Simplifying Expressions
Have you ever wondered why following a recipe in order of the given steps matters? What if you tried to bake cookies in reverse order of the recipe?
What is simplifying expressions?
Simplifying expressions can also be considered combining like terms. The idea of simplifying expressions is that we can take like terms and group them together to have a simpler looking expression. This occurs when we are simplifying an expression with all terms that are simply constants (just numbers) or many different looking terms that include constants and variables.
If you forgot what the different parts of an expression are, such as term, constant, variable, coefficient, check out the fundamental Parts of an Expression.
What are like terms?
Like terms share the exact same variable or product of variables. Were you ever the kid who liked to group their colored candies by color? If so, you were grouping like terms.
What are like terms.pdfNot only do we have to understand like terms when simplifying expressions, we must also understand and use the order of operations.
What is the order of operations?
The order of operations is like following a recipe. You wouldn’t start the recipe at the end or in the middle. When you have an expression to simplify you must always perform the given math operations in the same order. If not, we could get a different answer.
What is the order of operations.pdfWhat is combining like terms?
What is combining like terms.pdfHow do you simplify expressions?
Simplifying expressions without variables (an expression with all constants):
Simplifying expressions without variables.pdfSimplifying expressions with variables (combining like terms):
When expressions have terms that contain variables, the idea of combining like terms is going to be used. Many times, it is easiest to rewrite an expression that contains like terms without the subtraction operation. Any subtraction operation can be re-written with an addition operation and a negative sign: 4 – x is the same as 4 + (-x).
Simplifying expressions with variables.pdfWhy do we learn how to simplify expressions?
If we all used a different order to simplify an expression, we would many times get differing simplified expressions. This would make it near impossible to communicate effectively in mathematics.
Why do we learn how to simplify expressions.pdfWhat’s next? Being able to simplify expressions is a necessary skill for solving equations. Check out Solving 1-Variable Equations: Variable on One Side of the Equation and Solving 1-Variable Equations: Variable on Both Sides of the Equation.
