frac{1}{2} of 12 m
The Correct Answer and Explanation is:
The correct answer is 6 meters.
Explanation
The expression 12\frac{1}{2} of 12 meters represents multiplying the fraction 12\frac{1}{2} by 12 meters. This calculation is performed as follows:
12×12=122=6\frac{1}{2} \times 12 = \frac{12}{2} = 6
This result indicates that half of 12 meters is 6 meters. The concept being applied here is the multiplication of fractions and whole numbers, where division is used to find a portion of a given quantity.
Understanding fractions is essential in mathematics because they represent parts of a whole. The fraction 12\frac{1}{2} signifies division into two equal parts. When a quantity such as 12 meters is divided in half, each resulting part measures 6 meters.
This principle is frequently encountered in real-world applications. For instance, splitting a length of rope, dividing distances in construction, or allocating space in measurement-based tasks all require a comprehension of fractional operations. When measuring materials or designing layouts, precise calculations ensure accurate results, avoiding miscalculations that could impact construction or design plans.
Visual representations often enhance understanding. A rectangle or a segment marked as 12 meters can be divided into two equal sections, each measuring 6 meters. This visualization reinforces the concept that dividing by 2 distributes the total evenly, aligning with the fundamental properties of fractions.
Fractions extend beyond simple divisions, playing a critical role in algebra, proportions, and unit conversions. Mastery of this concept aids in grasping more complex mathematical principles that rely on systematic fraction manipulation.
Thus, the process of determining 12\frac{1}{2} of 12 meters is rooted in fundamental arithmetic principles, offering valuable insights into proportional reasoning and measurement applications.
