A sheet of address labels is 6 3/4 inches long and 4 1/3 inches wide. The length is divided into sections that are 1 1/8 inches long, and the width is divided into sections that are 1 1/12 inches wide. Solve this multi-step problem involving division with fractions. How many sections are there? (1 point)
To find the number of sections in the length, we need to divide the total length of the sheet by the length of each section.
Total length of the sheet = 6 3/4 inches
Length of each section = 1 1/8 inches
To divide 6 3/4 by 1 1/8, we can convert both fractions to a common denominator:
6 3/4 = (6 * 4 + 3) / 4 = 27/4
1 1/8 = (1 * 8 + 1) / 8 = 9/8
Now we can divide:
27/4 / 9/8 = 27/4 * 8/9 = (27 * 8) / (4 * 9) = 216/36 = 6
So there are 6 sections in the length.
Similarly, we can find the number of sections in the width by dividing the total width of the sheet by the width of each section.
Total width of the sheet = 4 1/3 inches
Width of each section = 1 1/12 inches
Provided the same approach, we can divide:
4 1/3 = (4 * 3 + 1) / 3 = 13/3
1 1/12 = (1 * 12 + 1) / 12 = 13/12
13/3 / 13/12 = 13/3 * 12/13 = (13 * 12) / (3 * 13) = 12/3 = 4
So there are 4 sections in the width.
Therefore, there are 6 sections in the length and 4 sections in the width of the sheet of address labels.