College Algebra

The fraction \(\frac{4}{3}\) is already in its simplest form because the numerator (4) and the denominator (3) do not have any common factors other than 1. Therefore, it cannot be simplified further. When a fraction is in its simplest form, it means that there is no number, except for 1, that can be divided evenly into both the numerator and the denominator. In real-world measurements, the fraction \(\frac{4}{3}\) is significant in various contexts. Here are a few examples: 1. **Aspect Ratio**: In visual media, the aspect ratio of \(\frac{4}{3}\) (or 4:3) is a standard dimension for television screens and computer monitors, particularly before the wide adoption of the 16:9 widescreen format. It means that for every 4 units of width, there are 3 units of height. 2. **Volume of a Sphere**: The formula for the volume of a sphere involves the fraction \(\frac{4}{3}\). The volume \(V\) is given by \(V = \frac{4}{3} \pi r^3\), where \(r\) is the radius of the sphere. This fraction is an integral part of the formula derived from calculus, and it is essential for calculations in geometry and physics. 3. **Photography**: In photography, the \(\frac{4}{3}\) ratio is used in the Four Thirds system, which is a standard created by Olympus and Eastman Kodak for digital single-lens reflex camera (DSLR) design and development. 4. **Cooking**: In recipes, fractions like \(\frac{4}{3}\) cups might be used to describe proportions of ingredients. This would be equivalent to 1 cup plus 1/3 cup of the ingredient. 5. **Engineering**: In engineering, the fraction \(\frac{4}{3}\) might appear in calculations of stress or strain, gear ratios, or other design parameters that involve ratios or proportions. In summary, the fraction \(\frac{4}{3}\) is already in its simplest form and cannot be reduced. It plays a significant role in various real-world applications, from technology and media to cooking and scientific calculations.

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