Understanding the properties of multiplication and division equations

There are different properties in place that describe the relationships within multiplication. As previously mentioned multiplication and division are inverse operations. There are some ways that you can visually read both types of equations that associate with certain properties.


The first property we will discuss is the commutative property of multiplication. The cumulative property states that regardless of what order the factors are in you will get the same product. For example, 4 \times 6 = 24 and 6 \times 4 = 24. We are still using the same numbers, but we are using them in a different order.


The next property would be the associative property of multiplication. This property is still using multiplication but instead of two factors, it uses three. We will use the factors in two separate equations to determine the product 5 \times 3 \times 2 = 30 (5 \times 3 =15 and  15 \times 2 = 30). Essentially you take the product of the first two factors and multiply it by the third factor.


The last property to discuss will be the distributive property. The distributive property using addition and the order of operations to solve multiplication equations. For example, 4 \times 5 =20 and 4 \times 2 = 8, one can find 4 \times 7 as 4 \times ( 5 + 2) = (4 \times 5) + ( 4 \times 2) = 20 + 8 = 28. Although this property seems longer than the others, if you take your time, you can see how it makes sense. Anytime a number is placed outside of parentheses that means to multiply.


Take a look at this example, identify which property is being demonstrated.


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