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The Distributive Property of Multiplication Worksheets

Multiplication has so many unique qualities that makes it one of the most helpful operations of math. In many situations you will find parathesis used in equations. Using the distributive property we can simplify these products to make them work with other operations that may exist within the equation or inequality. In some cases, students will feel that this differs from the order of operations that they have previously learned. They are correct in that it does differ from PEMDAS, but the result of the product is the equivalent. This lesson and worksheet series helps students understand the proper application of the distributive property of multiplication.

Aligned Standard: Grade 4 Operations - 4.OA.1

  • Answer Keys - These are for all the unlocked materials above.

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.

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 of the bunch. It allows you carry out multiplication easily and quickly and helps you rearrange all types of equation to help you organize all different forms of algebraic equations.

According to this property, when a number is multiplied with the sum or difference of two other numbers, it gives out the same result. This means that when the first number is distributed to both of those number, multiplied by each of them and then added or subtracted. The formula states:

a(b + c) = ab + ac

This really gives meaning to the use of parentheses and brackets in all types of different equations. Note that this movement from bracket to without does not interact or change the addition or subtraction portion of the equation.

To make it easier for you to understand, consider this example: 5 (5 - 2) = x

We can extend that product of five to each factor found within the parathesis. Based on what we know now, we can rewrite this as: 5(5) - 5(2) = x. We can carryout the math further to: 25 – 10 = 15.

In the above example, both the equations [5 (5 - 2) or 5(5) - 5(2)] yield the same results, which is 15. The property proves to be true and therefore justifies its claim. As you advance through higher levels of math this will come in very handy to help you plow through all types of algebra.

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.

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