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

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?