1/4 + 3/8 Reduce your Answer to the lowest term?
The Correct answer and Explanation is:
To solve the problem ( \frac{1}{4} + \frac{3}{8} ) and reduce the answer to its lowest terms, we can follow these steps:
Step 1: Find a Common Denominator
The denominators in the fractions are 4 and 8. The least common denominator (LCD) for these two numbers is 8, since 8 is the smallest multiple that both 4 and 8 share.
Step 2: Convert Fractions to Have the Same Denominator
Next, we need to convert ( \frac{1}{4} ) to an equivalent fraction with a denominator of 8. To do this, we can multiply both the numerator and the denominator of ( \frac{1}{4} ) by 2:
[
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
]
Now we can add ( \frac{2}{8} ) and ( \frac{3}{8} ).
Step 3: Add the Fractions
Now that both fractions have the same denominator, we can add them:
[
\frac{2}{8} + \frac{3}{8} = \frac{2 + 3}{8} = \frac{5}{8}
]
Step 4: Reduce the Fraction to Lowest Terms
The fraction ( \frac{5}{8} ) is already in its simplest form. This is because the numerator (5) and the denominator (8) have no common factors other than 1. In other words, 5 is a prime number, and it does not divide evenly into 8.
Conclusion
Thus, the final answer is:
[
\frac{1}{4} + \frac{3}{8} = \frac{5}{8}
]
This solution not only demonstrates the method for adding fractions with different denominators but also reinforces the importance of reducing fractions to their lowest terms. Understanding how to find a common denominator and simplifying fractions is fundamental in mathematics, especially in algebra and higher-level calculations where precise numerical representation is critical.