The relationship between multiplication and addition can also be seen in various mathematical properties.

The commutative property is one that applies to both multiplication and addition problems. The implications of this property are that in a multiplication equation, one can multiply the numbers in any order to get the same product, and in an addition equation, one can add the numbers in any order to get the same sum. An example of the commutative property being used in addition is the equation, "10 + 2 = 12." If the numbers 10 and 2 were to be switched (2 + 10), the sum would still be 12. The equation, "2 x 5," can be utilized to demonstrate the commutative property in multiplication. Two times 5 equals 10, and when the numbers switch places, 5 times 2 still yields a product of 10. The commutative property is connected to the thinking strategy of thinking about multiplication in terms of adding groups of numbers. When students see 5 x 2 they may first think that means 5 groups of 2, which is 2 + 2 + 2 + 2 + 2. The commutative property lets them know that it can also mean 2 groups of 5, which is a much simpler 5 + 5.

The associative property is similar to the commutative property, but applies to equations that have more than two numbers and have at least two of the num ...