Grade 7 Math: Use Distributive Property to Expand $ 6(x + 7) $ for Deck Area

Question

An architect plans to build an extension to Meiling’s rectangular deck. Let $ x $ represent the increase, in meters, of her deck’s length. The expression $ 6(x + 7) $ represents the area of the deck, where 6 is the width, in meters, and $ (x + 7) $ represents the extended length, in meters. Use the Distributive Property to write an expression that represents the total area of Meiling’s new deck.

Accepted Answer

6x + 42

Answer

1. Recall the Distributive Property: For any real numbers $ a $, $ b $, and $ c $, $ a(b + c) = ab + ac $. 2. Identify $ a = 6 $, $ b = x $, and $ c = 7 $ in the expression $ 6(x + 7) $. 3. Apply the Distributive Property: Distribute 6 to both $ x $ and 7 inside the parentheses. 4. Calculate $ 6 \cdot x = 6x $ and $ 6 \cdot 7 = 42 $. 5. Combine the results: $ 6x + 42 $.