What is the Distributive Property?
The mathematical property that states: “The product of the sum is equal to the sum of the products.”
The distributive property is a math rule that shows how multiplication interacts with addition and subtraction.
It tells us that multiplying a number by a group of numbers added or subtracted together gives the same result as multiplying each number individually, then adding or subtracting the results, like so:
- Distributive property with addition: a (b + c ) = ab + ac
- Distributive property with subtraction: a (b − c) = ab − ac
Let’s look at an example with addition, where a=3, b=4, and c=5:
3 (4 + 5)
According to the distributive property, we will multiply each number in the brackets by 3:
= 3 × 4 + 3 × 5
= 12 + 15
= 27
What happens if we followed the order of operations and solved the parentheses first?
3 (4 + 5)
= 3 × 9
= 27
We get the same answer (27)! Distributive property of addition works.
Let’s try with subtraction, where a = 2, b = 8, and c = 3:
2 (8 – 3) =
= 2 × 8 – 2 × 3
= 16 – 6
= 10
What happens if we follow the order of operations?
2 (8 – 3) =
= 2 × 5
= 10
There we have it: Both paths, the order of operations and distributive property, led us to the same answer (10) once again.
When Do Students Learn About the Distributive Property?
Grades 3–4 – Introduction to the Distributive Property
Students explore how multiplication can “break apart” addition using area models, number lines, and mental math strategies.
Grades 5+ – Applying the Distributive Property in Algebra
Students use the distributive property to simplify expressions, solve equations, and work with variables.
