Variables in Algebra

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.

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

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.

YOU TRY:

Evaluate the Expression when y = 3a. 4y

b.

c. y + 8

d. 18 - y

12

y

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 DivideTimes

ProductOf

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 __ partsCost eachQuotient

One-half (÷2), Third (÷3), Quarter (÷4)

IntoPer

Percent (out of 100)

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

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!

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?

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……

HOMEWORK

Pg 171 2-30 EVENS