Add or subtract as indicated. Write answers in lowest terms as needed. 3(1/8) + 2(1/4)

Verified step by step guidance

1. Convert the mixed numbers to improper fractions: \(3\left(\frac{1}{8}\right) = \frac{25}{8}\) and \(2\left(\frac{1}{4}\right) = \frac{9}{4}\).
2. Find a common denominator for the fractions. The least common denominator of 8 and 4 is 8.
3. Convert \(\frac{9}{4}\) to an equivalent fraction with a denominator of 8: \(\frac{9}{4} = \frac{18}{8}\).
4. Add the fractions: \(\frac{25}{8} + \frac{18}{8} = \frac{43}{8}\).
5. Since \(\frac{43}{8}\) is an improper fraction, you can convert it to a mixed number if needed.

Key Concepts

Fraction Addition

Fraction addition involves combining two or more fractions into a single fraction. To add fractions, they must have a common denominator. If they do not, you must find the least common denominator (LCD), convert each fraction, and then add the numerators while keeping the denominator the same.

Multiplication of Fractions

Multiplication of fractions is performed by multiplying the numerators together and the denominators together. For example, to multiply 3 by 1/8, you multiply 3 (which can be written as 3/1) by 1/8, resulting in 3/8. This concept is essential for simplifying expressions before performing addition.

Lowest Terms

Writing a fraction in lowest terms means simplifying it so that the numerator and denominator have no common factors other than 1. This is done by dividing both the numerator and denominator by their greatest common divisor (GCD). Ensuring fractions are in lowest terms is important for clarity and accuracy in mathematical expressions.