Distributive Property 03:33 minutes

Video Transcript

Transcript Distributive Property

The Distributive Property is one of the most frequently used math properties but many students have trouble recalling it. I will tell you a story to help you remember and apply this very important math property.

Distributive Property Example 1

Meet Anton and Bella. They both love ice cream. Imagine, on a hot summer day, each goes to buy scoops of ice cream. First, Anton buys a cone. There are three scoops of ice cream in his cone. You can express this mathematically. The three scoops of ice cream represent the number three, and Anton represents the number one. Three times one is three.
Next, Bella buys a cone. She also has three scoops of ice cream on her cone. You can also express this as the equation three times one. Anton and Bella meet! We can write this as a sum. Three times one plus three times one. They have six scoops of ice cream all together. Let's rewind back to the beginning of the story...

Distributive Property Example 2

Meet Anton and Bella, again. This time they meet each other first. You can express this as a sum. Anton plus Bella. Then, together they go to buy ice cream. You can express this as three multiplied by the sum of one plus one. Altogether they have six scoops of ice cream. Wait, isn't this the same outcome as the first version of this story?! Yes: It doesn't matter if they first buy their ice cream and meet then or first meet and buy it together. The result is the same.

Application of the Distributive Property

Let's write this using math symbols. Let A stand for Anton and B stand for Bella. C is the number of scoops. Now distribute... C times A plus C times B.
Let's try the Distributive Property out, using different numbers: three times the sum of four and five. You can distribute the three to each addend and then add the products. Three times four plus three times five which is equal to twenty-seven. Or you can follow order of operations and multiply the sum of the addends. Three times the quantity four plus five which equals three times nine is also equal to twenty-seven. Try it yourself. Assign different numbers for the variables A, B, and C and observe that the result will be the same, every time. Let's make a note:

  • The Distributive Property says that distributing a multiplier over a sum of numbers will result in the same answer as multiplying each addend separately and then summing.
  • C times the sum of A and B equals the same as C times A plus C times B.

Next time you need to use the Distributive Property, remember Anton and Bella!