Explanation: The concept of "half" in mathematics is a fundamental arithmetic operation that involves dividing a number by two. This operation is often used in various contexts, including everyday calculations, financial transactions, and competitive examinations.
To understand the concept of "half," let's break it down:
1. **Definition of Half**: Half of a number is the result of dividing that number by 2. Mathematically, if \( x \) is a number, then half of \( x \) is \( \frac{x}{2} \).
2. **Calculation**: To find half of 250, we perform the division \( 250 \div 2 \). This can be done step-by-step:
- First, divide the hundreds place: \( 2 \div 2 = 1 \).
- Next, divide the tens place: \( 5 \div 2 = 2 \) with a remainder of 1.
- Finally, divide the units place: \( 10 \div 2 = 5 \) (considering the remainder from the tens place).
Combining these results, we get \( 125 \).
3. **Verification**: To verify the result, we can multiply 125 by 2 to see if we get back to 250:
- \( 125 \times 2 = 250 \).
4. **Application in Competitive Exams**: Questions involving basic arithmetic operations like finding half of a number are common in various competitive examinations such as SSC, UPSC, Bank PO, Clerk, and RRB. These questions test the candidate's ability to perform quick and accurate calculations.
5. **Common Misconceptions**: Students might sometimes confuse the concept of "half" with other fractions like one-third or one-fourth. It is important to remember that "half" specifically means dividing by 2.
In conclusion, the statement "Half of 250 is 125" is true because the division \( 250 \div 2 \) yields 125. This is a straightforward application of the concept of halving a number, which is a basic arithmetic operation that is essential for solving various types of problems in competitive examinations.