College Algebra (Algebra 1)
1. order of operations for working on the same side of PEMDAS
the equation.
Parentheses, exponents, multiplication, division, addi-
tion, subtraction.
2. Using the REVERSE order of operations to UNDO a SADMEP
problem to get the variable by itself.
opposite of PEMDAS.
Used for 2 sided equations.
3. Same Opposite Always Positive SOAP
used for cubic polynomials, especially binomials.
for instance: (refer to image)
4. Kilo, Hecto, Deka, (Base Unit), Deci, Centi, Milli KHDUDCM (King Henry
1000, 100, 10, 1 , 0.1, 0.01, 0.001 Died Unexpectedly Drink
Chocolate Milk)
5. Plug in value given for the unknown value. Then solve. Equations with a variable
on one side.
If variable remains unknown, simplify like terms and
show in order of degree.
**like terms are terms with same variable and to the
same power.**
, College Algebra (Algebra 1)
**degree is the exponent the variable is raised to. a
constant would be the variable to the 0 power.**
6. You must use SADMEP to get the variables on one 2 sided Equations with
side, and the constants on the other. Then further variables.
simplify to isolate the variable.
7. For any real number a, a=a Reflexive Property of
A number equals itself. Equality
8. For all real numbers a and b, Symmetric Property of
If a = b, then b = a Equality
Order of equality does not matter.
9. For all real numbers a, b, and c, if a=b and b=c, then Transitive Property of
a=c Equality
Two numbers equal to the same number equal ea-
chother.
10. For all real numbers a, b, and c; Addition Property of
If a = b, then a + c = b + c Equality
11. For all real numbers a, b, and c, if a = b, then a - c = b Subtraction Property of
-c Equality
12. For all real numbers a, b, and c; Multiplication Property of
if x = y, then xz = yz Equality
13. for all real numbers a, b, and c; Division Property of
If a = b, and c is not = 0, then x/z = y/z Equality
14. For all numbers a and b, if a = b, then a may be Substitution Property of
replaced by b in any equation or expression Equality
, College Algebra (Algebra 1)
15. For all numbers a, b, & c, a(b + c) = ab + ac. Distributive Property of
Equality
16. Changing the order of the factors does not change the Commutative Property of
product. Multiplication
AxB=BxA
17. Changing the order of the addends does not change Commutative Property of
the sum. Addition
A+B=B+A
18. Changing the grouping of three or more addends Associative Property of Ad-
does not change the sum. dition
(A + B) + C = A + (B + C)
19. Changing the grouping of three or more factors does Associative Property of
not change the product. Multiplication
AxBxC=CxBxA
20. The sum of any number and zero is the number Additive Identity Property
A+0=A
21. When any number is multiplied by 1, the product is the Multiplicative Identity
number.
Ax1=A
22. The product of any number and zero is zero. Zero Property of Multipli-
Ax0=0 cation
23. The product of any positive value and -1 is negative. Multiplication Property of
Vice versa is applicable. -1
-1 x a = -a
-1 x -a = a
Product is opposite value from a.
1. order of operations for working on the same side of PEMDAS
the equation.
Parentheses, exponents, multiplication, division, addi-
tion, subtraction.
2. Using the REVERSE order of operations to UNDO a SADMEP
problem to get the variable by itself.
opposite of PEMDAS.
Used for 2 sided equations.
3. Same Opposite Always Positive SOAP
used for cubic polynomials, especially binomials.
for instance: (refer to image)
4. Kilo, Hecto, Deka, (Base Unit), Deci, Centi, Milli KHDUDCM (King Henry
1000, 100, 10, 1 , 0.1, 0.01, 0.001 Died Unexpectedly Drink
Chocolate Milk)
5. Plug in value given for the unknown value. Then solve. Equations with a variable
on one side.
If variable remains unknown, simplify like terms and
show in order of degree.
**like terms are terms with same variable and to the
same power.**
, College Algebra (Algebra 1)
**degree is the exponent the variable is raised to. a
constant would be the variable to the 0 power.**
6. You must use SADMEP to get the variables on one 2 sided Equations with
side, and the constants on the other. Then further variables.
simplify to isolate the variable.
7. For any real number a, a=a Reflexive Property of
A number equals itself. Equality
8. For all real numbers a and b, Symmetric Property of
If a = b, then b = a Equality
Order of equality does not matter.
9. For all real numbers a, b, and c, if a=b and b=c, then Transitive Property of
a=c Equality
Two numbers equal to the same number equal ea-
chother.
10. For all real numbers a, b, and c; Addition Property of
If a = b, then a + c = b + c Equality
11. For all real numbers a, b, and c, if a = b, then a - c = b Subtraction Property of
-c Equality
12. For all real numbers a, b, and c; Multiplication Property of
if x = y, then xz = yz Equality
13. for all real numbers a, b, and c; Division Property of
If a = b, and c is not = 0, then x/z = y/z Equality
14. For all numbers a and b, if a = b, then a may be Substitution Property of
replaced by b in any equation or expression Equality
, College Algebra (Algebra 1)
15. For all numbers a, b, & c, a(b + c) = ab + ac. Distributive Property of
Equality
16. Changing the order of the factors does not change the Commutative Property of
product. Multiplication
AxB=BxA
17. Changing the order of the addends does not change Commutative Property of
the sum. Addition
A+B=B+A
18. Changing the grouping of three or more addends Associative Property of Ad-
does not change the sum. dition
(A + B) + C = A + (B + C)
19. Changing the grouping of three or more factors does Associative Property of
not change the product. Multiplication
AxBxC=CxBxA
20. The sum of any number and zero is the number Additive Identity Property
A+0=A
21. When any number is multiplied by 1, the product is the Multiplicative Identity
number.
Ax1=A
22. The product of any number and zero is zero. Zero Property of Multipli-
Ax0=0 cation
23. The product of any positive value and -1 is negative. Multiplication Property of
Vice versa is applicable. -1
-1 x a = -a
-1 x -a = a
Product is opposite value from a.
