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.

- Welcome
- Learning Math Strategies (Online)Toggle Dropdown
- Study Skills for MathToggle Dropdown
- Simply Math
- Business Math
- How to use a scientific calculator
- Place Value in Decimal Number Systems
- Arithmetic Operations
- Basic Laws
- Operations on Signed numbers
- Order of Operations
- Fractions
- Decimals
- Percents
- Ratios and Proportions
- Exponents
- Statistics
- Factoring
- Rearranging Formulas
- Solving Linear Equations
- Solving Systems of Linear Equations
- Trade and Cash Discounts
- Multiple Rates of Discount
- Payment Terms and Cash Discounts
- Markup
- Markdown
- Simple Interest
- Equivalent Values
- Compound Interest
- Equivalent Values in Compound Interest
- Nominal and Effective Interest Rates
- Ordinary Simple Annuities
- Ordinary General Annuities

- Hospitality MathToggle Dropdown
- Place Value in Decimal Number Systems
- Arithmetic Operations
- Order of Operations
- Basic Laws
- Prime Factorisation and Least Common Multiple
- Fractions
- Decimals
- Percents
- Exponents
- Units of Measures
- Fluid Ounces and Ounces
- Metric Measures
- Yield Percent
- Recipe Size Conversion
- Ingredient Ratios
- Food-Service Industry Costs

- Engineering MathToggle Dropdown
- Basic Laws
- Order of Operations
- Prime Factorisation and Least Common Multiple
- Fractions
- Exponents
- Radicals
- Reducing Radicals
- Factoring
- Rearranging Formulas
- Solving Linear Equations
- Areas and Volumes of Figures
- Congruence and Similarity
- Functions
- Domain and Range of Functions
- Basics of Graphing
- Transformations
- Graphing Linear Functions
- Graphing Quadratic Functions
- Solving Systems of Linear Equations
- Solving Quadratic Equations
- Solving Higher Degree Equations
- Trigonometry
- Graphing Trigonometric Functions
- Graphing Circles and Ellipses
- Exponential and Logarithmic Functions
- Complex Numbers
- Number Bases in Computer Arithmetic
- Linear Algebra
- Calculus
- Set Theory
- Modular Numbers and Cryptography
- Statistics
- Problem Solving Strategies

- Upgrading / Pre-HealthToggle Dropdown
- Basic Laws
- Place Value in Decimal Number Systems
- Decimals
- Significant Digits
- Prime Factorisation and Least Common Multiple
- Fractions
- Percents
- Ratios and Proportions
- Exponents
- Radicals
- Reducing Radicals
- Metric Conversions
- Factoring
- Solving Linear Equations
- Solving Quadratic Equations
- Functions
- Domain and Range of Functions
- Polynomial Long Division
- Exponential and Logarithmic Functions
- Statistics

- Nursing MathToggle Dropdown
- Arithmetic Operations
- Order of Operations
- Place Value in Decimal Number Systems
- Decimals
- Fractions
- Percents
- Ratios and Proportions
- Nutrition Labels
- Interpreting Drug Orders
- Oral Dosages
- Dosage Based on Size of the Patient
- Parenteral Dosages
- Intravenous (IV) Administration
- Infusion Rates for Intravenous Piggyback (IVPB) Bag
- General Dosage Rounding Rules

- Transportation MathToggle Dropdown
- PhysicsToggle Dropdown
- Architectural MathToggle Dropdown

Believe it or not, there are many good reasons to develop your ability to rearrange equations that are important to the your field. It can save time, help you with units and save some brain space! Here are some reasons to develop your equation manipulation skills (in no particular order):

- Equations are easier to handle
*before*inserting numbers! And, if you can isolate a variable on one side of the equation, it is applicable to every similar problem that asks you to solve for that variable! - If you know how to manipulate equations, you only have to remember one equation that has all the variables of question in it - you can manipulate it to solve for any other variable! This means less memorization!
- Manipulating equations can help you keep track of (or figure out) units on a number. Because units are defined by the equations, if you manipulate, plug in numbers and cancel units, you'll end up with exactly the right units (for a given variable)!

- Apply the same operation to both sides of the equal sign.
- 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?

`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.

Designed by Matthew Cheung. This work is licensed under a Creative Commons Attribution 4.0 International License.

- Last Updated: Aug 1, 2024 10:46 AM
- URL: https://libraryguides.centennialcollege.ca/mathhelp
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