Find Area Using the Distributive Property
Find Area Using the Distributive Property is a Grade 3 math skill from Eureka Math applying the Distributive Property to rectangle area. When a rectangle has a large side length that is hard to multiply directly, break that side into two smaller parts. The total area equals the sum of the two smaller rectangles: Area = l × (w1 + w2) = (l × w1) + (l × w2). For example, the area of a 6 × 13 rectangle = (6 × 10) + (6 × 3) = 60 + 18 = 78. This strategy uses known facts to find products that would otherwise require more complex computation.
Key Concepts
To find the area of a rectangle with a large side length, you can break that side into two smaller parts. The total area is the sum of the areas of the two smaller rectangles created. $$Area = l \times w = l \times (w 1 + w 2) = (l \times w 1) + (l \times w 2)$$.
Common Questions
How does the Distributive Property apply to finding area?
Break one side of the rectangle into two smaller parts. Find the area of each smaller rectangle separately, then add. This is: l × (w1 + w2) = (l × w1) + (l × w2).
How do you find the area of a 7 × 12 rectangle using the Distributive Property?
Break 12 into 10 + 2. Then: (7 × 10) + (7 × 2) = 70 + 14 = 84 square units.
Why is breaking a side into smaller parts helpful?
Multiplying by 10 or other round numbers is easier than multiplying by larger irregular numbers. Decomposing the harder factor into simpler parts reduces the difficulty.
What is the Distributive Property formula for area?
Area = l × w = l × (w1 + w2) = (l × w1) + (l × w2), where w1 and w2 are the two parts that the width is broken into.
In which textbook is Find Area Using the Distributive Property taught?
This skill is taught in Eureka Math, Grade 3.