Follow these steps for rearranging formulas in science and math:

- Identify the formula you want to rearrange and the variable you want to solve for.
- Begin by isolating the variable on one side of the equation. To do this, you will need to perform operations (such as addition, subtraction, multiplication, or division) on both sides of the equation to cancel out terms that do not contain the variable.
- Keep track of the order of operations (PEMDAS) to ensure that you are performing the correct operations in the correct order.
- Simplify the equation by combining like terms and reducing fractions, if necessary.
- Check your work by substituting the value you found for the variable back into the original formula and making sure the equation is still balanced.

## What is PEMDAS?

PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It is a typical mnemonic method used in mathematics to memorize the order of operations.

Let’s break down each component of PEMDAS:

Parentheses: Operations inside parentheses should be performed first. If an expression has multiple sets of parentheses, you should start with the innermost ones and work your way out.

Example: 5 + (3 × 2) = 5 + 6 = 11

Exponents: After evaluating parentheses, you should perform any exponentiation or raising to a power. If there are multiple exponents in an expression, you should evaluate them from left to right.

Example: 2^3 + 4 = 8 + 4 = 12

Multiplication and Division: After parentheses and exponents, multiplication and division should be performed from left to right. These operations have the same priority, so they are evaluated in the order they appear.

Example: 6 ÷ 2 × 3 = 3 × 3 = 9

Addition and Subtraction: Finally, addition and subtraction should be performed from left to right. Like multiplication and division, these operations have the same priority and are evaluated in the order they appear.

Example: 10 – 4 + 2 = 6 + 2 = 8

PEMDAS ensures that mathematical expressions are evaluated consistently and accurately by following the order of operations. It gives a set of criteria for determining which operations should be executed first, avoiding ambiguity and assuring correct calculation.

### Example 1

Original formula: y = mx + b

Variable to solve for: m

Step 1: Isolate the variable m on one side of the equation.

y – b = mx

Step 2: Simplify the equation.

y – b = mx

Step 3: Check your work by substituting the value you found for m back into the original formula.

If y = 2, x = 3, and b = 1, then the value of m should be (2 – 1)/3 = 1/3.

If you substitute these values back into the original formula, you should get: y = (1/3)x + 1, which is balanced.

### Example 2

Original formula: V = 4/3πr^3

Variable to solve for: r

Step 1: Isolate the variable r on one side of the equation.

V = 4/3πr^3 V/4/3π = r^3

Step 2: Simplify the equation.

V/4/3π = r^3 (V/(4/3π))^(1/3) = r

Step 3: Check your work by substituting the value you found for r back into the original formula.

If V = 36π, then the value of r should be (36π/(4/3π))^(1/3) = 3.

If you substitute these values back into the original formula, you should get: V = 4/3π(3^3) = 36π, which is balanced.