Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b)

What you'll learn

1. Explain, using a visual model, why dividing each piece of a fraction into the same number of equal sub-pieces changes the number and size of the parts but not the amount represented
2. Demonstrate that multiplying the numerator and denominator of a fraction by the same nonzero whole number produces an equivalent fraction (e.g., 2/3 = (2 x 4)/(3 x 4) = 8/12)
3. Justify why multiplying by n/n is the same as multiplying by 1, and therefore does not change the value of the fraction
4. Use area models and number lines to verify that two fractions are equivalent by showing they represent the same amount or the same point
5. Generate equivalent fractions for a given fraction by choosing different values of n and applying the principle (n x a)/(n x b)

Prerequisites

• 3-nf-a-3b