Question

fill in the parts-whole model for the following equation. (2y) = (______) - (-8y)

Explanation:

Step1: Let the unknown be \( x \)

We have the equation \( 2y = x - (-8y) \).

Step2: Simplify the right - hand side

Simplify \( x-(-8y) \) using the rule \( a - (-b)=a + b \), so the equation becomes \( 2y=x + 8y \).

Step3: Solve for \( x \)

Subtract \( 8y \) from both sides of the equation \( 2y=x + 8y \).
\( x=2y-8y \)
\( x=- 6y \)

For the parts - whole model: The whole is \( x=-6y \) (the top rectangle), and the two parts are \( 2y \) and \( - 8y \) (the bottom two rectangles).

Answer:

The unknown value is \(-6y\). The parts - whole model has the whole as \(-6y\) (top rectangle) and the parts as \(2y\) and \(-8y\) (bottom two rectangles).