Question

fill in the parts-whole model for the following equation. (____) = (4y - 6z) - (4y)

Explanation:

Step1: Simplify the right - hand side

We have the expression \((4y - 6z)-(4y)\). Using the distributive property of subtraction \(a-(b)=a+(-b)\), we can rewrite it as \(4y-6z - 4y\).

Step2: Combine like terms

The \(4y\) and \(- 4y\) are like terms. When we combine \(4y-4y-6z\), \(4y-4y = 0\), so the result is \(-6z\).

For the parts - whole model:

• The top rectangle (the whole after subtraction) should be \(-6z\).
• The middle rectangle (the original whole before subtraction) should be \(4y - 6z\).
• The bottom left rectangle (the part we are subtracting) should be \(4y\).
• The bottom right rectangle (the result of the subtraction) should be \(-6z\) (or we can think of the two bottom rectangles as the parts: one is \(4y\) and the other is \(-6z\) when we consider the decomposition, but based on the subtraction \((4y - 6z)-(4y)\), the top is the result \(-6z\), the middle is the minuend \(4y - 6z\), and the bottom left is the subtrahend \(4y\), bottom right is the difference \(-6z\))

Answer:

The blank in the equation is \(\boldsymbol{-6z}\). For the parts - whole model:

• Top rectangle: \(-6z\)
• Middle rectangle: \(4y - 6z\)
• Bottom left rectangle: \(4y\)
• Bottom right rectangle: \(-6z\)