A piece of plywood, the surface of which measures 8/9 square yard, is cut into sections each containing 2/9 square yard. How many sections are there?
(8/9) / (2/9)
(8/9) * (9/2) = 72/18 = 4
poorly worded question:
the original piece could be an infinite number of dimensions,
e.g. 2/3 by 4/3 or 1/3 by 8/3
or 1.25/3 by 6.4/3 or √8/3 by √8/3 or ....
similarly, we are not given the dimensions of the cut-off piece only its area
it could be 1/3 by 2/3 or 1.25/3 by 1.6/3 etc.
If we only want exact values, off the top we can see that
a starting piece of 2/3 by 4/3 will let us take 4 pieces of 2/3 by 1/3
Since we are cutting plywood, we would be losing lengths due to sawcuts, but ...
oh, never mind.
To find the number of sections, we need to divide the total surface area of the plywood by the surface area of each section.
The surface area of the plywood is given as 8/9 square yard.
The surface area of each section is given as 2/9 square yard.
To find the number of sections, we divide the surface area of the plywood by the surface area of each section:
Number of sections = Surface area of plywood / Surface area of each section
Number of sections = (8/9) / (2/9)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Number of sections = (8/9) * (9/2)
The 9 in the numerator and the denominator of the fractions cancel out:
Number of sections = (8/1) * (1/2)
Multiply the numerators together and the denominators together:
Number of sections = (8 * 1) / (1 * 2)
Simplify the numerator and denominator:
Number of sections = 8/2
Finally, divide 8 by 2:
Number of sections = 4
Therefore, there are 4 sections in the plywood.