Imagine you’re riding a taxi. The base fare is ₱40, and for each kilometer you travel, the fare increases by ₱10. If you travel 5 kilometers, how would you calculate the total fare?
This is where understanding equations becomes useful.
An equation is a mathematical statement that shows that two things are equal. It’s like a balance scale where both sides must be equal.
Definition
Equation: A statement that the values of two mathematical expressions are equal (indicated by the sign =).
What symbol indicates that two mathematical expressions are equal?
Variables and Constants
In equations, we use variables to represent unknown values and constants to represent fixed values. Variables are usually denoted by letters like , , or , while constants are specific numbers.
Variables
Variable: A symbol, usually a letter, that represents a number we do not know yet. The value of the variable can change.
What is a variable in mathematics?
For example, in the equation , is the variable. It stands for a number that makes the equation true when added to 5.
Constants
Constant: A fixed value that does not change. It is a number on its own.
What is a constant in mathematics?
For example, in the equation , the numbers 5 and 10 are constants because their values do not change.
Coefficients
Coefficient: A number used to multiply a variable.
What is a coefficient?
For example, in , 3 is the coefficient because it is multiplied by .
Example Scenario
Suppose the taxi fare equation is , where:
is the total fare.
is the base fare (constant).
represents the additional cost per kilometer traveled (where is the number of kilometers).
Exponents
An exponent indicates how many times a number (the base) is multiplied by itself.
Example
In the expression , 2 is the base, and 3 is the exponent, meaning .
What does an exponent indicate in mathematics?
Practice with Basic Terms
Get familiar with these terms by identifying the variables and constants in simple expressions.
In the expression 3x+5=20, what is the variable?
In the expression 2x+7=15, what is the constant?
Identify the coefficient in the term 4y.
In the expression 53, what is the exponent?
Test Yourself
What is the variable in the equation y+3=8?
Identify the constant in the equation 4k−5=11.
In the expression 5m2, what is the exponent?
What is the base in the expression 73?
In the equation 3n+4=19, what is the variable?
Identify the exponent in 9x4.
In the equation a−6=2, what is the variable?
Find the constant in the equation 7y+8=22.
What is the variable in 5z3?
In the expression 8b+10, what is the coefficient of b?
Additional Context
Why is understanding basic algebra terms important?
Grasping the fundamentals of algebra, like variables and constants, is crucial as they form the building blocks for more advanced math topics. Understanding these basics helps in solving real-world problems efficiently.
How do variables and constants apply in everyday life?
Variables and constants are used in various real-life scenarios, such as calculating budgets, understanding scientific formulas, and even in computer programming where values change or remain the same.
How can I improve my familiarity with algebraic terms?
Practice regularly with examples and exercises, use visual aids to understand concepts better, and apply these terms to real-world scenarios to see their practical use.
Key Takeaways
An equation is a statement that two expressions are equal.
Variables represent unknown values in equations.
Constants are fixed values.
Coefficients multiply variables.
Exponents indicate repeated multiplication.
Understanding these terms is essential for progressing in algebra and solving real-world problems.
