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Bell Ringer
• In a factory of 200 people, 120 are men who earn $18 an hour. The women earn $20 an hour. What is the average salary of the employees at the factory?
• Men: 120 • $18 =
• Women: 80 • $20 =
• Total: $2160 + $1600 =
• Average: $3760 ÷ 200 =
$2160
$1600
$3760$18.80 an hour
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Variables and Expressions
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Variable
• A variable is a letter or symbol that represents a number (unknown quantity).
• 8 + n = 12
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Variable
• A variable can use any letter of the alphabet.
• n + 5
• x – 7
• w – 25
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Algebraic Expression
• a group of numbers, symbols, and variables that express an operation or a series of operations.
• m + 8• r – 3• 3n
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Evaluate Expressions
• Evaluate an algebraic expression – To find the value of an algebraic expression by substituting numbers for variables.
• m + 8 m = 2• r – 3 r = 5
2 + 8 = 105 – 3 = 2
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Simplify
• Combine like terms and complete all operations
• Simplify: m + 8 + m
• 2 m + 8
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The Great Dane
• Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua.
• An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua.
• When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.
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Expressions
• In order to translate a word phrase into an algebraic expression, we must first know some key word phrases for the basic operations.
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Words That Lead to Addition
• Sum
• More than
• Increased
• Plus
• Altogether
• Greater Than
• Add
• Total
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Words That Lead to Subtraction
• Decreased
• Less
• Difference
• Minus
• How many more
• Take away
• Subtract
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Words That Lead to Multiplication
• Product
• Times
• Multiply
• Of
• Twice
• Double
• Triple
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Words That Lead to Division
• Quotient
• Divide
• Divided by• Split equally
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Multiplication
• Multiplication expressions should be written in side-by-side form, with the number always in front of the variable.
• 3a 2t 1.5c 0.4f
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Division
Division expressions should be written using the fraction bar instead of the traditional division sign.
2
c5
t 3
x
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Addition Phrases
1. 3 more than xx + 3
2. the sum of 10 and a number c10 + c
3. a number n increased by 4.5
n + 4.5
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Subtraction Phrases
1. a number t decreased by 4t – 4
2. the difference between 10 and a number y
10 – y 3. 6 less than a number z
z – 6
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Multiplication Phrases
1. the product of 3 and a number t3t
2. twice the number x2x
3. 4 times a number e4e
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Division Phrases
1. the quotient of 25 and a number b
25 / b2. the number y divided by 2
y / 23. 5 divided by g
5 / g
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Write Algebraic Expressionsfor These Word Phrases
• Ten more than a number n
• A number w decreased by 5
• 6 less than a number x
• A number n increased by 8
• The sum of a number n & 9
• 4 more than a number y
n + 10
w - 5
x - 6
n + 8n + 9
y + 4
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Write Algebraic Expressionsfor These Word Phrases
• A number s plus 2
• A number k decreased by 1
• 31 less than a number x
• A number b increased by 7
• The sum of a number n & 6
• 9 more than a number z
s + 2
k - 1
x - 31
b + 7n + 6
z + 9
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Write an Algebraic Expression for These Situations
• Scott’s brother is 2 years younger than Scott
• The sum of two numbers is 12
• The difference between two numbers is 5
s - 2
v + c = 12
m – n = 5