Add or subtract, as indicated. 1/6m + 2/5m + 4/m

Verified step by step guidance

1. Identify the terms to be added: \(\frac{1}{6}m\), \(\frac{2}{5}m\), and \(\frac{4}{1}m\) (note that \(\frac{4}{m}\) means \(4 \times m\), so it can be written as \(\frac{4}{1}m\)).
2. Since all terms have the variable \(m\), you can combine the coefficients by adding the fractions: \(\frac{1}{6} + \frac{2}{5} + 4\).
3. Find the least common denominator (LCD) for the fractions \(\frac{1}{6}\) and \(\frac{2}{5}\). The denominators are 6 and 5, so the LCD is 30.
4. Rewrite each fraction with the denominator 30: \(\frac{1}{6} = \frac{5}{30}\) and \(\frac{2}{5} = \frac{12}{30}\). The whole number 4 can be written as \(\frac{120}{30}\) to have the same denominator.
5. Add the numerators over the common denominator: \(\frac{5}{30} + \frac{12}{30} + \frac{120}{30} = \frac{5 + 12 + 120}{30} = \frac{137}{30}\). Then multiply by \(m\) to get the combined expression: \(\frac{137}{30}m\).

Key Concepts

Like Terms in Algebraic Expressions

Like terms are terms that have the same variable raised to the same power. In this problem, all terms contain the variable 'm', so they can be combined by adding or subtracting their coefficients.

Adding and Subtracting Fractions

To add or subtract fractions, they must have a common denominator. Find the least common denominator (LCD) of the fractions involved, convert each fraction to an equivalent fraction with the LCD, then add or subtract the numerators.

Simplifying Algebraic Expressions

After combining like terms and performing fraction operations, simplify the resulting expression by reducing fractions if possible and combining coefficients to write the expression in its simplest form.