Add or subtract, as indicated. See Example 4. 1 2 4—— + —— + —— 6m 5m m

Verified step by step guidance

1. Identify the least common denominator (LCD) for the fractions. The denominators are \(6m\), \(5m\), and \(m\).
2. The LCD is the least common multiple of the denominators. Since all denominators have \(m\), focus on the numerical coefficients: 6, 5, and 1. The LCM of 6, 5, and 1 is 30.
3. Rewrite each fraction with the LCD as the new denominator. Multiply the numerator and denominator of each fraction by the necessary factor to achieve the LCD.
4. For \(\frac{1}{6m}\), multiply by \(\frac{5}{5}\) to get \(\frac{5}{30m}\). For \(\frac{2}{5m}\), multiply by \(\frac{6}{6}\) to get \(\frac{12}{30m}\). For \(\frac{4}{m}\), multiply by \(\frac{30}{30}\) to get \(\frac{120}{30m}\).
5. Add the fractions by combining the numerators over the common denominator: \(\frac{5}{30m} + \frac{12}{30m} + \frac{120}{30m} = \frac{5 + 12 + 120}{30m}\).

Key Concepts

Common Denominator

To add or subtract fractions, it is essential to have a common denominator. The common denominator is a shared multiple of the denominators of the fractions involved. In this case, for the fractions 6m, 5m, and m, the least common multiple must be determined to combine them effectively.

Fraction Addition/Subtraction

Adding or subtracting fractions involves combining the numerators while keeping the common denominator. The formula for this operation is (a/b) + (c/d) = (ad + bc) / bd. Understanding how to manipulate the numerators and maintain the denominator is crucial for accurate calculations.

Simplifying Fractions

After performing addition or subtraction on fractions, the result may need to be simplified. Simplifying involves reducing the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). This step ensures the final answer is presented in the simplest form.