Transcription
Let's take a look at some basic information about Expressions. So, Expressions is used a lot in sixth grade. I actually, I'm going to jump down here to expression versus equation because oftentimes equation will be used when the correct term is expression.
An expression does not have an equal sign. No equal sign. An equation does have an equal sign because an equation is saying that this part of the equation is equal to that part. So, basic difference right there. Expression versus equation. Expressions do not have equal signs. Equations do have equal signs.
So, we have a couple different types of expressions. And as we're moving into sixth grade math, we're going to start dealing more with algebraic expressions. But we do have numeric expressions. The difference between a numeric expression and algebraic expression is that a numeric expression is just numbers and operation symbols. So, 52 - 18, that is a numeric expression. 9 + 467, that is a numeric expression. It's just got the numbers and the operation symbols.
An algebraic expression on the other hand has at least one variable, variable, and the operation symbols. It might have some numbers too, but it doesn't have to. So, x + 7, that is an algebraic expression. 6 * W, that is an algebraic expression. 5 + 20 * y, that is an algebraic expression. It's got one variable at least and an operation symbol, actually two operation symbols.
Now, the other components in an algebraic expression can be a constant. So, this would be a constant. The variable is the letter. Sorry, seven is also a constant. The letter or symbol that represents an amount that can change. So, X is a variable because X could stand for any number. I could say, okay, what is this worth if x is 2? What is this worth if x is seven? What is this worth if X is 28? So, the x or the variable can change. So, it is something that can change.
The constant on the other hand does not change. So, the constant is something that is in the expression and is separated by an addition or subtraction symbol. Separated by addition or subtraction. So, this is a constant because it is separated from the rest with addition. The 20 and the six are actually separated or attached with multiplication. So, those are actually called a coefficient. And I should have typed this one in. Coefficient.
The coefficient is attached by multiplication or division to the variable. So, once again, a constant is a number that doesn't change. Seven is always seven. Five is always five. And it is separated in the expression by an addition or subtraction sign. The variables are the letters in the algebraic expressions that represent an amount that can change. They could stand for anything. And then the coefficients are the ones that are attached with multiplication.
One more word we would like to look at is term. Every part of the algebraic expression is called a term. So, X is a term in this one. In X + 7, seven is a term. Coefficients and variables are seen as a term. So, 6W is a term. 20Y is a term. Five is a term. So, we've got a, we can have any number of terms in an expression. It depends on how long the expression is.
So, those are our basic vocabulary terms when it comes to expressions. And we will revisit those as we start looking at other expression lessons and evaluating expressions. So, again, numeric is just numbers. Algebraic has to have a variable. A constant does not change. A variable represents an amount that can change. An expression does not have an equal sign. And an equation does have an equal sign. And then the different parts of the expression are terms. All right, that wraps up the vocab.