Properties and Facts of Addition
1. Review addition facts: Please review your addition facts and the
addition algorithm (the process for adding numbers). This skill will
be required throughout the course.
2. Vocabulary: If a and b are any two numbers, then
the sum of a and b is a + b. To find the sum of two numbers, we
add them.
English words 
Math symbols 
the sum of a and b 
a + b 
the sum of 4 and 8 
4 + 8 
the sum of y and 2 
y + 2 
8 more than 9 
8 + 9 
5 more than x 
5 + x 
y increased by 5 
y + 5 
Ex: Translate each English phrase into math symbols:
a. the sum of b and 10
b. the sum of p and q
c. p increased by 5
d. 7 more than z
3. Properties of Addition: The three properties of addition are:
â€¢ the addition property of zero
â€¢ the commutative property of addition
â€¢ the associative property of addition.
These properties are stated below. On the first test, you may be
asked to state these properties in proper mathematical vocabulary.
You should memorize them as given below:
Addition property of zero: If a is any number, then it is true that
a + 0 = 0 + a = a
Commutative property of addition: If a and b are any two
numbers, then it is true that:
a + b = b + a
Associative property of addition: If a, b, and c are any three
numbers, then it is true that:
(a + b) + c = a + (b + c)
Ex: (Addition property of zero)
Use the addition property of zero to
complete each statement.
a. 5 + 0 = 0 + 5 = 5
b. z + 0 =
c. y + 0 =
Ex: (Commutative property of addition)
Use the commutative
property of addition to complete each statement.
a. 5 + 7 = 7 + 5
b. z + 8 =
c. 2 + (4 + 5) =
d. x + (z + 9) =
Ex: (Associative property of addition)
Use the associative property
of addition to complete each statement.
a. 3 + (5 + 8) = (3 + 5) + 8
b. z + (x + 6) =
c. y + (p + 4) =
Ex: Name the property or properties used in each statement given
below.
a. 4 + 5 = 5 + 4
b. (x + 2) + 8 = x + (2 + 8)
c. y + 0 = y
d. 4 + (5 + 6) = (4 + 6) + 5=
4. Solving equations by simplifying and then guessing the answer: In
the given equations, first use the properties of addition to simplify,
then "guess" the solution.
Ex: Simplify and solve:
a. n + 3 = 8
n = 5 guess the solution
b. (x + 4) + 5 = 12 given equation
x + (4 + 5) = 12 associative prop. of addition
x + 9 = 12 addition facts
x = 3 guess the solution
c. 5 + ( 6 + x) = 14 + 2
