1. 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.

2. 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

3. 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.

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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.

10. 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

11. 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)

12. 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

13. 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!

14. 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?

15. 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……

16. 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

17. 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

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

19. 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?