Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

Formula Rearrangement

The goal of rearranging equations is to get the variable you're looking for alone on one side.

Rules for Rearranging Equations

1. Whenever you apply a new operation, you have to do the same thing to both sides.
2. Perform the inverse operation to move or cancel a constant or variable on one side of the equation.

Be aware of the order of operations! Which operation can you perform first?

Examples

Example 1

Rearrange the following formula for the variable $$m_2$$

$\frac{K_1}{K_2} = \frac{m_1 + m_2}{m_1}$

Solution

Since the goal is to isolate for $$m_2$$, we want to move the variable $$m_1$$.

We need to first move the $$m_1$$ at the bottom of the fraction by multiplying both sides by $$m_1$$

$\frac{K_1}{K_2} \times m_1 = \frac{m_1 + m_2}{\cancel{m_1}} \times \cancel{m_1}$

This will move $$m_1$$ from the bottom of the right fraction to the other side of the equation

$\frac{K_1}{K_2} \times m_1 = m_1 + m_2$

Now move we move the remaining $$m_1$$ on the right side by subracting both sides by $$m_1$$

$\frac{K_1m_1}{K_2} - m_1 = \cancel{m_1} + m_2 - \cancel{m_1}$

$\frac{K_1m_1}{K_2} - m_1 = m_2$

Example 2

Rearrange the following equation for $$k$$,

$\frac{4k^3}{m} - 3 = 10 + \frac{d}{2}$

Solution

Watch the video for the solution.