Question

a farmer has one square mile of land. ① if he divides his land into square fields that are \\(\frac{1}{2}\\) mile long and \\(\frac{1}{2}\\) mile wide, how many fields will he have? \\(\underline{\quad\quad}\\) fields

Explanation:

Step1: Find area of each small field

The area of a rectangle (or square, since length and width are equal here) is given by \( A = \text{length} \times \text{width} \). For each small field, length \( l=\frac{1}{2} \) mile and width \( w = \frac{1}{2} \) mile. So, the area of one small field is \( A_{\text{small}}=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4} \) square miles.

Step2: Find total number of fields

The total area of the land is 1 square mile. To find the number of small fields, we divide the total area by the area of one small field. Let \( n \) be the number of fields. Then \( n=\frac{\text{Total Area}}{\text{Area of one small field}}=\frac{1}{\frac{1}{4}} \). When dividing by a fraction, we multiply by its reciprocal, so \( n = 1\times4 = 4 \).

Answer:

4