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
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.