Algebra 1 – Variables in Algebra 1.1 Goals I can evaluate a variable expression. I can write variable expressions for word phrases. I can write a variable expression that models a real life situation. SPI Apply properties to evaluate expressions, simplify expressions and justify solutions to problems.

Section 1.1 – Variables and Expressions Special Vocabulary: variable, constant, numerical expression, algebraic expression Variable- a letter or symbol that can be used for a value that can change.  Numerical expression – a mathematical phrase that contains only constants and/or operations Constant – a value that does not change.  Algebraic expression – a mathematical phrase that may contain variables, constants, and/or operations

Section 1.1 – Variables and Expressions We can replace the variables with numbers and evaluate the expression. To evaluate an expression is to find it’s value. We evaluate when we simplify to the lowest possible value after substituting the number for the variable.

Evaluate the Expression when y = 3 a. 4y b. c. y + 8 d y

We have to be able to “translate” words into expressions What words indicate a particular operation? AddSubtract Sum Plus More than Increase(d) by Perimeter Deposit Gain Greater than Up (flights of stairs) Total Minus Take away Difference Reduce(d) by Decrease(d) by Withdrawal Less than Fewer (than) Loss of

We have to be able to “translate” words into expressions What words indicate a particular operation? MultiplyDivide Times Product Of Twice (×2), double (×2), triple (×3), etc. Half (×½), Third (×⅓), Quarter (×¼) Area (by) Percent (of) Square (times itself 2 times) Cube (times itself 3 times) … to the power of ___ (times itself ___ times) Split into __ parts Cost each Quotient One-half (÷2), Third (÷3), Quarter (÷4) Into Per Percent (out of 100)

1.1 – Variables and Expressions Let’s try an example of “translating” a phrase into an algebraic expression: Nine more than a number y Can you identify the operation? “more than” means add Answer: y + 9

1.1 – Variables and Expressions Let’s try another example of “translating” a phrase into an algebraic expression: 4 less than a number n Can you identify the operation? “less than” means Subtract Answer: n – 4. Why not 4 – n????? **Expressions that contain subtracting will be the hardest for us!

1.1 – Variables and Expressions Let’s try another example of “translating” a phrase into an algebraic expression: A number a divided by 12 Can you identify the operation?

1.1 – Variables and Expressions This one is harder…… 5 times the quantity 4 plus a number c Can you identify the operation(s)? What does the word quantity mean? Hmm……

1.1 – Variables and Expressions 1.John types 62 words per minute. Write an expression for the number of words he types in m minutes. 2.Joey earns $5 for each car he washes. Write an expression for the number of cars Joey must wash to earn d dollars.

Section 1.1 – Variables in Algebra We can use an expression to represent a real life situation.  d = rt (Distance traveled equals rate (speed) multiplied by time traveled.)  I=Prt - Simple interest earned by an amount of money P, at an annual rate r, multiplied by the amount of time (t) in years.

Example Find the average speed (d/t), of a car that traveled 89 miles in 2 hours.

Example Find the simple interest ( I = Prt), you will earn in two years on a deposit of $870 at a rate of 5% a year.

Example You plan to ride your bicycle to school and back at an average rate of 6 miles per hour for a distance of 10.5 miles. How long will it take you?

Example Approximately fourteen 20 ounce plastic bottles must be recycled to produce 1 square foot of carpet. a.Write an expression for the number of bottles needed to make c square feet of carpet. b.Find the number of bottles needed to make 40, 120, and 224 square feet of carpet.

Reinforcement Work P9, even, 48-50, 55-64