Algebra 1 Common Core Student Edition, Grade 8-9

Pl an

H o w is th is P ro b le m

like ones you've seen

before?

You begin by

substituting numbers

for the variables. After

substituting, you have

numerical expressions

ju s t like th e ones in

Problem 2.

Thinks
How can a model
help you w rite the
expression?
This m odel show s th a t
spending money equals
your wages w minus the
amount you save: |w.

Y.............w.................

When two or more variables, or a number and variables, are written together, treat them

as if they were within parentheses. So 4xy is equivalent to (4xy), and xy 2 = (xy2). You

evaluate an algebraic expression by replacing each variable with a given number. Then

simplify the expression using the order of operations.

I E v a l u a t i n g A l g e b r a i c E x p r e s s i o n s

What is the value of the expression for x = 5 and y = 2?

Ox2 + x - 12 + y2

x^2 + x - 1 2 = y 2 = 5 2 + 5 - 1 2 •+ 2 2 S u b s titu te 5 f o r x and 2 for y.

= 25 + 5 - 12 = 4 Simplify powers.

= 25 + 5 -3 Divide.

= 27 Add and subtract from left to right.

0 [xy)2 + (xy)

(xy)2 = xy = ( 5 • 2 ) 2 = ( 5 • 2 ) S u b s titu te 5 fo r x a n d 2 fo r y.

= 102 + 10 Multiply inside parentheses.

= 100 = 10

= 10

Simplify the power.

Divide.

s§ G o t It? 3. What is the value of each expression when a = 3 and b = 4 in

parts (a)-(b)?

a. 3b - a2 b. 2b2 - la

Ev a l u a t i n g a Re a l - W o r l d Ex p r e ssi o n

Banking o What is an expression for the spending money you have left after depositing

5 of your wages in savings? Evaluate the expression for weekly wages of $40, $50, $75,

and $100.

In. JElflo.

• Savings equals | of
  wages.


• Various weekly wages

Expression for spending W rite an algebraic expression

and evaluate it for each am ount

o f w e e k ly w ages. Use a ta b le to

organize your results.

money

A m o u n t o f s p e n d in g m oney

for various weekly wages

Relate spending money equals

wages minus | of wages

Define Let w = your wages.

Write

Spending Money

w w

2

The expression w — 5 • w represents

the amount of money you have left after

depositing^5 of your wages in savings.

100 - I (100)

12 Ch ap t er 1 Fo u n d a t i o n s f o r A l g e b r a