Order of Operations (Algebra1 1_2)

Slide 2: Order of Operations  Evaluate numerical expressions by using the order of operations.  Evaluate algebraic expressions by using the order of operations. 1) order of operations

Slide 3: Order of Operations Internet service costs $4.95 per month which includes 100 hours. Additional time costs $0.99 per hour.

Slide 4: Order of Operations Internet service costs $4.95 per month which includes 100 hours. Additional time costs $0.99 per hour. Nicole used her internet connection for 117 hours this past month. Write an expression describing her cost for the month?

Slide 5: Order of Operations Internet service costs $4.95 per month which includes 100 hours. Additional time costs $0.99 per hour. Nicole used her internet connection for 117 hours this past month. Write an expression describing her cost for the month? Cost = $4.95 + $0.99(117 – 100)

Slide 6: Order of Operations Internet service costs $4.95 per month which includes 100 hours. Additional time costs $0.99 per hour. Nicole used her internet connection for 117 hours this past month. Write an expression describing her cost for the month? Cost = $4.95 + $0.99(117 – 100) Numerical expressions often contain more than one operation.

Slide 7: Order of Operations Internet service costs $4.95 per month which includes 100 hours. Additional time costs $0.99 per hour. Nicole used her internet connection for 117 hours this past month. Write an expression describing her cost for the month? Cost = $4.95 + $0.99(117 – 100) Numerical expressions often contain more than one operation. A rule is needed to let you know which operation to perform first.

Slide 8: Order of Operations Cost = $4.95 + $0.99(117 – 100)

Slide 9: Order of Operations Cost = $4.95 + $0.99(117 – 100) order of operations This rule is called the _________________

Slide 10: Order of Operations Cost = $4.95 + $0.99(117 – 100) order of operations This rule is called the _________________ Step 1: Evaluate expressions inside grouping symbols.

Slide 11: Order of Operations Cost = $4.95 + $0.99(117 – 100) order of operations This rule is called the _________________ Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(17)

Slide 12: Order of Operations Cost = $4.95 + $0.99(117 – 100) order of operations This rule is called the _________________ Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers.

Slide 13: Order of Operations Cost = $4.95 + $0.99(117 – 100) order of operations This rule is called the _________________ Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers. Cost = $4.95 + $0.99(17) there are no powers to evaluate

Slide 14: Order of Operations Cost = $4.95 + $0.99(117 – 100) order of operations This rule is called the _________________ Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers. Cost = $4.95 + $0.99(17) there are no powers to evaluate Step 3: Do all multiplication and / or division from left to right.

Slide 15: Order of Operations Cost = $4.95 + $0.99(117 – 100) order of operations This rule is called the _________________ Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers. Cost = $4.95 + $0.99(17) there are no powers to evaluate Step 3: Do all multiplication and / or division from left to right. Cost = $4.95 + $16.83

Slide 16: Order of Operations Cost = $4.95 + $0.99(117 – 100) order of operations This rule is called the _________________ Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers. Cost = $4.95 + $0.99(17) there are no powers to evaluate Step 3: Do all multiplication and / or division from left to right. Cost = $4.95 + $16.83 Step 4: Do all addition and / or subtraction from left to right.

Slide 17: Order of Operations Cost = $4.95 + $0.99(117 – 100) order of operations This rule is called the _________________ Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers. Cost = $4.95 + $0.99(17) there are no powers to evaluate Step 3: Do all multiplication and / or division from left to right. Cost = $4.95 + $16.83 Step 4: Do all addition and / or subtraction from left to right. Cost = $21.78

Slide 18: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction)

Slide 19: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression:

Slide 20: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression: 3+2•3+5

Slide 21: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression: 3+2•3+5 3+2•3+5=3+2•3+5

Slide 22: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression: 3+2•3+5 3+2•3+5=3+2•3+5 =3+6+5

Slide 23: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression: 3+2•3+5 3+2•3+5=3+2•3+5 =3+6+5 =9+5

Slide 24: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression: 3+2•3+5 3+2•3+5=3+2•3+5 =3+6+5 =9+5 = 14

Slide 25: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression: 3+2•3+5 15 ÷ 3 • 5 – 42 3+2•3+5=3+2•3+5 =3+6+5 =9+5 = 14

Slide 26: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression: 3+2•3+5 15 ÷ 3 • 5 – 42 3+2•3+5=3+2•3+5 15 ÷ 3 • 5 – 42 = 15 ÷ 3 • 5 – 16 =3+6+5 =9+5 = 14

Slide 27: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression: 3+2•3+5 15 ÷ 3 • 5 – 42 3+2•3+5=3+2•3+5 15 ÷ 3 • 5 – 42 = 15 ÷ 3 • 5 – 16 =3+6+5 = 5 • 5 – 16 =9+5 = 14

Slide 28: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression: 3+2•3+5 15 ÷ 3 • 5 – 42 3+2•3+5=3+2•3+5 15 ÷ 3 • 5 – 42 = 15 ÷ 3 • 5 – 16 =3+6+5 = 5 • 5 – 16 =9+5 = 25 – 16 = 14

Slide 29: Order of Operations Some students remember the order by using the following mnemonic: P lease (parentheses / grouping symbols) E xcuse (exponents) My (multiplication) D ear (division) A unt (addition) S ally (subtraction) Evaluate each expression: 3+2•3+5 15 ÷ 3 • 5 – 42 3+2•3+5=3+2•3+5 15 ÷ 3 • 5 – 42 = 15 ÷ 3 • 5 – 16 =3+6+5 = 5 • 5 – 16 =9+5 = 25 – 16 = 14 =9

Slide 30: Order of Operations Evaluate each expression: P lease E xcuse My D ear A unt S ally

Slide 31: Order of Operations Evaluate each expression: P lease E xcuse 2(5) + 3(4 + 3) My D ear A unt S ally

Slide 32: Order of Operations Evaluate each expression: P lease E xcuse 2(5) + 3(4 + 3) My D ear 2(5) + 3(4 + 3) = 2(5) + 3(7) A unt S ally

Slide 33: Order of Operations Evaluate each expression: P lease E xcuse 2(5) + 3(4 + 3) My D ear 2(5) + 3(4 + 3) = 2(5) + 3(7) A unt = 10 + 21 S ally

Slide 34: Order of Operations Evaluate each expression: P lease E xcuse 2(5) + 3(4 + 3) My D ear 2(5) + 3(4 + 3) = 2(5) + 3(7) A unt = 10 + 21 S ally = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol.

Slide 35: Order of Operations Evaluate each expression: P lease E xcuse 2(5) + 3(4 + 3) My D ear 2(5) + 3(4 + 3) = 2(5) + 3(7) A unt = 10 + 21 S ally = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6)2]

Slide 36: Order of Operations Evaluate each expression: P lease E xcuse 2(5) + 3(4 + 3) My D ear 2(5) + 3(4 + 3) = 2(5) + 3(7) A unt = 10 + 21 S ally = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6)2] 2[5 + (30 ÷ 6)2] = 2[5 + (5)2]

Slide 37: Order of Operations Evaluate each expression: P lease E xcuse 2(5) + 3(4 + 3) My D ear 2(5) + 3(4 + 3) = 2(5) + 3(7) A unt = 10 + 21 S ally = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6)2] 2[5 + (30 ÷ 6)2] = 2[5 + (5)2] = 2[5 + 25]

Slide 38: Order of Operations Evaluate each expression: P lease E xcuse 2(5) + 3(4 + 3) My D ear 2(5) + 3(4 + 3) = 2(5) + 3(7) A unt = 10 + 21 S ally = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6)2] 2[5 + (30 ÷ 6)2] = 2[5 + (5)2] = 2[5 + 25] = 2[30]

Slide 39: Order of Operations Evaluate each expression: P lease E xcuse 2(5) + 3(4 + 3) My D ear 2(5) + 3(4 + 3) = 2(5) + 3(7) A unt = 10 + 21 S ally = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6)2] 2[5 + (30 ÷ 6)2] = 2[5 + (5)2] = 2[5 + 25] = 2[30] = 60

Slide 40: Order of Operations P A fraction bar is another type of grouping symbol. E It indicates that the numerator and denominator should each be treated as a single value. M D Evaluate the expression: A S

Slide 41: Order of Operations P A fraction bar is another type of grouping symbol. E It indicates that the numerator and denominator should each be treated as a single value. M D Evaluate the expression: A 6  42 S 32  4

Slide 42: Order of Operations P A fraction bar is another type of grouping symbol. E It indicates that the numerator and denominator should each be treated as a single value. M D Evaluate the expression: A 6  42 S 32  4 6  42 6  16  94 2 3 4

Slide 43: Order of Operations P A fraction bar is another type of grouping symbol. E It indicates that the numerator and denominator should each be treated as a single value. M D Evaluate the expression: A 6  42 S 32  4 6  42 6  16  94 2 3 4 22  or 36

Slide 44: Order of Operations P A fraction bar is another type of grouping symbol. E It indicates that the numerator and denominator should each be treated as a single value. M D Evaluate the expression: A 6  42 S 32  4 6  42 6  16  94 2 3 4 11 22  or 18 36

Slide 45: Order of Operations Like numerical expressions, algebraic expressions often contain more than one operation.

Slide 46: Order of Operations Like numerical expressions, algebraic expressions often contain more than one operation. Evaluate: a2 – (b2 – 4c) Algebraic expressions can be evaluated when _______________________________.

Slide 47: Order of Operations Like numerical expressions, algebraic expressions often contain more than one operation. Evaluate: a2 – (b2 – 4c) the value of the variables are known Algebraic expressions can be evaluated when _______________________________.

Slide 48: Order of Operations Like numerical expressions, algebraic expressions often contain more than one operation. Evaluate: a2 – (b2 – 4c) if a = 7, b = 3, and c = 5 the value of the variables are known Algebraic expressions can be evaluated when _______________________________.

Slide 49: Order of Operations Like numerical expressions, algebraic expressions often contain more than one operation. Evaluate: a2 – (b2 – 4c) if a = 7, b = 3, and c = 5 the value of the variables are known Algebraic expressions can be evaluated when _______________________________. First, replace the variables with their values.

Slide 50: Order of Operations Like numerical expressions, algebraic expressions often contain more than one operation. Evaluate: a2 – (b2 – 4c) if a = 7, b = 3, and c = 5 the value of the variables are known Algebraic expressions can be evaluated when _______________________________. First, replace the variables with their values. a2 – (b2 – 4c) = 72 – (33 – 4•5)

Slide 53: Order of Operations Like numerical expressions, algebraic expressions often contain more than one operation. Evaluate: a2 – (b2 – 4c) if a = 7, b = 3, and c = 5 the value of the variables are known Algebraic expressions can be evaluated when _______________________________. First, replace the variables with their values. Then, find the value of the numerical a2 – (b2 – 4c) = 72 – (33 – 4•5) expression using the order of operations.

Slide 54: Order of Operations Like numerical expressions, algebraic expressions often contain more than one operation. Evaluate: a2 – (b2 – 4c) if a = 7, b = 3, and c = 5 the value of the variables are known Algebraic expressions can be evaluated when _______________________________. First, replace the variables with their values. Then, find the value of the numerical a2 – (b2 – 4c) = 72 – (33 – 4•5) expression using the order of operations. = 49 – (27 – 20)

Slide 55: Order of Operations Like numerical expressions, algebraic expressions often contain more than one operation. Evaluate: a2 – (b2 – 4c) if a = 7, b = 3, and c = 5 the value of the variables are known Algebraic expressions can be evaluated when _______________________________. First, replace the variables with their values. Then, find the value of the numerical a2 – (b2 – 4c) = 72 – (33 – 4•5) expression using the order of operations. = 49 – (27 – 20) = 49 – ( 7)

Slide 56: Order of Operations Like numerical expressions, algebraic expressions often contain more than one operation. Evaluate: a2 – (b2 – 4c) if a = 7, b = 3, and c = 5 the value of the variables are known Algebraic expressions can be evaluated when _______________________________. First, replace the variables with their values. Then, find the value of the numerical a2 – (b2 – 4c) = 72 – (33 – 4•5) expression using the order of operations. = 49 – (27 – 20) = 49 – ( 7) = 42

Slide 57: Order of Operations Write an expression involving division in which the first step in evaluating the expression is addition.

Slide 58: Order of Operations Write an expression involving division in which the first step in evaluating the expression is addition. Sample answer: 2+4 ÷ 3

Slide 59: Order of Operations Write an expression involving division in which the first step in evaluating the expression is addition. Sample answer: 2+4 ÷ 3 How can you “force” the addition to be done before the division?

Slide 60: Order of Operations Write an expression involving division in which the first step in evaluating the expression is addition. ( 2 + 4) ÷ 3 Sample answer: How can you “force” the addition to be done before the division?

Slide 61: Order of Operations Finding error(s) in your calculations is a skill that you must develop. Determine which calculation is incorrect and identify the error. 3[4 + (27 ÷ 3)]2 = 3(4 + 92) 3[4 + (27 ÷ 3)]2 = 3(4 + 9)2 = 3(4 + 81) = 3(13)2 = 3(85) = 3(169) = 255 = 507

Slide 62: Order of Operations Finding error(s) in your calculations is a skill that you must develop. Determine which calculation is incorrect and identify the error. Incorrect quantity raised The exponent is outside to the second power. the grouping symbol. 3[4 + (27 ÷ 3)]2 = 3(4 + 92) 3[4 + (27 ÷ 3)]2 = 3(4 + 9)2 = 3(4 + 81) = 3(13)2 = 3(85) = 3(169) = 255 = 507

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