Constant vs. Variable
Grade 8 math lesson on the difference between constants and variables in algebra. Students learn to identify fixed quantities as constants and changing or unknown quantities as variables, and understand how this distinction forms the foundation for writing algebraic expressions and equations.
Key Concepts
Property A constant is a number whose value never changes, like 4 or 10. A variable is a letter, like x or s, that is used to represent a number whose value can change or is unknown.
Examples In the expression $7y + 2$, the numbers 7 and 2 are constants, while $y$ is the variable. In the taxi fare formula $3m + 2 = c$, the 3 (cost per mile) and 2 (flat fee) are constants. The letters $m$ (miles) and $c$ (cost) are variables.
Explanation Imagine a constant is your birthday—the date is fixed! A variable is like the weather; it can be different every day. In algebra, numbers stand still, but letters represent values that can change.
Common Questions
What is the difference between a constant and a variable?
A constant is a fixed number that never changes, like 5 or -3.14. A variable is a letter representing a quantity that can change or is unknown, like x or y. In 3x + 7, 3 and 7 are constants (or coefficients/constants) and x is the variable.
What are examples of constants in math?
Examples of constants include specific numbers like 5, -2, 3.14, or mathematical constants like pi or e. In an expression like 2x + 3, the number 3 is a constant because it never changes regardless of the value of x.
What are examples of variables in algebra?
Variables are letters like x, y, n, or t that represent unknown or changing quantities. In the equation d = rt (distance = rate times time), all three letters are variables that can take different values.
Why do we use variables in math?
Variables allow us to write general rules and equations that work for any number, not just a specific one. Instead of writing a separate equation for each situation, one equation with variables covers all cases.