what is Rearranging formulas to solve for one of the variables
Rearranging formulas involves changing the formula in such a way that one specific variable is isolated on one side of the equation. This is done by applying algebraic operations to rearrange the terms of the formula.
For example, let's say we have the formula for the area of a rectangle: A = l * w, where A represents the area, l represents the length, and w represents the width.
To solve for one variable, we rearrange the formula to isolate that variable.
If we want to solve for the length (l), we can rearrange the formula as follows:
1. Start with the formula: A = l * w
2. Divide both sides of the equation by w: A/w = (l * w) / w
3. Simplify the right side of the equation: A/w = l * (w / w)
(w / w) cancels out to 1, so we have: A/w = l
4. The equation now says that the length (l) is equal to the area (A) divided by the width (w).
Similarly, if we want to solve for the width (w), we can rearrange the formula as follows:
1. Start with the formula: A = l * w
2. Divide both sides of the equation by l: A/l = (l * w) / l
3. Simplify the right side of the equation: A/l = w * (l / l)
(l / l) cancels out to 1, so we have: A/l = w
4. The equation now says that the width (w) is equal to the area (A) divided by the length (l).
By rearranging the formula, we can solve for any variable by isolating it on one side of the equation. This is useful in many mathematical and scientific applications where we need to find the value of a particular variable.