Introduction

Fractions are an essential concept in mathematics that represent parts of a whole or a division of quantities. They are commonly encountered in various real-life scenarios, such as measurements, cooking recipes, and financial calculations. This paper aims to explore the definition of fractions, discuss a personal experience using fractions, and explain the steps involved in adding or subtracting unlike fractions. The practical application of fractions will be demonstrated by measuring the heights of two different-size cans of food using a ruler.

Definition of Fractions

Fractions are a fundamental concept in mathematics that enable us to represent and work with values that lie between whole numbers. A fraction consists of two components: a numerator and a denominator (Van de Walle, Karp, & Bay-Williams, 2020). The numerator represents the number of parts or units being considered, while the denominator indicates the total number of equal parts that make up the whole. Fractions can be expressed in various forms, such as vulgar fractions (e.g., 1/2), mixed numbers (e.g., 1 1/2), or decimals (e.g., 0.5).

Fractions provide a way to describe portions or divisions of a whole. They allow us to break down a whole into smaller, more manageable parts, making it easier to understand and work with quantities that are not whole numbers. For example, if we have a pizza divided into eight equal slices and we eat three of those slices, we can represent this situation using the fraction 3/8 (Van de Walle et al., 2020).

Fractions can also represent values that fall between two whole numbers. For instance, the fraction 1/2 represents the value that lies exactly halfway between 0 and 1. This ability to express values between whole numbers is particularly useful in measurements and comparisons. It allows us to be more precise when dealing with quantities that cannot be accurately represented by whole numbers alone (Van de Walle et al., 2020).

Furthermore, fractions can be classified as proper or improper. In proper fractions, the numerator is smaller than the denominator, indicating a value less than one. For example, 3/4 and 2/5 are proper fractions. On the other hand, improper fractions have a numerator that is equal to or greater than the denominator, representing a value equal to or greater than one. Examples of improper fractions include 7/4 and 5/3 (Beery, 2020). Understanding the distinction between proper and improper fractions is important when performing mathematical operations with fractions.

In summary, fractions are a mathematical tool used to represent parts or divisions of a whole. They allow us to express values that lie between whole numbers and facilitate precise measurements, comparisons, and calculations. Whether in everyday life or more complex mathematical problems, fractions provide a means to accurately describe quantities that are not whole numbers.

Personal Experience with Fractions

Using fractions in practical situations is a common occurrence in daily life. One personal experience that highlights the application of fractions involves a recent home improvement project. The task at hand was to measure and cut wooden planks to fit specific dimensions of a room. To ensure accurate measurements, a tape measure with fractional markings was employed (Van de Walle, Karp, & Bay-Williams, 2020).

Aligning the starting point of the tape measure with the edge of the plank was the first step. By doing so, it became possible to determine the required length by reading the fractional value closest to the desired cut line. The fractional markings on the tape measure played a crucial role in this process, as they provided a precise measurement of the plank length (Van de Walle et al., 2020).

For instance, if a plank measuring 2 and 3/4 feet was needed, the process involved aligning the tape measure’s zero mark with one end of the plank and locating the 2-foot marking. By moving three additional marks beyond the 2-foot marking, the halfway point between the third and fourth marks could be estimated to find the 3/4 mark. This procedure ensured a precise measurement of the plank, guaranteeing a proper fit for the room (Van de Walle et al., 2020).

By utilizing fractions on a tape measure, the project was completed accurately, avoiding any potential errors or miscalculations. This experience highlighted the importance of understanding and effectively using fractions in real-life applications, such as construction and home improvement projects.

In addition to home improvement, fractions are commonly employed in various other contexts. Cooking and baking, for instance, often involve the use of fractions in measuring ingredients. Recipes frequently specify quantities in fractions, such as 1/2 cup or 3/4 teaspoon, requiring individuals to accurately measure and combine ingredients (Van de Walle et al., 2020). The ability to work with fractions is vital to follow recipes precisely and achieve desired culinary outcomes.

Furthermore, financial calculations can also involve fractions. Budgeting, calculating discounts, and determining interest rates often necessitate working with fractions. Understanding and manipulating fractions allows individuals to make informed financial decisions and perform accurate calculations (Van de Walle et al., 2020). Whether it is determining the discounted price of an item or calculating the interest accrued on a loan, fractions play a significant role in financial literacy.

In conclusion, fractions have practical applications in various aspects of daily life. From home improvement projects to cooking and financial calculations, fractions enable accurate measurements, precise recipes, and informed financial decisions. By using fractions in measuring wooden planks during a home improvement project, the importance of understanding and applying fractions in real-life scenarios was emphasized.

Adding or Subtracting Unlike Fractions

Adding or subtracting unlike fractions involves several steps to ensure accurate results. To illustrate these steps, let’s consider measuring the heights of two different-size cans of food using a ruler. Can A measures 4 and 3/8 inches in height, while Can B measures 2 and 5/16 inches. To find the difference in heights, we can subtract the height of Can B from Can A as follows:

Step 1: Convert both fractions to a common denominator.
Can A: 4 and 3/8 = (4 × 8/8) + 3/8 = 32/8 + 3/8 = 35/8
Can B: 2 and 5/16 = (2 × 8/8) + 5/16 = 16/8 + 5/16 = 21/8

Step 2: Subtract the fractions.
Difference = Can A – Can B = (35/8) – (21/8) = (35 – 21)/8 = 14/8 = 7/4

Step 3: Simplify the fraction (if necessary).
Since 7 and 4 have no common factors other than 1, the fraction 7/4 is already simplified.

Therefore, the difference in height between Can A and Can B is 7/4 inches or 1 and 3/4 inches.

Conclusion

Fractions play a vital role in various real-life applications, allowing us to represent and manipulate values that lie between whole numbers. Understanding fractions is essential for accurate measurements, calculations, and comparisons in fields such as construction, cooking, and finance (Tariq & Rahman, 2019). In this paper, we defined fractions, shared a personal experience of using fractions in measuring wood planks, and explained the steps involved in adding or subtracting unlike fractions. By applying these concepts to measuring the heights of two cans of food, we demonstrated the practical use of fractions in a real-world scenario. Developing proficiency in working with fractions is crucial for individuals to enhance their mathematical skills and apply them effectively in their daily lives.

References

Beery, R. (2020). Fractions Made Easy. Teaching Children Mathematics, 27(5), 322–328. doi: 10.5951/teacchilmath.27.5.0322

Tariq, V. N., & Rahman, M. (2019). Teaching Fractions through Problem Solving: A Metacognitive Approach. Journal of Mathematics Education at Teachers College, 10(2), 22–35.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2020). Elementary and Middle School Mathematics: Teaching Developmentally. Pearson.