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Warm-up: 1.) 98 - 12 =86 2.) 49 + 13 =62 3.) 9 - 6 ÷ 3 = 9 - 7 = 2

Today we will learn How to Evaluate Expressions. Warm-up: 1.) 98 - 12 =86 2.) 49 + 13 =62 3.) 9 - 6 ÷ 3 = 9 - 7 = 2 4.) 4 + 5 x 8 = 4 + 40 = 44 5.) 7 2 - 20 = 49 – 20 = 29. Remember. ORDER OF OPERATIONS. A set of rules that tells us which operation to perform first.

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Warm-up: 1.) 98 - 12 =86 2.) 49 + 13 =62 3.) 9 - 6 ÷ 3 = 9 - 7 = 2

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  1. Today we will learn How to Evaluate Expressions Warm-up: 1.) 98 - 12 =86 2.) 49 + 13 =62 3.) 9 - 6 ÷ 3 = 9 - 7 = 2 4.) 4 + 5 x 8 = 4 + 40 = 44 5.) 72 - 20 = 49 – 20 = 29 CONFIDENTIAL

  2. Remember... ORDER OF OPERATIONS A set of rules that tells us which operation to perform first We can recall the Order of Operations as P E M D A S Addition Parentheses Multiplication Subtraction Exponents Division CONFIDENTIAL

  3. P E M D A S We multiply and divide in order from left to right. THEN we add and subtract in order from left to right. 63 ÷ (10 - 3) x 3 + 6 Do the Parentheses first Then we Divide 63 ÷ 7 x 3 + 6 9 x 3 + 6 Then we Multiply Finally we Add 27 + 6 32 CONFIDENTIAL

  4. ALGEBRA is a mathematical language in which symbols represent numbers and they are related by operations. t w t x h q q y We call the symbols "VARIABLES". n s c "VARIABLES" are usually letters which are used to represent Numbers. u p w t x x m b z d k s f h l CONFIDENTIAL

  5. 3 + n is an "ALGEBRAIC EXPRESSION" Numbers Variables Operations Algebraic Expressions consist of Numbers, Operations, and Variables. CONFIDENTIAL

  6. The VARIABLES in an expression can be replaced with any number. 3 + x If I substitute a 5 for the x ........... I have 3 + 5 or 8 This is how we Evaluate (or find the value of) the Expression CONFIDENTIAL

  7. Let's Evaluate the Algebraic Expression 16 + b if b = 25 We replace b with the number 25 16 + b = 16 + 25 = 41 41 The Value of the Algebraic Expression when b = 25 is CONFIDENTIAL

  8. Let's Evaluate the Algebraic Expression x- y if x = 64 and y = 27 In other words, in the Expression x - y , let's replace x with the number 64 and replace y with the number 27. x - y = 64 - 27 = 37 CONFIDENTIAL

  9. There are several ways to show multiplication. . 2 3 means 2 x 3 6t means 6 x t We always write the number BEFORE the variable. st means s x t CONFIDENTIAL

  10. Evaluate the expression 5t + 4 if t = 3 Replace t for the number 3 5t + 4 = 5 x 3 + 4 = 15 + 4 Remember PEMDAS! = 19 CONFIDENTIAL

  11. Your Turn! Evaluate each expression if a = 6 and b = 4 1.) a + 8 = 6 + 8 = 14 2.) a - b = 6 – 4 = 2 3.) a x b = 6 x 4 = 24 4.) 2a - 5 = 2 x 6 – 5 = 12 – 5 = 7 CONFIDENTIAL

  12. Complete the Table (2) (1) 2w - 3x + 4y Algebraic Expressions 7a - 3b w, x, y Name the Variables a, b 7, 3 2, 3, 4 Name the Numbers X, - X, -, + Name the Operations CONFIDENTIAL

  13. Let us take a short break!!! CONFIDENTIAL

  14. Got you!!! Try this out! Molly milked eight cows. How many M's are in that? There are no Ms in the word that I'm a god & a planet, & my name also denotes something used in an instrument for determining how hot you are. Who am I? ____________ mercury CONFIDENTIAL

  15. Distance can be calculated using the formula D = rt where r = rate and t = time Find the distance (D) from Dallas to Houston if I am travelling in my car at a rate (r) of 60 miles per hour AND it take me 4 hours (t) without stopping. Remember that rt means r x t D = r t D = r t D = 60 x 4 That's 240 miles! D = 240 CONFIDENTIAL

  16. Find the value of 2x2 - 6 x 2 if x = 7 2 x 72 – 6 x 2 = First replace the x with the number 7 2 x 49 – 6 x 2 = Remember PEMDAS and handle the exponents first. 98 – 12 = Do the multiplication in the order in which it occurs. 86 Finally, do the subtraction. CONFIDENTIAL

  17. Which one of these expressions is NOT an Algebraic Expression? 1.) ab 2.) 16 + 3 3.) 3x + 2 4.) 7x CONFIDENTIAL

  18. 1.) In the Algebraic Expression 3x + 5 - 2y - what are the variables? -what are the numbers? -what are the operations? x, y 3, 5, 2 x, +, - Evaluate each expression if a = 3, b = 12, and c = 8. 2.) 7c ÷ 4 + 5a = 7x8 ÷4 +5x3 = 56 ÷4 +15 = 14 + 15 = 29 3.) a2 + 5b - c2 = 32 + 5x12 – 82 = 9 +5x12 – 64 = 9 + 60 – 64 = 69 – 64 = 5 4.) b2÷ ( 3 c) = 122÷ (3x8) = 144 ÷(3x8) = 144 ÷24 = 6 5.) 15 + 9a ÷ 3= 15 + 9x3 ÷3 = 15 + 27 ÷3 = 15 + 9 = 24 . CONFIDENTIAL

  19. Good Job! You worked hard today! Let's review what we learned..... Algebraic Expressions consist of Variables, Numbers, and Operations. Example: 4x + 8 Variables are symbols (usually letters) that represent Numbers. Example: x or y or a or b etc. The Variables in an Expression can be replaced with Numbers. Example: In the Expression 4b - 2 , we can replace b with a Number. . We can Evaluate Expressions by finding the value of the Expression when we replace the Variable with a Number. Example: When b = 3, the Expression 3b +10 has a value of 19 We can write multiplication as 3 x a OR 3a OR 3 a CONFIDENTIAL

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