Question

4
a. suppose the farmer buys another \\(\frac{1}{2}\\) square mile of land and divides all his land into square fields \\(\frac{1}{4}\\) mile long and \\(\frac{1}{4}\\) mile wide. how many fields will he have?
\underline{32} fields
b. what is the total area of his land in square miles?
\underline{2} square miles
(image shows a rectangle with length \\(1\frac{1}{2}\\) miles and width 1 mile)

Explanation:

Part a

Step1: Find original land area

The original land is a rectangle with length \(1\frac{1}{2}=\frac{3}{2}\) miles and width \(1\) mile. Area = length × width = \(\frac{3}{2}×1=\frac{3}{2}\) square miles.

Step2: Add new land area

New land is \(\frac{1}{2}\) square mile. Total area = \(\frac{3}{2}+\frac{1}{2}=\frac{4}{2} = 2\) square miles.

Step3: Find area of one field

Each field is a square with side \(\frac{1}{4}\) mile. Area = \(\frac{1}{4}×\frac{1}{4}=\frac{1}{16}\) square miles.

Step4: Calculate number of fields

Number of fields = total area ÷ area per field = \(2\div\frac{1}{16}=2×16 = 32\).

Step1: Identify original land dimensions

Original land length: \(1\frac{1}{2}=\frac{3}{2}\) miles, width: \(1\) mile. Area = \(\frac{3}{2}×1=\frac{3}{2}\) square miles.

Step2: Add new land area

New land: \(\frac{1}{2}\) square mile. Total area = \(\frac{3}{2}+\frac{1}{2}=\frac{4}{2}=2\) square miles.

Answer:

32

Part b