Which student used the commutative property and the associative property to correctly simplify the expression? \[ \begin{array}{l}\text { Maria: } 20(17 \cdot 5) \\ \text { Carly: } 20(17 \cdot 5)=20(85)=1700 \\ \text { Sing: } 20(17 \cdot 5)=20(85)=20(80+5)=1600+100=1700 \\ \text { None of these students used the commutative property and the associative property to correctly } \\ \text { simplify the expression. }\end{array} \]
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The Deep Dive
Carly correctly simplified the expression by applying numerical multiplication, but she didn’t explicitly mention using the commutative or associative properties. In contrast, Sing creatively breaks down \( 20(85) \) into \( 20(80 + 5) \) using association and distribution which helps in understanding how numbers can be rearranged and grouped for easier calculation. This shows that while both arrived at the same answer, Sing's method explicitly demonstrates these properties. To give a little extra flair to the math magic here, remember that the commutative property lets you swap numbers around—like flipping cards in a game—while the associative property lets you group terms however you like, making math feel a bit like a puzzle! It's all about finding that perfect play to simplify your moves.
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