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Letโs take a look at how we evaluate simple algebraic expressions.
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Algebra is the branch of mathematics that deals with variables.
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And a variable is a symbol that represents an unknown quantity.
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But those are all just words.
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Letโs look at some examples.
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๐ plus three.
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In this expression the letter ๐ is the variable.
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This ๐ represents an unknown quality, an amount that we donโt know.
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An ๐ plus three together is an algebraic expression.
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Itโs algebraic, or from algebra, because this expression ๐ plus three contains a variable; it contains ๐.
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And itโs an expression because it contains a number or numbers and at least one operation.
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So, here, we have the operation of addition and the number three to make this an expression.
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๐ plus three is an example of an algebraic expression.
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But remember our goal is solving algebraic expressions.
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So, in order to do that, weโre going to need a little bit more information.
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Here is our extra information.
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Evaluate ๐ plus three if ๐ equals five.
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My first step here is just to copy down exactly the expression ๐ plus three.
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Our next step is to replace the ๐ with a five.
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After that, I add five and three.
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And I understand that ๐ plus three when ๐ equals five is eight.
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So, weโve evaluated, or solved, our expression ๐ plus three with the given information.
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Letโs take a look at this example.
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Solve for the expression below if ๐ equals seven and ๐ equals five.
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Our expression is eight plus ๐ minus ๐.
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We just need to start by copying down the expression exactly how itโs listed in the problem.
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Then, I wanna replace ๐ and ๐ with their corresponding values, in this case ๐ being equal to five and ๐ being equal to seven.
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Now, I have an expression thatโs full of numbers and I can follow the order of operations.
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Iโll add eight and five to give me 13.
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I added the eight and five first because in the order of operations we want to add and subtract from left to right.
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And finally, weโll subtract the seven from the 13, which equals six.
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When weโre given these values for ๐ and ๐, when weโre given ๐ equals seven and ๐ equals five, we can understand that eight plus ๐ minus ๐ equals six.
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Remember how I said earlier that algebraic expressions contain at least one operation.
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So far, weโve only seen examples of addition and subtraction in expressions.
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But expressions can also contain multiplication and division.
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In fact, hereโs an example of an algebraic expression with multiplication.
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Are you curious how this is an example of an expression with multiplication?
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Five ๐ equals five times ๐.
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In algebra the multiplication sign is often omitted.
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You might see something like nine ๐ , three ๐๐, or even ๐ง๐ฆ.
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Nine ๐ is the same thing as saying nine times ๐ .
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Three ๐๐ equals three times ๐ times ๐.
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And ๐ฆ๐ง equals ๐ฆ times ๐ง.
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Now, I want you to take a look at the numbers that Iโve highlighted in green.
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In algebra thereโs a special name for these numbers that are being multiplied by variables.
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These numbers are called the coefficient.
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Coefficient is a factor of a multiplication expression.
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Hereโs an example of a multiplication expression.
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Evaluate seven ๐ค if ๐ค equals four.
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First, copy down the expression.
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Next, Iโm gonna replace my ๐ค with the four.
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And I also added a multiplication symbol in this time.
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After that I multiply seven times four.
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The solution to this expression is seven times four, which is 28.
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Hereโs a slightly harder example.
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Evaluate ๐ฆ squared minus four plus three if ๐ฆ equals six.
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Even though this expression has three different operations, we always start with the same procedure.
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Iโm sure you guessed copy down the expression.
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And if you did, you would be right; thatโs the first thing we need to do.
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Next, weโre gonna replace ๐ฆ with six because that was our given value.
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As you solve more and more complicated expressions, the most important thing you can remember is that you have to follow the order of operations.
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We have correctly substituted the six for the ๐ฆ.
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But now, what operation comes first?
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Since we donโt have any parentheses or brackets in this problem, order of operations would tell us to go ahead and solve your exponents next.
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So, Iโve solved for six squared which equals 36 and copied the rest of the problem down.
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Following order of operations, I now need to add and subtract from left to right.
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In this step, I subtracted four from 36.
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And our next order of operations step will be to add 32 plus three.
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Our final answer for this expression when ๐ฆ equals six, ๐ฆ squared minus four plus three equals 35.
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Okay, so letโs review.
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The first thing that weโll do when weโre trying to evaluate algebraic expressions is to substitute given values for the variables.
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And after that, you need to be very careful to follow the order of operations to evaluate each operation thatโs in your expression.
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The best way for you to get good at evaluating expressions is to try it and then practice.
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So, now, itโs your turn.