Evaluating Expressions and Combining Like Terms Evaluating Expressions

Evaluating Expressions and Combining Like Terms

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? Variable Expression Meaning Operation 5 x, 5·x, (5)(x) (same as x· 5) 5 times x Multiplication 5 divided by Division x 5 + x (same as x + 5 plus x Addition 5) 5–x 5 minus x subtraction

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

Evaluate an Algebraic Expression • Example 2: Evaluate each expression if x = 8. a. 5 x 5 x = 5(8) Substitute 8 for x. Simplify Using parenthesis is the preferred method to show Solution: = 40 multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8. b. x ÷ 4 = 8 ÷ 4 Substitute 8 for x. Simplify Solution: =2 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. Substitute 4 for x; 6 for y. simplify a. 5 xy Solution: 5 xy = 5(4)(6) = 120 Substitute 24 for z; 6 for y. Simplify. b. Solution: =4

Now You Try… Evaluate each expression given that a = 6, b = 12, and c = 3. 1. 2. 3. 4. 5. 6. 4 ac a÷c a+b+c ba b–c c÷b A A A

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

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

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

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

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

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

Combining Like Terms

Combining Like Terms • Now that we have seen some algebraic expressions, we need to know how to simplify them.

Vocabulary • 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. 4 x and 3 x or 2 y 2 and 13 y 2 – Coefficient: A constant that multiplies a variable. • i. e. the 3 in 3 a or the 1 in b • 3 a really means 3 x a • The term b means 1 x 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 variables that are the same.

Let’s watch a short video • Video (with Chuck Norris)https: //www. khanacademy. org/math/ cc-sixth-grade-math/cc-6 thexpressions-and-variables/cc-6 thequivalent-expressions/v/combininglike-terms

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

Another example… • 10 x + 4 y + 3 x 2 + 2 x – 2 y 3 x 2 Remember you cannot 10 x + 2 x combine terms with the same variable but different exponents. 4 y – 2 y • Simplified expression = 3 x 2 + 12 x + 2 y

Now you try… Simplify the following: 1. 5 x + 3 y + 6 x + 4 y + 3 z 2. 3 b + 3 a - 5 c + 4 b 3. 4 ab – 2 a 2 b + 5 – ab + ab 2 + 2 a 2 b + 4 4. 5 xy – 2 xy + 7 y + 3 x – xy + 2 x A A

You Try #1 • Simplify the following: 1. 5 x + 3 y + 6 x + 4 y + 3 z 5 x + 6 x 3 y + 4 y 3 z Simplified expression = 11 x + 7 y + 3 z

You Try #2 • Simplify the following: 2. 3 b + 3 a - 5 c + 4 b 3 b + 4 b 3 a -5 c Simplified expression = 3 a + 7 b – 5 c

You Try #3 • Simplify the following: 3. 4 ab – 2 a 2 b + 5 – ab + ab 2 + 2 a 2 b + 4 4 ab -2 a 2 b + 2 a 2 b 5+4 ab 2 Simplified expression = 3 ab + ab 2 + 9

You Try #4 • Simplify the following: 4. 5 xy – 2 xy + 7 y + 3 x – xy + 2 x 5 xy - 2 x - 1 xy 7 y 3 x + 2 x Simplified expression = 5 x + 2 xy + 7 y

Conclusion • In an expression, _____ are like terms that have the same variables ____, raised to the same power ____ (same exponents). • A coefficient is a number that multiplies ____ a variable.

Take out your device • If you do not have a device, partner with someone who does. • Open a web browser and go to kahoot. it • Enter the game pin____ and your name

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