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In algebra, like terms are terms that have the same variables raised to the same power. This is an important concept because only like terms can be combined or simplified. Understanding like terms is crucial in simplifying algebraic expressions.

For example, in the expression \(3.4m - 4 - 3.4m - 7\), we identify like terms by looking at the variable part. Here, \(3.4m\) and \(-3.4m\) are like terms because they both contain the variable \(m\). The numerical parts (coefficients) can differ, but as long as the variable factors match, they are considered like terms.

When simplifying, the first step is to group like terms together. In some expressions, terms might look different at first glance but focus on the variables to group them correctly. Recognizing like terms allows you to simplify expressions efficiently and avoid mistakes that could complicate further calculations.

Arithmetic operations involve the basic math processes of addition, subtraction, multiplication, and division. In the context of simplifying expressions, these operations are used to combine numbers and adjust terms.

Once like terms are identified and combined, arithmetic operations are performed on the standalone numbers, or constants. In the example \(3.4m - 4 - 3.4m - 7\), once like terms are combined to zero \((0 - 4 - 7)\), this leaves us with straightforward arithmetic to handle.

Subtract 4 from 0, which remains \(-4\), then continue the subtraction with \(-7\), resulting in \(-11\). Keep an eye on negative signs; they are crucial when determining the final outcomes of these operations. Practicing these operations helps in swiftly handling even complex expressions, as arithmetic becomes second nature.

Combining like terms is a fundamental step in simplifying algebraic expressions. This process involves merging terms that have the same variables, balancing the equation to make it as simple as possible.

Take our original example, \(3.4m - 4 - 3.4m - 7\). We identified \(3.4m\) and \(-3.4m\) as like terms. To combine them, you simply add or subtract their coefficients. In this case, doing the math gives you \(3.4m - 3.4m = 0\). Once combined, these terms effectively cancel each other out, simplifying the expression significantly by removing variable terms.

The skill of efficiently combining like terms saves time and effort, especially when handling large expressions. It also ensures that expressions are reduced to their simplest form, making them easier to work with for further calculations or problem-solving.