and each student would do 1 part or ½ the total project. • The fraction ½ also represents part of a set. If there are 2 cookies in a set and one is eaten, then 1 out of 2 cookies is eaten. The relationship between the cookie eaten and the total number of cookies is 1 out of 2 or 1/2. • Because sets come in a variety of sizes, fractional parts will have a variety of denominators. The fraction 1/2, for instance, has many equivalents: 1 2 3 4 5 6 7 8 9 10 12 15 19 31 44 50 100 2 4 6 8 10 12 14 16 18 20 24 30 38 62 88 100 200 • The ratio of all the fractions in this table is 1 to 2. As a result, all the fractions in the table are equivalents of ½. • Any number times 1 equals itself. For example 1 x 4 = 4, 1 x 37 = 37, 1 x 576 = 576. Therefore, 1 x ½ = ½. • Like ½, the number 1 has a multitude of equivalents: 2/2, 4/4, 10/10, 50/50. Whenever the numerator and denominator are the same numbers, the fraction is equivalent to one. 1 x 5 = 5 3/3 x ½ = 3/6 6/6 x ½ = 6/12 © 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.

How to calculate an equivalent fraction: • To calculate an equivalent fraction, multiply the fraction by 1 or one of its equivalent fractions. Choose a number that when multiplied by the denominator will produce a sum that helps you solve a problem. • For example: 1/5 = n/25 1/5 x 5/5 = 5/25 n = 5 ------------------------------------------------- 3/7 = n/21 3/7 x 3/3 = 9/21 n = 9 • Calculating equivalent fractions allows us to solve a problem in which the two fractions do not have the same denominators. For example: 2/5 + 7/15 = (2/5 x 3/3) + 7/15 = 6/15 + 7/15 = 13/15 • Changing the denominator of 2/5 to 15 allows us to add the two fractions. This is accomplished by multiply 2/5 x 1 which equals 2/5, but using 3/3 (an equivalent of 1). Any fraction can be changed to an equivalent by multiplying times a fraction equivalent to 1. © 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! 1. What is an equivalent fraction for 4/5? _________________________________________ 2. What is the numerator for this equivalent fraction? 5/8 = n/40 _________________________________________ 3. Are 15/20 and 30/40 equivalent fractions? _________________________________________ 4. What is the numerator for this equivalent fraction? 21/24 = n/72 _________________________________________ 5. Are 5/10 and 25/55 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.