What is the common denominator of 3/8 and 1/4 ?
The Correct Answer and Explanation is:
To find the common denominator of the fractions ( \frac{3}{8} ) and ( \frac{1}{4} ), we first identify the denominators of the two fractions, which are 8 and 4, respectively. The common denominator is the least common multiple (LCM) of these two numbers.
Step 1: List the multiples.
We begin by listing the multiples of each denominator:
- Multiples of 8: 8, 16, 24, 32, 40, …
- Multiples of 4: 4, 8, 12, 16, 20, 24, …
Step 2: Identify the least common multiple.
From the lists, we see that the smallest common multiple is 8. Therefore, the least common multiple of 8 and 4 is 8.
Step 3: Convert fractions if necessary.
Next, we need to express both fractions with this common denominator:
- The fraction ( \frac{3}{8} ) already has a denominator of 8, so it remains ( \frac{3}{8} ).
- The fraction ( \frac{1}{4} ) needs to be converted. To do this, we can multiply the numerator and denominator of ( \frac{1}{4} ) by 2 (since ( 4 \times 2 = 8 )):
[
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
]
Now, both fractions are expressed with the common denominator of 8:
- ( \frac{3}{8} )
- ( \frac{2}{8} )
Conclusion:
The common denominator of ( \frac{3}{8} ) and ( \frac{1}{4} ) is 8. This common denominator allows us to add, subtract, or compare these fractions more easily. It is important to find the least common denominator when working with fractions to ensure operations can be performed accurately. Understanding the concept of common denominators is foundational in fraction operations and helps streamline mathematical processes involving fractions.