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Evaluating Expressions R. Portteus Order of Operations Review How do you follow the order of operations? Order of Operations 1. 2. 3. 4. ( ) Exponents Ex. 3² = 3 x 3 = 9 x or ÷, from Left to Right + or ─, from Left to Right Order of Operations Review 20 ÷ 4 x 23 + (5 - 8) = A. 43 C. 1 B. 27 D. 37 20 ÷ 4 x 23 + (5 - 8) = A. 43 B. 27 C. 1 D.37 20 ÷ 4 x 23 + (5 - 8) = 20 ÷ 4 x 23 + (-3) = 20 ÷ 4 x 8 + (-3) = 5 x 8 + (-3) = 40 + -3 = 37 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 5x, 5·x, (5)(x) (same as x·5) 5 times x Multiplication 5 ,5 x x 5 divided by x Division 5 + x (same as x + 5) 5 plus x Addition 5–x subtraction 5 minus x Journal Reflection • Evaluate Expressions Video • Write your reflection from the video. Journal Reflection • Let’s watch a short video Write your reflection from the video. How do we evaluate expressions for each math operation, + - x ÷ ? Evaluate a Variable Expression with each operation • 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: Substitute 4 for n. Simplify n+3= 4+3=7 b. n – 3 Substitute 4 for n. Simplify n–3= Solution: 4–3=1 Evaluate an Algebraic Expression • Example 2: Evaluate each expression if x = 8. a. 5x Substitute 8 for x. Simplify 5x = 5(8) 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 x ÷ 4 = 8 ÷ 4 Substitute 8 for x. Simplify Solution: =2 x 8 Recall that division problems are also fractions – this problem could be written as: 4 4 2; because x x4 4 Let’s go to the next level! What if an expression has more than one variable? How do I evaluate expressions with more than one variable? Evaluating Expressions with more than one variable • Example 3: Evaluate each expression if x = 4, y = 6, and z = 24. Substitute 4 for x; 6 for y. simplify a. 5xy Solution: 5xy = 5(4)(6) = 120 Substitute 24 for z; 6 for y. Simplify. b. z y Solution: z 24 y 6 =4 Now You Try… Evaluate each expression given that a = 6, b = 12, and c = 3. 1. 2. 3. 4. 5. 6. 4ac a÷c 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. Substitute the value for a = 6 and c = 3 1. 4ac into the problem and multiply 4ac = 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, and c = 3 into the problem, then add. 3. a + b + c 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 into the problem, then multiply. 4. ba 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 into the problem, then subtract. 5. b - c 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 c 3 Note: It is better to rewrite this division Divide both c b problem as a fraction. numerator and b 12 This fraction can now be reduced to its denominator by the GCF = (3) to simplest form. reduce this 3 3 1 fraction. It is OK to have a fraction 12 3 4 as an answer. Click to return to “You try it” slide Summary To evaluate expressions: 1. Replace a variable with a number 2. Follow order of operations to find the solution. 3. Follow the algorithms for integers. Exit Ticket 5 x 6 = 30 2(8) – 4 = 16 – 4 = 12 3 x 4 = 12 9 x 5 = 45 18/3 + 18 = 6 + 18 = 24 10 ÷ 2 + 10 = 5 + 10 = 15 9(4) – 25 = 36 – 25 = 11 9 x 9 = 81 56/8 – 5 = 7– 5= 2 14 + 3(6) = 14 + 18 = 32 Homework • Homework Evaluate Expressions 3 Terms Add/Subtract A and B here