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 MathToggle Dropdown
- 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 Math
- 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

The **Commutative Law** states that even if we switch the order of the numbers, the resulting answer is the same. The commutative law holds for addition and multiplication.

The **Commutative Law of Addition**: a + b = b + a

`Example`

The **Commutative Law of Multiplication**: a × b = b × a

`Example`

The commutative law does not hold for subtraction or division.

For instance:

- 3 - 2 ≠ 2 - 3
- 2 ÷ 3 ≠ 3 ÷ 2

__Uses of Commutative Law__

It is sometimes easier to compute the answer to a multiplication or addition question by switching the order of numbers.

`Example`

For addition question: In the question 3 + 44 + 17, it is easier if we add 17 and 3 first, so 3 + 44 + 17 = 44 + 3 + 17 = 44+20 = 64

`Example`

For multiplication question: In the question, 5 × 10 × 6, it is easier if we multiply 6 and 5 first, so 5 × 10 × 6 = 10 × 5 × 6 = 10 × 30 = 300

The **Associative Law** states that even if we group numbers differently, the answer is still the same. The associative law holds for addition and multiplication.

The **Associative Law of Addition**: (a + b) + c = a + (b + c)

`Example`

The **Associative Law of Multiplication**: (a × b) × c = a × (b × c)

`Example`

The associative law does not hold for subtraction or division.

For instance,

- (5 - 10) - 4 = -5 - 4 = -9 but 5 - (10 - 4) = 5 - 6 = -1
- (8 ÷ 4) ÷ 2 = 2 ÷ 2 = 1 but 8 ÷ (4 ÷ 2) = 8 ÷ 2 = 4

__Uses of Associative Law__

It is sometimes easier to add or multiply if we group numbers differently.

`Example`

For addition: In the question, 23 + 45 + 5, it is easier to add 45 and 5 first, rather than adding 23 and 45 first. So, 23 + 45 + 5 = 23 + (45 + 5) = 23 + 50 = 73

`Example`

For multiplication: In the question, 15 × 5 × 2, it is easier to first multiply 5 and 2 rather than 15 and 5. So, 15 × 5 × 2 = 15 × (5 × 2) = 15 × 10 = 150

The **Distributive Law**: a × (b + c) = a × b + a × c and a × (b - c) = a × b - a × c.

`Example`

_{The distributive law }_{does not hold }_{for division. }

_{For instance, 16 ÷ (8 + 2) = 16 ÷ 10 = 1.6 but 16 ÷ 8 + 16 ÷ 2 = 2 + 8 = 10. }

_{The }_{correct way}_{ is 16 ÷ (8 + 2) = 16 ÷ 10 = 1.6.}

__Uses of Distributive Law__

A difficult multiplication question’s numbers can be broken up or combined, resulting in an easier multiplication question using the distributive law.

Example where we break up a number: In the question, 3 × 502, 502 can be broken up into (500 + 2) and so the question becomes, 3 × (500 + 2) and using the distributive law, this is equal to 3 × 500 + 3 × 2 = 1500 + 6 = 1506

Example where we combine numbers: In the question, 15 × 3 + 15 × 7, we can combine 3 and 7, so 15 × 3 + 15 × 7 = 15 × (3 + 7) = 15 × 10 = 150

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

chat loading...