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Transcript of Equivalent Fractions:
To develop a deep understanding of fraction equivalency, it is necessary for students to understand that multiplying or dividing by n/n does not affect the value of fractions - only the way they are represented.
McNamara, J., & Shaughnessy, M. M. (2010).
Beyond pizzas & pies: 10 essential strategies for supporting fraction sense
, grades 3-5. Sausalito, CA: Math Solutions.
Students are quick to assume when you multiply or divide the numerator and denominator by the same number you change the value of the number.
Defining Equivalent Fractions
Equivalent fractions are fractions that represent the same number.
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
1/4 can be represented as a shaded part of area in which a rectangle is divided into four parts of equal size. One of those parts is 1/4 of the entire rectangle.
When those parts are divided in half, eight parts of equal size have been created. An equivalent fraction for 1/4 can be seen: 2/8. Importantly, 1/4 and 2/8 are the same number because they represent equal areas of the rectangle.
2/6 can be represented as a shaded part of area in which a rectangle is divided into six parts of equal size. Two of those parts make up 2/6 of the entire rectangle.
When every 2 of those parts are combined, 3 parts of equal size have been created. An equivalent fraction for 2/6 can be seen: 1/3. Importantly, 2/6 and 1/3 are the same number because they represent equal areas of the rectangle.