Solving for one variable
Solving for One Variable explains how to rearrange a formula or equation involving multiple variables to isolate a specific variable by treating all others as constants and applying inverse operations. Taught in Yoshiwara Elementary Algebra Chapter 5: Exponents and Roots, this skill is critical for Grade 6 students working with geometry formulas, physics equations, and multi-variable algebraic formulas. The same equation-solving steps apply, with the target variable treated as the unknown.
Key Concepts
Property To solve a formula for one variable, treat it as the unknown and all other variables as constants. Isolate the desired variable by applying inverse operations to both sides of the equation. Remember to follow the order of operations in reverse and do not combine unlike terms.
Examples To solve the perimeter formula $P = 2l + 2w$ for $l$, first subtract $2w$ from both sides: $P 2w = 2l$. Then, divide by 2: $l = \frac{P 2w}{2}$.
To solve the interest formula $A = P + Prt$ for $r$, first subtract $P$: $A P = Prt$. Then, divide by $Pt$ to isolate $r$: $r = \frac{A P}{Pt}$.
Common Questions
How do you solve a formula for one variable?
Treat all other variables as constants, then use inverse operations (addition/subtraction, multiplication/division) to isolate the target variable on one side of the equation.
How do you solve d = rt for r?
Divide both sides by t to get r = d/t. This isolates r while treating d and t as known quantities.
Why do we need to solve formulas for different variables?
Different problems give different information. Rearranging the formula lets you solve for whichever quantity is unknown in a given situation.
Where is solving for one variable in Yoshiwara Elementary Algebra?
This topic is covered in Chapter 5: Exponents and Roots of Yoshiwara Elementary Algebra.
Is solving for one variable in a formula different from solving a regular equation?
The process is identical. The only difference is that some quantities are represented by letters (other variables) instead of numbers.