bell ringer in a factory of 200 people, 120 are men who earn $18 an hour. the women earn $20 an...

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

Variables and Expressions

Variable

• A variable is a letter or symbol that represents a number (unknown quantity).

• 8 + n = 12

Variable

• A variable can use any letter of the alphabet.

• n + 5

• x – 7

• w – 25

Algebraic Expression

• a group of numbers, symbols, and variables that express an operation or a series of operations.

• m + 8• r – 3• 3n

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

Simplify

• Combine like terms and complete all operations

• Simplify: m + 8 + m

• 2 m + 8

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.

Expressions

• In order to translate a word phrase into an algebraic expression, we must first know some key word phrases for the basic operations.

Words That Lead to Addition

• Sum

• More than

• Increased

• Plus

• Altogether

• Greater Than

• Add

• Total

Words That Lead to Subtraction

• Decreased

• Less

• Difference

• Minus

• How many more

• Take away

• Subtract

Words That Lead to Multiplication

• Product

• Times

• Multiply

• Of

• Twice

• Double

• Triple

Words That Lead to Division

• Quotient

• Divide

• Divided by• Split equally

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

Division

Division expressions should be written using the fraction bar instead of the traditional division sign.

2

c5

t 3

x

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

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

Multiplication Phrases

1. the product of 3 and a number t3t

2. twice the number x2x

3. 4 times a number e4e

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

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

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

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