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What is the Distributive Property?

Tricia Christensen
Updated May 21, 2024
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The distributive property is expressed in math terms as the following equation: a(b + c) = ab + ac. You can read this as the sum of a(b + c) is equal to the sum of a times b and a times c. When you’re looking at an equation like this, you can see that the multiplication part distributes evenly to all the numbers within the parentheses. It would be incorrect to multiply ab and just add c, or to multiply ac and add b. The distributive property reminds us that everything within the parentheses needs to be multiplied by the outside number.

Students may first learn the distributive property when they are learning order of operations. This is the concept that in problems where there are different mathematical operations, such as multiple, addition, subtraction, parenthesis, you have to work in a certain order to get the right answer. This order is parentheses, exponents, multiplication and division. and addition and subtraction, which may be abbreviated to PEMDAS.

When you have a math problem that uses parentheses you need to solve what’s in the parenthesis first, before you can move on to solving other problems. If the math problem simply has known numbers, it’s fairly easy to solve. 2(10+5) becomes 2(15) or is also equal under the distributive property to 2(10) + 2(5). What gets more complicated is when you are working with variables (a, b, x, y, and so on) in algebra, and when these variables cannot be combined together.

Consider the equation 9(10a + 2). If we don’t know what the variable a stands for, we can’t add 10a + 2, but using the distributive property still allows us to simply this expression because we know this equation is equal to 9(10a) + 9(2). In order to simply the expression we can take each part separately and multiply it to 9, and we get 90a + 18.

Another way to use the distributive property is if you want to figure out the similarities in an equation. In the example 90a + 18, although the terms are not like, they have something in common. You can work backward to take out the factor of 9 and put the unlike terms in parentheses. Thus 90a + 18 can equal 9(a +2). We have removed the element that is common to these terms, the common factor of 9.

Why on earth would you want to work the distributive property backward? Say you have an equation that 4a + 4= 8. Using the distributive property before we get to subtracting terms to solve for a, can simplify the work. You can divide the entire equation on both sides by 4, giving us the answer a + 1 =2. From there it’s easy to determine that a =1. Sometimes it makes sense to reduce unlike terms by their common factor to more easily solve an equation.

All The Science is dedicated to providing accurate and trustworthy information. We carefully select reputable sources and employ a rigorous fact-checking process to maintain the highest standards. To learn more about our commitment to accuracy, read our editorial process.
Tricia Christensen
By Tricia Christensen
With a Literature degree from Sonoma State University and years of experience as a All The Science contributor, Tricia Christensen is based in Northern California and brings a wealth of knowledge and passion to her writing. Her wide-ranging interests include reading, writing, medicine, art, film, history, politics, ethics, and religion, all of which she incorporates into her informative articles. Tricia is currently working on her first novel.
Discussion Comments
By Viranty — On Mar 09, 2014

@Chmander - Have you ever thought about getting a tutor? During my freshmen year, I was struggling with math a lot, until I had someone tutor me in algebra. There's no doubt that algebra and mathematical equations are tricky, but here's one of the best pieces of advices - The rules in math never change. What you do for one problem, you do for the other.

By Chmander — On Mar 08, 2014

No matter how hard I try, I always end up getting stumped on mathematical equations, regardless of what kind they are. Does anyone have some tips and solutions? I'm required to take one in one of my freshmen courses, and I have to pass the next test.

Tricia Christensen
Tricia Christensen
With a Literature degree from Sonoma State University and years of experience as a All The Science contributor, Tricia...
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