Final answer:
The fraction representing one filled section out of the total sections on two bulletin boards divided into 4 equal parts each is 1/8. This is because each board has 4 sections, for a total of 8, and a single section represents 1/8 of the combined areas of both boards.
Step-by-step explanation:
If two bulletin boards are divided into 4 equal sections each, we can write a fraction to represent the parts of the bulletin boards that can be filled. Since each board is divided into 4 equal parts, one section of a board would be represented by the fraction 1/4 (one quarter). When considering both bulletin boards together, we have a total of 8 sections. Each section still represents 1/4 of a single board. Therefore, the fraction that represents one filled section out of the total sections on both boards is 1/8.
When multiplying fractions, you multiply the numerators and denominators separately. Here, however, since we are just trying to determine the fraction of one section out of the total, we don't need to multiply, we simply write down the fraction that represents one part out of the whole.
Understanding fractions and how to manipulate them involves recognizing how to divide, multiply, and visually represent them, like envisioning slices of pie or quarters in a dollar. The intuitive sense of fractions is a great foundation which can then be built upon with the mechanics of mathematical operations.