Distributive Property – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

For now, Practice Problems are only available on tablets and desktop computers. Please log in on one of these devices.

Do you need help? Watch the Video Lesson for this Practice Problem. Distributive Property

The Distributive Property is an easy rule which you need for all your future math magic.

It helps you with simplifying equations and simplifying expressions, whenever you come across a sum (addition) or difference (subtraction) inside parantheses (brackets) that you have to multiply (multiplication) by a factor.

For example: 2·(3+4).

The Order of Operations, or PEMDAS (BEDMAS, BODMAS), tells you, to first start with the addition inside the parentheses (brackets), giving you 2·(7). Now you multiply by 2 and end up with 14.

But what happens, if instead of simple numbers or like terms you have to operate with unlike terms such as 2·(3-y)? Is there any chance to simplify this expression?

Here, the Distributive Property comes into play. It tells you how to solve any combination of terms looking like a·(b+c) or a·(b-c), where you can put in any number or monomial for a, b, and c. The Distributive Property tells you that if you have to multiply a sum by any factor, you can multiply each summand by this factor and add the resulting products. This works as well with subtraction inside the parentheses!

In this video you will discover the Distributive Property step by step with the help of a real-life example and learn in this lesson how to use it the right way. After watching the video you will never, ever have to be frightened again by scary-looking parentheses with sums or differences of unlike terms inside and with factors in front of them, such as x(a+b) or x(a-b).

With this method, you can simplify unlike terms such as 2·(3-y) into 6-2y. See? This doesn't look as difficult as before, does it?

Do you want to know how it works? Start the video right away and never get lost in expressions or equations with terns like a(b+c) again.

Use properties of operations to generate equivalent expressions.

Go to Video Lesson
Exercises in this Practice Problem
Describe what the Distributive Property means for Bella and Anton.
Explain how to use the Distributive Property for scenarios with more than 3 scoops of ice cream.
Describe how the Distributive Property changes when a third kid buys ice cream.
Use the Distributive Property to demonstrate what happens when Mrs. Harper bakes fewer pancakes.
Use the Distributive Property to solve the expression: $3 \times (4 + 5)$.
Simplify the expression $(27 + 12 - 21) \div 3$ using the Distributive Property.