Distributive Property
In short: The distributive property says a number times a sum equals the sum of the products, so 6(40 + 3) = 6 x 40 + 6 x 3 = 258.
6th GradeAlgebra6.EE.A.3
What is Distributive Property?
The distributive property lets you split a hard multiplication into two easy ones. A rectangle 6 units tall and 43 units wide can be cut into a 6 by 40 piece and a 6 by 3 piece, and the two areas add up to the whole.
Precisely, for any numbers \(a\), \(b\) and \(c\), \(a(b + c) = ab + ac\). It also works with subtraction, \(a(b – c) = ab – ac\), and in reverse it is the idea behind factoring out a common number.
How to spot it
- A product has parentheses with a sum or difference inside, such as 7(2x + 9).
- A mental math trick turns 7 x 98 into 7 x 100 minus 7 x 2.
- An expression like 12x + 18 can be rewritten as 6(2x + 3) by taking out a shared factor.
- A rectangle is cut into two smaller rectangles whose areas you add.
The method
- Identify the number outside the parentheses and the terms inside.
- Multiply the outside number by the first inside term, then by the second inside term.
- Keep the sign that sits between the inside terms for the new sum or difference.
- Simplify each product and combine, then test with a number if you are unsure.
Distributive Property: solved example
Problem
A theater in Omaha sells 9 tickets at $12 each plus $4 booking fees on each ticket. Use the distributive property to find the total.
Solution
Each ticket costs \(12 + 4\) dollars, so the total is \(9(12 + 4)\).
Distribute: \(9 \cdot 12 + 9 \cdot 4 = 108 + 36 = 144\). The family pays $144.
Try it
Question 1
Expand \(5(3x – 8)\).
Show the answer
\(5 \cdot 3x – 5 \cdot 8 = 15x – 40\).
Question 2
Compute \(8 \times 97\) by splitting 97 as \(100 – 3\).
Show the answer
\(8(100 – 3) = 800 – 24 = 776\).
Distributive Property vs. Like Terms
The distributive property is a rule for multiplying across parentheses. Combining like terms is a rule for adding terms that share the same variable part, as in \(4x + 9x = 13x\). Often you distribute first, then combine.
Keep going
Lessons
Worksheets and quizzes
- Equivalent Expressions and the Distributive Property – Worksheet
- Equivalent Expressions and the Distributive Property – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Algebra