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 ExpressionsSpecial 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 each expression when a = 6, b = 12, and c = 3
ac4 1.
)3()6)(4(4 ac Substitute the value for a = 6 and c = 3 into the problem and multiply
Substitute the value for a = 6 and c = 3 into the problem and multiply
)3()24(
72
multiplymultiply
SimplifiedSimplified
Evaluate each expression when a = 6, b = 12, and c = 3
ca 2.36 ca Substitute the value for a = 6 and c = 3
into the problem and divide
Substitute the value for a = 6 and c = 3 into the problem and divide
2 SimplifiedSimplified
Evaluate each expression when a = 6, b = 12, and c = 3
cba 3.
3126 cba
Addition problem Addition problem
Substitute the value for a = 6, b=12, and c = 3 into the problem, then add
Substitute the value for a = 6, b=12, and c = 3 into the problem, then add
318
SimplifiedSimplified21
AddAdd
Click to return to “You try it” slide
Click to return to “You try it” slide
Click in the middle of the window to view each answer
Click in the middle of the window to view each answer
Evaluate each expression when a = 6, b = 12, and c = 3
ba 4.
)6)(12(ba
multiplication problem multiplication problem
Substitute the value for b=12 and a = 6 into the problem, then multiply
Substitute the value for b=12 and a = 6 into the problem, then multiply
72 SimplifiedSimplified
Click to return to “You try it” slide
Click to return to “You try it” slide
Click in the middle of the window to view each answer
Click in the middle of the window to view each answer
Evaluate each expression when a = 6, b = 12, and c = 3
cb 5.
312 cb
Subtraction problem Subtraction problem
Substitute the value for b=12 and a = 3 into the problem, then Subtract
Substitute the value for b=12 and a = 3 into the problem, then Subtract
9 SimplifiedSimplified
Click to return to “You try it” slide
Click to return to “You try it” slide
Click in the middle of the window to view each answer
Click in the middle of the window to view each answer
Evaluate each expression when a = 6, b = 12, and c = 3
bc 6.123bc
Division problem 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.
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.
12
3
SimplifiedSimplified
3
3
12
3
4
1
Divide both numerator and denominator by the GCF = (3) to reduce this fraction.
Divide both numerator and denominator by the GCF = (3) to reduce this fraction.
It is OK to have a fraction as an answer.
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 SumPlus
More thanIncrease(d) by
PerimeterDeposit
GainGreater than
Up (flights of stairs)Total
MinusTake awayDifference
Reduce(d) byDecrease(d) by
WithdrawalLess than
Fewer (than)Loss of
We have to be able to “translate” words into expressions
What words indicate a particular operation?Multiply Divide
TimesProduct
OfTwice (×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 __ partsCost eachQuotient
One-half (÷2), Third (÷3), Quarter (÷4)
IntoPer
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.
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