Which expression represents “one half of x
A. x × 2
B. x÷2
C. x -1/2
D. x +1/ 2
The Correct answer and Explanation is:
The expression that represents “one half of xxx” is B. x÷2x \div 2x÷2.
Explanation:
To understand why x÷2x \div 2x÷2 is the correct representation of “one half of xxx, we need to delve into the basic concepts of fractions and division.
- Understanding One Half: The term “one half” mathematically translates to the fraction 12\frac{1}{2}21. When we say “one half of xxx, we are referring to taking the total value of xxx and dividing it into two equal parts. Thus, we can express this as:12×x\frac{1}{2} \times x21×xor equivalently,x÷2x \div 2x÷2Both expressions yield the same result, confirming that dividing xxx by 2 gives us one half of its value.
- Analysis of Other Options:
- Option A: x×2x \times 2x×2: This expression means multiplying xxx by 2, which results in double the value of xxx, not half. For example, if x=4x = 4x=4, then x×2=8x \times 2 = 8x×2=8, which is incorrect.
- Option C: x−12x – \frac{1}{2}x−21: This expression indicates that we are subtracting 12\frac{1}{2}21 from xxx. For instance, if x=4x = 4x=4, then x−12=3.5x – \frac{1}{2} = 3.5x−21=3.5, which does not represent half of xxx.
- Option D: x+12x + \frac{1}{2}x+21: This expression adds 12\frac{1}{2}21 to xxx. For example, if x=4x = 4x=4, then x+12=4.5x + \frac{1}{2} = 4.5x+21=4.5. Again, this does not represent half of xxx.
- Mathematical Operations: Dividing by a number is a fundamental operation that allows us to find parts of a whole. In this case, x÷2x \div 2x÷2 efficiently computes what half of xxx would be.
In conclusion, the expression that correctly represents “one half of xxx” is B. x÷2x \div 2x÷2, as it directly applies the mathematical concept of division to determine half the value of xxx.