Answer: To determine if Mr. Simon's estimate is reasonable, we can use benchmark fractions. A benchmark fraction is a common fraction that is easy to use as a reference, such as 1/2, 1/4, 1/8, etc.
Since Mr. Simon is cutting 5 feet from a board that is longer, we can compare 2 feet to a benchmark fraction. The closest benchmark fraction to 2 feet is 1/4 of 8 feet, which is also 2 feet. This means that if Mr. Simon's estimate is correct, he would be left with a board that is about 1/4 of the original length.
Now, let's write an equation to find the exact amount of the longer board that will be left over:
Length of longer board - 5 feet = Length of leftover board
We know that the length of the longer board is L feet. Substituting L into the equation, we get:
L - 5 = Length of leftover board
To solve for L, we can add 5 to both sides of the equation:
L - 5 + 5 = Length of leftover board + 5
L = Length of leftover board + 5
Since Mr. Simon estimates that 2 feet of the longer board will be left over, we can substitute 2 for Length of leftover board:
L = 2 + 5
L = 7
Therefore, the exact amount of the longer board that will be left over is 7 feet. This is larger than Mr. Simon's estimate of 2 feet, so his estimate is not reasonable.
Explanation: