Interpreting the parts of expressions and equations gives students a basic level of understanding that is vital to higher level processes. This “vocabulary” knowledge in mathematics holds the key to future understanding of theorems, solving equations, and working with complex processes and number systems.
The important vocabulary for this concept is:
terms coefficients constants like terms
The parts of an expression that are added(or subtracted) together are called the terms. This expression has 4 terms, 4x, -8, y, and -3.
The number part of a term with a variable part is called the coefficient of the term, 4 and 1 are the coefficients in this equation.
A constant term has a number part but no variable part, such as -8 and -3 in the expression above.
Like terms are terms that have the same variable parts. Notice 4x and y are not like terms, because their variables are different, and all constants are like terms with each other because of the absence of a variable.
The expression below also does not have any like terms. Even though each of the variable terms contain an x, they are different types of x. The only number that will not affect the “nature” of the term in terms of like terms is the coefficient. Here, the variable (or smaller number) distinguishes theses are different types of x.
As you progress through your mathematical journey you will be faced with a growing level of complexity in the expressions and equations you encounter. Fear not because even the most difficult formulas and equations can be broken down into the basic features outlined above.
For example, the following equation is how compound interest is calculated. This equation is used for investments and payments such as monthly car payments. It may seem complicated at first, however when we see that it is simply the product of P (the principal amount, or original amount) and a factor not depending on P, in this case the rate of interest. For example, if you decide to take out a loan from a bank to buy a car, many banks have a set interest for loans based on your financial stability, not on the value of the loan.