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

Answer 1

To find the number of sections in the length, we divide the total length of the sheet by the length of each section:

6 3/4 ÷ 1 1/8

First, convert the mixed numbers to improper fractions:

6 3/4 = (6*4 + 3)/4 = 27/4
1 1/8 = (1*8 + 1)/8 = 9/8

Now, divide the fractions:

27/4 ÷ 9/8 = (27/4) * (8/9) = (27*8)/(4*9) = 216/36

Simplify the numerator and denominator by dividing both by 4:

216/36 = (216/4) / (36/4) = 54/9

Now, divide both numerator and denominator by 9:

54/9 = 6/1

There are 6 sections in the length.

To find the number of sections in the width, we divide the total width of the sheet by the width of each section:

4 1/3 ÷ 1 1/12

Convert the mixed numbers to improper fractions:

4 1/3 = (4*3 + 1)/3 = 13/3
1 1/12 = (1*12 + 1)/12 = 13/12

Now, divide the fractions:

13/3 ÷ 13/12 = (13/3) * (12/13) = (13*12)/(3*13) = 156/39

Simplify the numerator and denominator by dividing both by 3:

156/39 = (156/3) / (39/3) = 52/13

Now, divide both numerator and denominator by 13:

52/13 = 4/1

There are 4 sections in the width.

Therefore, there are 6 sections in the length and 4 sections in the width.