use a common denominator to write an equivalent fraction for 1/2 and 3/8
The Correct Answer and Explanation is:
To write equivalent fractions for 1/2 and 3/8 using a common denominator, the least common denominator (LCD) of the two fractions must be found. The denominators are 2 and 8. The least common multiple (LCM) of 2 and 8 is 8. Therefore, both fractions will be rewritten with 8 as the denominator.
The fraction 3/8 already has 8 as the denominator, so it remains unchanged.
To convert 1/2 to a fraction with a denominator of 8, multiply both the numerator and the denominator by 4:1/2=(1×4)/(2×4)=4/81/2 = (1 × 4) / (2 × 4) = 4/81/2=(1×4)/(2×4)=4/8
So, the two equivalent fractions with the same denominator are:1/2=4/8and3/8=3/81/2 = 4/8 \quad \text{and} \quad 3/8 = 3/81/2=4/8and3/8=3/8
Explanation (300 words):
Fractions are mathematical expressions that represent parts of a whole. When comparing or combining fractions, it is important to have a common denominator. This common denominator helps align the fractions to the same “unit size,” which makes addition, subtraction, and comparison possible.
In this case, the fractions 1/2 and 3/8 need to be rewritten with the same denominator. The process begins by identifying the least common denominator. The original denominators are 2 and 8. Listing the multiples of each helps determine the least common multiple. The multiples of 2 are 2, 4, 6, 8, 10, and so on. The multiples of 8 are 8, 16, 24, and so on. The first shared value is 8, making it the least common denominator.
The next step involves rewriting 1/2 with 8 as the denominator. Since 2 multiplied by 4 equals 8, the numerator must also be multiplied by 4 to keep the value of the fraction the same. This transforms 1/2 into 4/8. The other fraction, 3/8, already has 8 as the denominator, so no change is needed.
With both fractions now having the same denominator, 4/8 and 3/8 can be directly compared or combined. This method ensures that operations involving fractions are accurate and consistent.
