Final answer:
The Lowest Common Denominator (LCD) for the pair of fractions 1/2 and 1/4 is 4, and when expressed with this LCD, the fractions are 2/4 and 1/4 respectively.
Step-by-step explanation:
To find the Lowest Common Denominator (LCD) for the pair of fractions (1/2 and 1/4), you must find the smallest number that both denominators can divide into without leaving a remainder. In this case, the denominators are 2 and 4. We can see that 4 is the largest denominator and that 2 can divide into 4 without leaving a remainder. Therefore, the LCD is 4.
Once you've identified the LCD, you can express both fractions with that common denominator. For 1/2, multiply the numerator and denominator by 2 to get 2/4. The fraction 1/4 already has the denominator of 4, so it remains the same. Thus, the two fractions with the common denominator are 2/4 and 1/4.