Proportions/Equivalent Fractions Topic

Proportions/Equivalent Fractions

Mathematics, Grade 6

Back

Study Guide

Provides a quick overview of the topic selected!

Flash Cards

Practice and review the topic selected with illustrated flash cards!

Quiz

Assess students’ understanding of the topic selected!

Worksheets

Print illustrated worksheets!

Games

Engage students with interactive games.

Study Guide Proportions/Equivalent Fractions Mathematics, Grade 6

❮

❯

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.