Problem 17 - Elementary Algebra

Question

For the following problems, simplify each of the algebraic expressions. $$ 5 m-3 m $$

Step-by-Step Solution

Answer

Answer: The simplified form of the algebraic expression is \(2m\).

Step 1: Identify Like Terms

In the expression \(5m - 3m\), both terms involve the variable \(m\). So, these two terms are like terms.

Step 2: Combine Like Terms

Since the terms are like terms, they can be combined by simply performing the subtraction operation. Subtract the coefficients of the like terms: \(5 - 3 = 2\). Keep the variable (\(m\)) as it is.

Step 3: Write the Simplified Expression

After combining the like terms, the simplified expression is \(2m\). So the simplified algebraic expression is: $$ 2m $$

Key Concepts

Like Terms

Understanding like terms in algebra is crucial for simplifying expressions. Like terms are terms within an algebraic expression that have exactly the same variable parts raised to the same powers. For example, in the terms 2x and 5x, both have the variable x. This means these two are like terms. However, 3x^2 and 2x are not like terms because the variable x is raised to different powers. Identifying like terms is the first step in simplifying an algebraic expression.

• Terms with the same variable and power are considered 'like terms'
• Constants without any variables are also like terms with each other

Combining Like Terms

Once like terms are identified, the next step is to combine like terms. This means that we add or subtract the coefficients (numbers in front of the variables) while keeping the variable part unchanged. In our example, 5m and -3m are like terms, so we can combine them. Think of it like bringing together similar fruits; if you have 5 apples and you take away 3 apples, you end up with 2 apples. Similarly, with like terms, if you have 5m and take away 3m, you get 2m.

• Adding or subtracting the coefficients of like terms simplifies the expression
• The variables do not change when combining like terms

Algebraic Expression Simplification

The simplification of an algebraic expression involves reducing it to its simplest form. This is done by combining like terms and performing operations according to the order of operations, if necessary. The goal is to make the expression as straightforward and as easy to understand as possible. When simplifying, always remember to first combine like terms, then use the correct arithmetic operations (addition, subtraction, multiplication, and division) as needed.

• Simplify expressions step by step, combining like terms first
• Follow the order of operations (parentheses, exponents, multiplication and division, addition and subtraction)

Subtraction of Coefficients

In algebra, the subtraction of coefficients occurs when we are combining like terms that involve subtraction. The coefficients are the numbers that are multiplied by the variables. When you subtract coefficients, you're essentially calculating the difference between the amounts each term contributes to the total. For example, in 5m - 3m, we subtract the coefficient 3 from the coefficient 5, which simplifies to 2m. The variable m stays the same because we are only interested in how many ms we have after taking some away.

• Only subtract coefficients when combining like terms with subtraction involved
• Keep the variable part of the term the same