Final answer:
Only equation a, 3 × 1/3 = 1, and equation b, 1 × 3/3 = 1, are correct. Equations c and d are incorrect as they do not result in a whole when using pattern blocks to represent the multiplication by fractions.
Step-by-step explanation:
The question revolves around the concept of understanding and representing multiplication of whole numbers by fractions using pattern blocks, with a trapezoid representing 1 whole. Only one of the equations provided is correct.
Examining the Equations
a. 3 × 1/3 = 1: This equation is correct. Multiplying 3 by 1/3 gives us 3/3, which simplifies to 1. Conceptually, if you have 3 trapezoids, each representing a whole, and you multiply them by 1/3, you would take one third of each trapezoid, effectively ending up with one trapezoid or one whole.
b. 1 × 3/3 = 1: This equation is also correct since 3/3 represents one whole, and 1 multiplied by one whole is still one whole.
c. 2 × 1/3 = 1: This equation is incorrect. Multiplying 2 by 1/3 would give us 2/3, not 1. In terms of pattern blocks, this represents taking one third of two trapezoids, which would not combine to form a full trapezoid.
d. 1 × 2/3 = 1: This equation is also incorrect. Multiplying 1 by 2/3 gives us 2/3, indicating that we have only two thirds of a whole, not one whole.