Write an Equation for the Distributive Property
Writing an Equation for the Distributive Property teaches Grade 3 students to record the break-apart multiplication strategy as a formal equation. From Eureka Math Grade 3, the distributive property states that a × (b + c) = a×b + a×c. A student who finds 6 × 7 by computing 6×5 + 6×2 = 30 + 12 = 42 is applying this property. Writing the full equation — 6×7 = 6×(5+2) = 6×5 + 6×2 = 42 — makes the reasoning explicit and connects the mental strategy to algebraic notation used in middle and high school math.
Key Concepts
The distributive property states that a multiplication fact can be broken into the sum of two smaller multiplication facts. This can be written as an equation: $$(a + b) \times c = (a \times c) + (b \times c)$$.
Common Questions
What equation expresses the Distributive Property?
a × (b + c) = a×b + a×c. Multiply each addend inside the parentheses by the factor outside.
How do you write a Distributive Property equation for 6 × 7?
6×7 = 6×(5+2) = 6×5 + 6×2 = 30 + 12 = 42.
Can you use any decomposition of 7 in the equation?
Yes. 6×7 = 6×(4+3) = 6×4 + 6×3 = 24 + 18 = 42 works equally well.
How does writing the equation help beyond just getting the answer?
The equation makes the mathematical reasoning visible, connecting the mental strategy to the formal algebraic property.
How is the Distributive Property equation used in middle school?
It forms the basis for expanding algebraic expressions like 3(x + 4) = 3x + 12.
What Eureka Math grade formalizes writing Distributive Property equations?
Grade 3, within operations and algebraic thinking.