Home > Grade Levels > Grade 4 >

The Distributive Property of Multiplication

Answer Keys Here

Aligned To Common Core Standard:

Grade 4 Operations - 4.OA.1

What is the Distributive Property of Multiplication? - Each mathematical operation in itself is magical. Having said that, multiplication is both fun and challenging. Having four properties, it is the only mathematical operation that entails four comprehensive properties (commutative, associative, multiplicative identity property, and distributive) to make the operation easy for large and complex equations. Though all the properties of this mathematical operation have their own importance, one in particular, the distributive property is the most useful property that let's you carry out multiplication easily and quickly without hating this operation forever. According to this property, when a number is multiplied with the sum or difference of two other numbers, it gives out the same result when the first number is distributed to both of those number, multiplied by each of them and then added or subtracted. To make it easier for you to understand, consider this example: 5 x (5 – 2) = 15 ::: 5(5) – 5(2) = 15
In the above example, both the equations yield the same results, which is 15. The property proves to be true and therefore justifies its claim. This lesson and worksheet series helps students understand the proper application of the distributive property of multiplication.

Printable Worksheets And Lessons

Practice Writing Full Equations Sheets

Pick the Correct Form

  • Multiple Choice 2 - Which equation below represents the distributive property of multiplication?
  • Multiple Choice 3 - Complete each problem displaying the distributive property of multiplication.

Fill in the Missing Numbers

  • Practice 2 - Complete the missing parts of the equations.
  • Practice 3 - We step up the values a bit here for you.

The Importance and Uses of the Distributive Property of Multiplication

This simple property can be a lifesaver in helping you organize your operations and in many cases, it can help you be a great deal more accurate with your solutions. You can use it to break down problems into much more digestible pieces. For example, if you presented with the problem 23 x 6. You can break this into two pieces and work off of the smaller value. We can rewrite this as 20 x 6 + 3 x 6. Based on this property it identical. You can then do your calculations mentally. Using this technique will help you make better decisions in everyday math routines. You can also use this to rearrange complex problems such as 4(24 – 7). Using this same mindset, this can be rewritten as: 4 x 24 – 4 x 7. You can also use this method to cheat, a bit, with values that end in zeros. For example, when tackling the problem: 400 x 320. You can ignore the ending zeros. Think of those ending zeros as place holders and remove them. That would allow us to restate this problem as 4 x 32 with three terminating zeros. 4 x 32 = 128. Now we just need to add those ending zeros: 128,000. That makes life a little simpler for you. When you discover this technique and master it, multiplication problems will not be that scary for you from here on.