Adding Fractions – Example

UNDERSTANDING THE ADDITION OF FRACTIONS

Adding fractions is a key mathematical skill that students learn in elementary school. This process is important for understanding how to combine parts of a whole or compare different parts. Fractions are composed of a numerator, which is the number above the line, and a denominator, which is the number below the line. The numerator tells us how many parts of the whole we have, and the denominator tells us into how many equal parts the whole is divided.

When we add fractions with like denominators, the process involves simply adding the numerators, while the denominator remains unchanged. This is because the same denominator means that all parts are of equal size. For example, when adding 1/4 and 3/4, we add the numerators 1 and 3, while the denominator 4 remains the same, resulting in 4/4 or 1.

If, however, we are adding fractions with different denominators, we must first find a common denominator. A common denominator is a number that is a multiple of all the denominators of the fractions being considered (typically the least common multiple, LCM). Once we find a common denominator, we adjust the numerators to reflect the new common denominator, and then add the adjusted numerators.

This skill is useful in many everyday situations, such as cooking, measuring distances, or solving mathematical problems. Understanding this concept helps students develop good mathematical skills and better understand the world around them.

EXAMPLE

For a practical example, let's take the fractions 1/6 and 2/6. Since both fractions have the same denominator (6), we can simply add the numerators:

1/6 + 2/6 = (1 + 2) / 6 = 3/6.

After simplification (by dividing the numerator and denominator by their greatest common divisor, which is 3), we get 1/2. This means that the total value of the fractions 1/6 and 2/6 is equal to 1/2. This example shows how easily we add fractions with like denominators and how we can simplify the result.