Question

question
enter the missing values in the area model to find 5(5n - 7)
answer attempt 1 out of 2
according to the model above, 5(5n - 7) =
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Explanation:

Step1: Analyze the area model

The area model represents the multiplication \(5(5n - 7)\). The first part of the area model is \(25n\), which comes from \(5\times5n\). Now we need to find the other part of the area model and then combine like terms.

Step2: Find the missing area part

To find the area corresponding to \(5\times(-7)\), we calculate \(5\times(-7)= - 35\). So the missing value in the area model (the rectangle with height - 7 and width 5) is \(-35\), and the top - right missing value (the width corresponding to the area \(25n\)) is \(5n\) (since \(25n\div5 = 5n\)).

Step3: Combine the terms

Now, using the distributive property (which is represented by the area model), \(5(5n-7)=5\times5n+5\times(-7)\). We know that \(5\times5n = 25n\) and \(5\times(-7)=-35\). So combining these terms, we get \(25n-35\).

Answer:

For the area model: the top - right missing value is \(5n\), the bottom - left missing value is \(-35\), and \(5(5n - 7)=25n-35\)