Find the least common denominator (LCD) of 3/8 and 1/2
The Correct Answer and Explanation is:
The least common denominator (LCD) of 3/8 and 1/2 is 8.
To find the least common denominator, first identify the denominators of both fractions. In this case, the denominators are 8 and 2. The LCD is the smallest number that both 8 and 2 divide into evenly.
Begin by listing a few multiples of each denominator:
- Multiples of 8: 8, 16, 24, 32, 40, …
- Multiples of 2: 2, 4, 6, 8, 10, 12, …
The smallest number common to both lists is 8. Therefore, 8 is the least common denominator.
Next, convert each fraction so that it has a denominator of 8.
- The fraction 3/8 already has 8 as its denominator, so it remains unchanged.
- The fraction 1/2 must be converted to an equivalent fraction with 8 as the denominator. Since 2 × 4 = 8, multiply both the numerator and denominator of 1/2 by 4:
1/2=(1×4)/(2×4)=4/81/2 = (1 × 4)/(2 × 4) = 4/81/2=(1×4)/(2×4)=4/8
Now both fractions—3/8 and 4/8—have the same denominator. This makes addition, subtraction, or comparison of the fractions easier.
The importance of using the least common denominator lies in its efficiency. By choosing the smallest shared multiple of the denominators, calculations become simpler and require less simplification afterward. Using a larger common denominator, such as 16 or 32, would still work but would involve unnecessary steps and possible reduction later.
In summary, the least common denominator of 3/8 and 1/2 is 8. Converting both fractions to have this denominator allows for straightforward comparison or arithmetic operations. This technique is essential in handling problems involving fractions with different denominators.
