A teacher wants to tape sheets of paper together to make a science banner. He wants the banner to be 127 1/3 inches long, and each sheet of paper is 8 1/2 inches wide. How many sheets of paper will he need?
To find out how many sheets of paper the teacher will need, we first need to determine the total length of the banner.
Given that each sheet of paper is 8 1/2 inches wide, we need to add up the widths until we reach or exceed the desired length of 127 1/3 inches.
To do this, we divide the desired length by the width of each sheet of paper:
127 1/3 inches ÷ 8 1/2 inches
To simplify things, let's convert the mixed fraction to an improper fraction:
127 1/3 inches = (3 * 127 + 1) / 3 = 382/3 inches
Now we can perform the division:
(382/3 inches) ÷ (8 1/2 inches)
To divide fractions, we multiply by the reciprocal of the second fraction:
(382/3 inches) × (2/17 inches)
Multiplying the numerators and denominators, we get:
(382 * 2) / (3 * 17) = 764 / 51
Therefore, the teacher will need approximately 764/51 sheets of paper to make a banner that is 127 1/3 inches long.
To calculate the exact number of sheets, we can divide the numerator by the denominator:
764 ÷ 51 = 14 remainder 10
So, the teacher will need 14 whole sheets of paper, plus an additional partial sheet.
Therefore, the teacher will need 15 sheets of paper to make the science banner.