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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:

• the addition property of zero

• the commutative property of addition

• 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

 
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