Simplifying Algebraic Expressions: (m + n + 3) + (m + n + 4)
In mathematics, we often encounter expressions involving variables and constants. Simplifying these expressions makes them easier to understand and work with. Let's take a look at how to simplify the expression (m + n + 3) + (m + n + 4).
Understanding the Expression
The expression consists of two sets of parentheses, each containing a combination of variables (m, n) and constants (3, 4). The plus sign between the parentheses indicates that we need to add the terms within each set.
Simplifying the Expression

Remove the parentheses: Since there are only addition signs within the parentheses, we can remove them without changing the expression's value.
(m + n + 3) + (m + n + 4) = m + n + 3 + m + n + 4

Combine like terms: We can combine the terms that have the same variables or are constants:
m + n + 3 + m + n + 4 = 2m + 2n + 7
The Simplified Expression
The simplified form of the expression (m + n + 3) + (m + n + 4) is 2m + 2n + 7.
Key Points
 Commutative property of addition: The order of addition doesn't change the result (e.g., m + n = n + m).
 Associative property of addition: The grouping of terms doesn't change the result (e.g., (m + n) + 3 = m + (n + 3)).
 Combining like terms: We can add terms with the same variables or constants together.
Simplifying algebraic expressions is an essential skill in mathematics. By understanding the properties of addition and how to combine like terms, we can effectively manipulate expressions to make them easier to work with.