Variables and Expressions Advanced Algebra 1 Section 1.1 Variables and Expressions 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.

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. Constant – a value that does not change. Numerical expression – a mathematical phrase that contains only constants and/or operations 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 a Variable Expression You Try IT: Answers Evaluate each expression when a = 6, b = 12, and c = 3 Substitute the value for a = 6 and c = 3 into the problem and multiply multiply Simplified

Evaluate a Variable Expression You Try IT: Answers Evaluate each expression when a = 6, b = 12, and c = 3 Substitute the value for a = 6 and c = 3 into the problem and divide Simplified

Evaluate a Variable Expression Click in the middle of the window to view each answer You Try IT: Answers Evaluate each expression when a = 6, b = 12, and c = 3 Addition problem Substitute the value for a = 6, b=12, and c = 3 into the problem, then add Add Simplified Click to return to “You try it” slide

Evaluate a Variable Expression Click in the middle of the window to view each answer You Try IT: Answers Evaluate each expression when a = 6, b = 12, and c = 3 multiplication problem Substitute the value for b=12 and a = 6 into the problem, then multiply Simplified Click to return to “You try it” slide

Evaluate a Variable Expression Click in the middle of the window to view each answer You Try IT: Answers Evaluate each expression when a = 6, b = 12, and c = 3 Subtraction problem Substitute the value for b=12 and a = 3 into the problem, then Subtract Simplified Click to return to “You try it” slide

Evaluate a Variable Expression You Try IT: Answers Evaluate each expression when a = 6, b = 12, and c = 3 Division problem Substitute the value for c=3 and b = 12 into the problem, then Divide Note: It is better to rewrite this division problem as a fraction. This fraction can now be reduced to its simplest form. Divide both numerator and denominator by the GCF = (3) to reduce this fraction. Simplified It is OK to have a fraction as an answer.

We have to be able to “translate” words into expressions What words indicate a particular operation? Add Subtract 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? Multiply Divide 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 John types 62 words per minute. Write an expression for the number of words he types in m minutes. Joey earns $5 for each car he washes. Write an expression for the number of cars Joey must wash to earn d dollars. 62/m 5c = d

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.) Distance Formula Video

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

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?