Imagine you have a wall, and you decide to paint a portion of it. To determine what fraction of the wall is painted, we need to follow a few simple steps. Let’s break it down.
Step-by-Step Process
- Measure the Total Area of the Wall
First, you need to measure the total area of the wall. If the wall is rectangular, you can find the area by multiplying the height by the width. For example, if the wall is 10 feet high and 15 feet wide, the area is:
$A_{total} = text{height} times text{width} = 10 text{ ft} times 15 text{ ft} = 150 text{ square feet}$
- Measure the Painted Area
Next, measure the area that has been painted. Suppose you painted a section that is 5 feet high and 10 feet wide. The painted area is:
$A_{painted} = text{height} times text{width} = 5 text{ ft} times 10 text{ ft} = 50 text{ square feet}$
- Calculate the Fraction
To find the fraction of the wall that is painted, divide the painted area by the total area of the wall. Using our example:
$text{Fraction Painted} = frac{A_{painted}}{A_{total}} = frac{50 text{ square feet}}{150 text{ square feet}} = frac{1}{3}$
Practical Example
Let’s consider a practical example to make it clearer. Suppose you have a wall in your room that measures 8 feet in height and 12 feet in width. The total area of the wall is:
$A_{total} = 8 text{ ft} times 12 text{ ft} = 96 text{ square feet}$
You decided to paint a section that is 4 feet high and 6 feet wide. The painted area is:
$A_{painted} = 4 text{ ft} times 6 text{ ft} = 24 text{ square feet}$
Now, to find the fraction of the wall that is painted:
$ text{Fraction Painted} = frac{A_{painted}}{A_{total}} = frac{24 text{ square feet}}{96 text{ square feet}} = frac{1}{4}$
So, one-fourth of the wall is painted.
Conclusion
Understanding how to calculate the fraction of a painted wall is a useful skill, especially for home improvement projects. By measuring the total area of the wall and the painted area, you can easily determine what fraction of the wall is painted. This method can be applied to any wall, regardless of its size or shape.
3. ThoughtCo – How to Calculate Area