Evaluating Expressions and Combining Like Terms R. Portteus

Evaluating Expressions Vocabulary: Variable – A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number. Variable expression (A.K.A. - Algebraic Expression) – An expression, such as n – 5, that consists of one or more numbers and variables along with one or more arithmetic operations. (Note: No equal sign) Evaluate a Variable Expression – write the expression, substitute a number for each variable, and simplify the result.

How do you describe a variable expression? Meaning Operation 5x, 5·x, (5)(x) (same as x·5) 5 times x Multiplication 5 divided by x Division 5 + x (same as x + 5) 5 plus x Addition 5 – x 5 minus x subtraction

Evaluate a Variable Expression Example 1: Evaluate each expression when n = 4. a. n + 3 n + 3 = 4 + 3 = 7 b. n – 3 n – 3 = 4 – 3 = 1 Simplify (means to solve the problem or perform as many of the indicated operations as possible.) Solution: Substitute 4 for n. Simplify Substitute 4 for n. Simplify Solution:

Evaluate an Algebraic Expression Example 2: Evaluate each expression if x = 8. a. 5x 5x = 5(8) = 40 b. x ÷ 4 x ÷ 4 = 8 ÷ 4 = 2 Substitute 8 for x. Simplify Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8. Solution: Substitute 8 for x. Simplify Solution: Recall that division problems are also fractions – this problem could be written as:

Evaluating More Expressions Example 3: Evaluate each expression if x = 4, y = 6, and z = 24. a. 5xy 5xy = 5(4)(6) = 120 b. = 4 Substitute 4 for x; 6 for y. simplify Solution: Substitute 24 for z; 6 for y. Simplify. Solution:

Now You Try… Evaluate each expression given that a = 6, b = 12, and c = 3. a + b + c ba b – c c ÷ b A A A A A A

You Try #1 Evaluate each expression given that a = 6, b = 12, and c = 3. 4ac 4ac = 4(6)(3) = (24)(3) = 72 Substitute the value for a = 6 and c = 3 into the problem and multiply Click to return to “You try it” slide

You Try #2 Evaluate each expression given that a = 6, b = 12, and c = 3. 2. a ÷ c a ÷ c = 6 ÷ 3 = 2 Substitute the value for a = 6 and c = 3 into the problem and divide Click to return to “You try it” slide

You Try #3 Evaluate each expression given that a = 6, b = 12, and c = 3. a + b + c a + b + c = 6 + 12 + 3 = 18 + 3 = 21 Substitute the value for a = 6, b=12, and c = 3 into the problem, then add. Click to return to “You try it” slide

You Try #4 Evaluate each expression given that a = 6, b = 12, and c = 3. 4. ba ba = (12)(6) = 72 Substitute the value for b=12 and a = 6 into the problem, then multiply. Click to return to “You try it” slide

You Try #5 Evaluate each expression given that a = 6, b = 12, and c = 3. 5. b - c b – c = 12 – 3 = 9 Substitute the value for b=12 and a = 3 into the problem, then subtract. Click to return to “You try it” slide

You Try #6 Evaluate each expression given that a = 6, b = 12, and c = 3. 6. c ÷ b Substitute the value for c=3 and b = 12 into the problem, then Divide Note: It is better to rewrite this division problem as a fraction. This fraction can now be reduced to its simplest form. Divide both numerator and denominator by the GCF = (3) to reduce this fraction. It is OK to have a fraction as an answer. Click to return to “You try it” slide

Combining Like Terms Now that we have seen some algebraic expressions, we need to know how to simplify them. Vocabulary Like terms: In an expression, like terms are the terms that have the same variables, raised to the same powers (same exponents). i.e. 4x and -3x or 2y2 and –y2 Coefficient: A constant that multiplies a variable. i.e. the 3 in 3a or the -1 in –b

Combining Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms. Like terms include letters that are the same and numbers.

Let’s try one… Step One: Write the expression. 4x + 5x -2 - 2x + 7 Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. 4x, 5x, and -2x -2 and 7 Simplify the variable terms. 4x+5x-2x = 9x-2x = 7x Simplify the constant (number) terms. -2+7 = 5 You have a simplified expression by writing all of the results from simplifying. 7x + 5

Another example… 10x – 4y + 3x2 + 2x – 2y 3x2 10x, 2x -4y – 2y Remember you cannot combine terms with the same variable but different exponents.

Now you try… Simplify the following: 5x + 3y - 6x + 4y + 3z 3b - 3a - 5c + 4b 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 5xy – 2yx + 7y + 3x – 4xy + 2x A A A A

You Try #1 Simplify the following: 5x + 3y - 6x + 4y + 3z 5x, -6x 3y, 4y 3z -x + 7y + 3z

You Try #2 Simplify the following: 3b - 3a - 5c + 4b 3b, 4b -3a -5c -3a + 7b – 5c

You Try #3 Simplify the following: 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 4ab, -ab -2a2b, 2a2b 5, 4 ab2 3ab + ab2 + 9

You Try #4 Simplify the following: 5xy – 2yx + 7y + 3x – 4xy + 2x 5xy, -2yx, -4xy 7y 3x, 2x -xy + 7y + 5x

Conclusion A variable or algebraic expression is an expression that consists of one or more ________ and _________ along with one or more ________ _________. (Note: No _______ sign) To evaluate an expression write the _________, substitute a _______ for each variable, and _________ the result. numbers variables arithmetic operations equal expression number simplify

Conclusion Continued… In an expression, __________ are the terms that have the same ________, raised to the same ________ (same exponents). A coefficient is a number that ________ a variable. like terms variables power multiplies