Question

1. mr. huynh wrote the sum of 7 fifteens and 38 fifteens on the board. draw a model, and write the correct expression. (7 + 38)×15 or 7×15 + 38×15 7 fifteens means 7×15 and 38 fifteens means 38×15 5. two students wrote the following numerical expressions. angeline: (7 + 15)×(38 + 15) meiling: 15×(7 + 38) are the students’ expressions equivalent to your answer in problem 4? explain your answer.

Explanation:

Step1: Recall the correct expression from Problem 4

The correct expressions for the sum of 7 fifteens and 38 fifteens are $(7 + 38)\times15$ or $7\times15+38\times15$.

Step2: Analyze Angeline's expression

Angeline's expression is $(7 + 15)\times(38 + 15)$. Using the FOIL - like expansion (first - outer - inner - last), we get $7\times38+7\times15+15\times38 + 15\times15$. This is not equivalent to $(7 + 38)\times15=7\times15+38\times15$.

Step3: Analyze MeiLing's expression

MeiLing's expression is $15\times(7 + 38)$. By the distributive property of multiplication over addition $a\times(b + c)=a\times b+a\times c$, we have $15\times(7 + 38)=15\times7+15\times38 = 7\times15+38\times15$, which is equivalent to the correct expressions from Problem 4.

Answer:

Angeline's expression is not equivalent. MeiLing's expression is equivalent.