Question

Find the terms of the expression. $$4 w-11$$

Short answer

The terms of the expression \(4w - 11\) are \(4w\) and \(-11\).

Step-by-step solution

Identify the terms

An algebraic expression like \(4w - 11\) is made up of different parts. The terms are parts of the expression that are added or subtracted. Here, \(4w\) and \(-11\) are the two terms.

Define the terms

The term \(4w\) is a variable term, where \(w\) is the variable and 4 is the coefficient. The term \(-11\) is a constant term because it does not change its value.

Key concepts

Terms of an Expression

Understanding algebraic expressions is a foundational aspect of algebra. An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y), and operators (such as add, subtract, multiply, and divide).

Within these expressions, we have terms. The terms are the building blocks of algebraic expressions. They are separated by addition or subtraction signs. For example, in the expression 4w - 11, there are two terms: 4w and -11. It's important to recognize that these terms can vary greatly in complexity, from simple numbers to more complex variables with coefficients. To successfully identify the terms in an expression, simply look for parts of the expression that are added or subtracted from each other.

Variable Terms

When dissecting algebraic expressions, we'll often spot variable terms. These are terms that include variables – placeholders for any number – combined typically with numbers called coefficients.

A variable term can change its value depending on what number the variable represents. Take the term 4w from our earlier example. Here, w is the variable, and it could represent any number. The number 4 is the coefficient, which multiplies the variable. In this case, the value of 4w can change based on the value of w, hence, it is a variable term. Variable terms are crucial because they allow algebraic expressions to represent patterns and general mathematical relationships, rather than one specific number.

Constant Terms

Not all terms in an algebraic expression will change their value. Constant terms are the terms in an equation that remain the same, no matter what the variables are. In the expression 4w - 11, while 4w is a variable term that can change, the -11 is a constant term.

It's called 'constant' because it doesn't contain any variables, so it always represents the same value. These constants are the fixed parts of algebraic expressions. If you have a numerical term without a variable, you've identified a constant term. Being able to identify constant terms correctly is essential, as they are a key part of solving equations and simplifying expressions.