Calculating the Fractional Part of an Uncut Lawn

In this article, we will explore a typical problem in geometry and arithmetic related to calculating the fractional part of an uncut lawn. This kind of problem often appears in mathematics and can help students and teachers better understand the concepts of area, fractions, and problem-solving techniques.

Problem Overview

Josh has a rectangular lawn measuring 40 feet in length and 30 feet in width. He has mowed most of the lawn but left a small rectangular section uncut, measuring 12 feet in length and 9 feet in width. To determine how much of the lawn remains uncut, we must calculate the area of the entire lawn and the area that Josh has left uncut.

Solution Steps

Total Area of the Lawn

To start, we calculate the total area of the lawn using the formula for the area of a rectangle: Area Length x Width.

Total Area 40 feet x 30 feet 1200 square feet (ft2)

Uncut Area of the Lawn

Next, we calculate the area of the uncut section of the lawn using the same formula.

Uncut Area 12 feet x 9 feet 108 square feet (ft2)

Fractional Part of the Uncut Area

Now, we need to determine what fractional part of the lawn remains uncut. This involves dividing the uncut area by the total area.

Fractional Part Uncut 108 ft2 / 1200 ft2

After simplifying the fraction, we get:

108 / 1200 9 / 100

Thus, the fractional part of the lawn that remains uncut is 9 / 100.

Alternative Methods

There are multiple ways to approach this problem:

Method 1: Direct Calculation

Using the direct method, we calculate the area of the remaining uncut section and then divide it by the total area.

The remaining uncut area is a small rectangle with 20 ft x 15 ft 300 ft2. The total area is 1200 ft2.

The fractional part of the uncut area is 300 ft2 / 1200 ft2 1/4.

Method 2: Visualization

A more intuitive method involves visualizing the lawn and breaking it into sections. The lawn is a large rectangle (40 feet by 30 feet) with a smaller rectangular section (12 feet by 9 feet) left uncut. By mentally dividing the lawn into four equal rectangles, it becomes clear that the uncut section represents one quarter of the whole lawn.

Thus, the fractional part of the lawn that remains uncut is 1/4.

Conclusion

Understanding how to calculate the fractional part of an uncut lawn not only helps in solving practical problems but also enhances problem-solving skills in mathematics. This problem demonstrates the application of basic arithmetic and the importance of visualizing geometric shapes.