Properties
There are four properties involving addition that will help make problems easier to solve. They are the commutative, associative, additive identity and distributive properties.
Commutative property: When two numbers are added, the sum is the same regardless of the order of the numbers (also known as “addends”). This property is also known as the “order property” and states that the order of addends does not matter: 3 + 4 = 4 + 3. In other words, you can switch the order or any addition problem and it will still result in the SAME answer. For example 4 + 2 = 2 + 4
Associative Property: When three or more numbers are added, the sum is the same regardless of the order of addition. You can “associate” or add together any 2 (which are put in parenthesis and added FIRST before the next number(s). For example (2 + 3) + 4 = 2 + (3 + 4)
Additive Identity Property: The sum of any number and zero “0” is the original number. For example 5 + 0 = 5. Also, known as the “zero property,” it states that zero added to any number is the same as the original number.
The 4th Property over-laps with Multiplication. It is known as the “Distributive property.” This states that the sum of two numbers times a third number is equal to the sum of each addend (number) times the third number. For example 4 * (6 + 3) = 4*6 + 4*3 (You just DISTRIBUTE the “4” by multiplying it with EACH number inside the parenthesis.)
Subtraction Rules: There are two rules for using zero in subtraction. Zero subtracted from any number is the original number (this is the counterpart of the zero property of addition), and any number subtracted from itself equals zero.
Remember: There is an inverse relationship between addition and subtraction.
If a math fact is considered, for example 3 + 7 = 10. Then the following are also true:
• 10 - 3 = 7
• 10 - 7 = 3
Similar relationships exist for subtraction, for example 10 - 3 = 7. Then the following are also true:
• 3 + 7 = 10
• 7 + 3 = 10
The reason for this is that we are dealing with an equation. An equation is balanced or the same on either side of the equals (=) sign. If exactly the same thing is done to both sides of the equation, it will still be balanced or equal.
In the example above we start with the equation 3 + 7 = 10
• Subtract the same number from both sides 3 + 7 - 3 = 10 - 3
• On the left side the 3 and -3 produce 0 which leaves 7 = 10 - 3
• Turning the equation around to be in more normal form 10 - 3 = 7
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