The commutative property of addition and multiplication shows us that numbers can easily be swapped within operations of an equation. Commutative Property - With respect to addition - the sum of two added numbers remain same. No matter, in which order you have added the numbers. For example. 3 + 5 = 8 or 5 + 3 = 8. With respect to multiplication - The multiplied answer will be the same after multiplying two numbers together. The order will also be same in which you multiplied the numbers. For example; 3 × 5 = 15 or 5 × 3 = 15. When we see problems like this we know for sure that the order of the integers does not matter. The associative property tells us that how we group numbers within an equation does not matter, if the operations are the same. Associative Property - With respect to addition - The sum of the three or more added numbers will be the same. No matter, in what ways you have grouped the numbers. For example; 6 + (4 + 3) = 13 or (6 + 4) + 3 = 13. With respect to multiplication - The product will remain same when you multiply three or more numbers together. No matter, in what ways you have made a group of multiplied numbers. For example; 6 × (4 × 3) = 72 or (6 × 4) × 3 = 72. The distributive property is the most used property in math. Distributive Property - The third number after two times additions will be equal to the sum of the number of times you have added the third number. For example; 5 × (7 + 2) = 45 or 5 × 7 + 5 × 2 = 4. It lets us multiply a sum by multiplying each addend by itself and then we finish off by adding the products.
These worksheets review the commutative, associative, and distributive properties, and identify the correct property for given expressions. While these are defined, students should have some prior knowledge.