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)
Responses
To find how many sections there are in the length, we need to divide the total length by the length of each section:
6 3/4 ÷ 1 1/8
To make the fractions easier to work with, let's convert 6 3/4 and 1 1/8 to improper fractions:
6 3/4 = (4*6 + 3)/4 = 27/4
1 1/8 = (8*1 + 1)/8 = 9/8
Now we can divide:
27/4 ÷ 9/8
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
27/4 * 8/9 = (27*8)/(4*9) = 216/36
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4:
216/36 ÷ 4/4 = (216/4)/(36/4) = 54/9
54/9 = 6
So there are 6 sections in the length.
To find how many sections there are in the width, we need to divide the total width by the width of each section:
4 1/3 ÷ 1 1/12
Let's convert 4 1/3 and 1 1/12 to improper fractions:
4 1/3 = (3*4 + 1)/3 = 13/3
1 1/12 = (12*1 + 1)/12 = 13/12
Now we can divide:
13/3 ÷ 13/12
Again, we multiply the first fraction by the reciprocal of the second fraction:
13/3 * 12/13 = (13*12)/(3*13) = 156/39
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 3:
156/39 ÷ 3/3 = (156/3)/(39/3) = 52/13
52/13 = 4
So there are 4 sections in the width.
Therefore, there are a total of 6 sections in the length and 4 sections in the width of the address labels.