Question

James is covering a cupboard door with plywood, which requires of a square yard of plywood. He only has of a square yard of plywood. What fraction of the door can James cover with the amount of plywood he has?


A.

B.

C.

D.

Answer 1

To determine the fraction of the cupboard door that James can cover with the plywood he has, we need to express the amount of plywood he has in relation to the amount he needs.

Let's denote the amount of plywood James needs to cover the cupboard door as \( N \) square yards, and the amount of plywood he has as \( H \) square yards.

If he requires \( N \) and has \( H \), the fraction of the door he can cover is given by:

\[
\text{Fraction covered} = \frac{H}{N}
\]

However, you provided placeholders \( \frac{A}{B}, \frac{C}{D} \), etc., without specific values for \( N \) and \( H \).

If you replace \( H \) and \( N \) with their specific values, you can compute the fraction. For example:

If:
- \( N = \frac{3}{4} \) (square yards needed)
- \( H = \frac{1}{2} \) (square yards available)

Then:

\[
\text{Fraction covered} = \frac{\frac{1}{2}}{\frac{3}{4}} = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}
\]

If you provide the specific quantities for how much plywood he requires versus how much he has, I can give you a precise answer.