Final answer:
When a piece of fabric measuring 2/3 yard is divided so that each third consists of 4 equal parts, the equivalent fraction representing the length of the fabric is 8/12.
Step-by-step explanation:
Sadie measures a piece of fabric that is 2/3 yard long. To find an equivalent fraction representing the length of the fabric when each third is partitioned into 4 equal parts, we need to multiply both the numerator and denominator of 2/3 by 4. This is because each third is divided into 4 equal parts.
2/3×4/4=8/12
So, 8/12 is an equivalent fraction. This fraction represents the length of the fabric when each third is further divided into 4 equal parts. The numerator, 8, indicates the number of parts Sadie would have if she measured the fabric using the smaller partitions, and the denominator, 12, represents the total number of those smaller parts in the whole length of the fabric