Algebra 1 Common Core Student Edition, Grade 8-9

Pr o p er t i es and Fo r m u l as

Ch ap t er 1 Foundations for A lgebra

Order of O perations

1. Perform an operation(s) inside grouping symbols.


2. Simplify powers.


3. Multiply and divide from left to right.


4. Add and subtract from left to right.

Commutative Property of Addition
For every real n u m b e r a and b, a + b = b + a.
Commutative Property of Multiplication
For every real n u m b e r a and b, a • b = b • a.

Associative Property of Addition
For every real n u m b e r a, b, and c,
(a + b) + c = a + (b + c).

Associative Property of M ultiplication
For every real n u m b e r a, b, and c,
(a • b) • c = a • (b • c).
Id e n tity P ro p e rty o f A d d itio n
For every real n u m b e r a, a + 0 = a.
Id e n tity P ro p e rty o f M u ltip lic a tio n
For every real n u m b e r a, 1 • a = a.
Multiplication Property of - 1
For every real n u m b e r a, - 1 • a = - a.
Zero Property of M ultiplication
For every real n u m b e r a, a • 0 = 0.
In v e rs e P ro p e rty o f A d d itio n
For every real n u m b e r a, there is an additive inverse
-a such th a t a + ( - a ) = 0.
In ve rs e P ro p e rty o f M u ltip lic a tio n
For every nonzero n u m b e r a, there is a multiplicative inverse
such th a t a • \ = 1.
Distributive Property
For every real n u m b e r a, b, and c:
a{b + c) = ab + ac
(b + c)a = ba + ca
a(b - c) = ab - ac
(b - c)a = ba - ca

Addition Property of Equality

For every real n u m b e r a, b, and c, if a = b, then

a + c = b + c.

Subtraction Property of Equality

For every real n u m b e r a, b, and c, if a = b, then

a - c = b - c.

Multiplication Property of Equality

For every real n u m ber a, b, and c, if a = b, then a • c = b • c.

Division Property of Equality

For every real n u m b e r a, b, and c, w h e re c A 0, if a = b,

then | =

Cross Products o f a P ro portion

If § = §, then ad = be.

Percent Proportion

I = 1 ^ 0 # w h e r e b + 0.

Percent Equation

a = p % • b, where b + 0.

Simple Interest Formula

I = prt

Percent of Change

o/ _ amount of increase or decrease

" original amount

amount of increase = new amount - original amount

amount of decrease = original amount - new amount

Relative Error

,. I m e a s u r e d o r e s t i m a t e d v a l u e - a c t u a l v a l u e

relative error = --------------------------------actual value-------------------

Chap ter 2 Solving Equations

Ch ap t er 3 Solving Inequalities

The follow ing properties of inequality are also true for

> and -.

Addition Property of Inequality

For every real n u m b e r a, b, and c,

if a > b, then a + c > b + c;

if a < b, th e n a + c < b + c.