Alec B. answered • 09/12/17
Tutor
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Masters Level Physicist with Enthusiasm to Teach Math and Physics!
The first step in making sure we understand this question is to make sure we know what SHAPE we are talking about (different shapes may have different equations to solve for the area of that shape).
In this instance it sounds like the shape we are dealing with is a rectangle. For a rectangle, the area is the length multiplied by the width. The equation would look like this: (A = L*W); where A = area, L = length (one mile), and W = width (one and one half miles).
From that we know that the area is equal to one mile multiplied by one and a half miles. Important side note!: we want to make sure we have everything in the same units which we do in this case (miles).
Now, some students are more comfortable with numbers written as fractions while others are more comfortable with numbers written with decimal points. I will do both below:
Fractions: one multiplied by one and one half is easiest to discuss in terms of halves, since that's our smallest fraction we are working with. The number "one" in terms of halves: (1 = 2/2) or two halves. The number "one and one half" written in terms of halves would be: (1 + 1/2) = (2/2 + 1/2) = (3/2) or three halves. Multiplying the length by the width would then give us the solution for the area: (2/2)*(3/2) = (6/4) which could also be simplified to (3/2) square miles for your final answer.
Decimals: one multiplied by one and one half is the same as saying: (1)*(1.5). Therefor, to find the area we have A = L*W = (1)*(1.5) = 1.5 square miles which agrees with the above solution as 1.5 is equal to (3/2).
