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

1 answer

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.