Distributive Property: 5 Clear Examples to Use in Class
All Posts- Definition of distributive property
- Distributive property of addition
- Distributive property of subtraction
- Distributive property of variables
- Distributive property of exponents
- Distributive property of fractions
- Engaging ways to teach distributive property
Distributive property definition
For expressions in the form of a(b+c), the distributive property shows us how to solve them by:- Multiplying the number immediately outside parentheses with those inside
- Adding the products together

Distributive property of multiplication over addition
Regardless of whether you use the distributive property or follow the order of operations, you’ll arrive at the same answer. In the first example below, we simply evaluate the expression according to the order of operations, simplifying what was in parentheses first.
- Multiply, or distribute, the outer term to the inner terms.
- Combine like terms.
- Solve the equation.

Distributive property of multiplication over subtraction
Similar to the operation above, performing the distributive property with subtraction follows the same rules -- except you’re finding the difference instead of the sum.
Distributive property with variables
Remember what we said about algebraic expressions and variables? The distributive property allows us to simplify equations when dealing with unknown values.Using the distributive law with variables involved, we can isolate x:- Multiply, or distribute, the outer term to the inner terms.
- Combine like terms.
- Arrange terms so constants and variables are on opposite sides of the equals sign.
- Solve the equation and simplify, if needed.

Distributive property with exponents
An exponent is a shorthand notation indicating how many times a number is multiplied by itself. When parentheses and exponents are involved, using the distributive property can make simplifying the expression much easier.- Expand the equation.
- Multiply (distribute) the first numbers of each set, outer numbers of each set, inner numbers of each set, and the last numbers of each set.
- Combine like terms.
- Solve the equation and simplify, if needed.

Distributive property with fractions
Solving algebraic expressions with fractions looks more complicated than it is. Follow the steps outlined below to see how it’s done.Hopefully this step-by-step process helps your students understand how and why the distributive property can come in handy when simplifying fractions.- Identify the fractions. Using the distributive property, you’ll eventually turn them into integers.
- For all fractions, find the lowest common multiple (LCM) -- the smallest number that both denominators can fit neatly into. This will allow you to add fractions.
- Multiply every term in the equation by the LCM.
- Isolate variables adding or subtracting like terms on both sides of the equals sign.
- Combine like terms.
- Solve the equation and simplify, if needed.

Exploring distributive property in different ways
1. Prodigy
Prodigy is a no-cost, adaptive math platform loved by 1.5 million teachers and more than 50 million students around the world! It offers curriculum-aligned content from every major math topic in 1st to 8th grade, including how to:- Use the distributive property to expand and solve expressions
- Fill in the missing numbers in equivalent expressions using the distributive property

2. Word problems
The distributive property may not see applicable to everyday life, but let’s see it in action through some word problems!Liam has diverse taste in music. Scrolling through the music on his phone, Liam’s friends find songs from three different genres: pop, metal, and country. There are six times as many metal songs as there are pop songs, and 11 times as many country songs as there are pop songs. If x represents the number of pop songs, what are the total number of songs Liam has on his phone? Write an expression. Simplify.To get the number of metal songs, multiply the number of pop songs by five -- 5x. To get the number of country songs, multiply the number of pop songs by 11 -- 11x. Since you know x is the number of pop songs, you can write the expression as:


3. Arrays
Visual or hands-on manipulatives help students make sense of math and concretize abstract concepts. They’re especially helpful for deepening your students’ understanding of the distributive property.Use objects, pictures, numbers -- anything! -- in rows and columns as a useful way to represent mathematical expressions like 45 and 59. Check out the example below on Indulgy:

Final thoughts on the distributive property
As one of the most commonly used properties, it’s important to learn how to perform and apply the distributive property. Without it, clearing the parentheses wouldn’t be possible!By incorporating EdTech resources, arrays, or math word problems, students should see the hands-on, practical applications of the distributive property.Give them a try. Did one example work more effectively to engage students and deepen their understanding? Let us know in the comments!Create or log into your teacher account on Prodigy -- a zero-cost, game-based learning platform for math that’s easy to use for educators and students alike. Aligned with curricula across the English-speaking world, it’s loved by 1.5 million teachers and more than 50 million students!
