Given the formula for the volume of a box, V=lwh , which equation best represents the remaining units when justifying your rearrangement to solve for the width?
The equation that represents the remaining units when justifying the rearrangement to solve for the width is:
V / (lh)
In this equation, we divide the volume (V) by the product of the length (l) and height (h) to isolate the width. The units of the volume and the product of length and height would cancel out, leaving us with the remaining units of width.
To solve for the width (w) in the formula for the volume of a box (V=lwh), we need to rearrange the equation. To do this, we need to isolate the width on one side of the equation.
First, we can divide both sides of the equation by the length (l):
V/l = (lwh)/l
This simplifies to:
V/l = wh
Next, we can divide both sides of the equation by the height (h):
(V/l)/h = (wh)/h
This simplifies to:
(V/l)/h = w
Alternatively, we can rearrange the equation as follows:
V = lwh
Dividing both sides of the equation by both length (l) and height (h):
V/(lh) = w
Therefore, the equation that best represents the remaining units when rearranging to solve for the width is:
(V/l)/h = w
or
V/(lh) = w
To justify rearranging the equation V = lwh to solve for the width, we need to first determine which equation best represents the remaining units after the rearrangement.
Let's rearrange the formula step by step to solve for the width, w:
1. Start with the equation V = lwh.
2. Divide both sides of the equation by lh to isolate w: V / (lh) = w.
Now, let's analyze the remaining units in the rearranged equation.
On the left side of the equation, V represents the volume of the box, which is measured in cubic units (e.g., cubic meters, cubic inches).
On the right side of the equation, (lh) represents the product of the length and height of the box. The units for length and height are both linear units (e.g., meters, inches).
Therefore, after rearranging the equation, the remaining units are cubic units divided by the product of linear units.
Thus, the equation that best represents the remaining units when justifying the rearrangement to solve for the width is:
w = V / (lh)