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
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- Simply Math
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- Place Value in Decimal Number Systems
- Arithmetic Operations
- Basic Laws
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- Order of Operations
- Fractions
- Decimals
- Percents
- Ratios and Proportions
- Exponents
- Statistics
- Factoring
- Rearranging Formulas
- Solving Linear Equations
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- Place Value in Decimal Number Systems
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- Basic Laws
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- 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
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- Upgrading / Pre-HealthToggle Dropdown
- Basic Laws
- Place Value in Decimal Number Systems
- Decimals
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- Prime Factorisation and Least Common Multiple
- Fractions
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- Ratios and Proportions
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- Reducing Radicals
- Metric Conversions
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- Solving Linear Equations
- Solving Quadratic Equations
- Functions
- Domain and Range of Functions
- Polynomial Long Division
- Exponential and Logarithmic Functions
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- 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
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- Intravenous (IV) Administration
- Infusion Rates for Intravenous Piggyback (IVPB) Bag
- General Dosage Rounding Rules

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You will be encountering ratios, rates, and proportions in various contexts. It is to know the differences between them.

The ratio of \(a\) to \(b\) is expressed by the fraction \(\frac{a}{b}\), where \(a\) is the numerator and \(b\) is the denominator, or by the colon notation \(a:b\) |

When a ratio is used to compare two different kinds of measures, it is called a rate. A unit rate, is the ratio comparing units. |

When two ratios are compared, it is called a proportion. |

Ratios compare the same unit to each other.

`Example 1`

Find the fraction and colon notation for the ratio 3.8 to 7.4.

`Solution`

Fraction notation:

\[\frac{3.8}{7.4}\]

multiply numerator and denominator by 10

\[\frac{38}{74}\]

divide numerator and denominator by 2

\[\frac{19}{37}\]

Colon notation: \(19:37\)

`Example 2`

Ling and Taylor took 12 days and 2 weeks respectively to complete the task. Find the ratio of Ling to Taylor in terms of time it took to complete the task.

`Solution`

For ratios, we have to convert them to the same unit. \(2\) weeks equals to \(14\) days

\[\frac{12}{14}=\frac{6}{7}\]

Rates are used to compare different units.

`Example 1`

1. An airplane traveled 2514 kilometers in 3 hours. What was the rate per hour (or speed)?

`Solution`

\[\frac{2514\,km}{3\,hrs}=\frac{838\,km}{1\,hr}\]

The airplane was travelling at \(838\) km/hr.

`Example 2`

The heart of an elephant, at rest, beats an average of 1500 beats in 60 minutes. What is the rate in beats per minute?

`Solution`

\[\frac{1500\,beats}{60\,minutes}=\frac{25\,beats}{1\,minute}\]

The elephant at rest has a heart rate of \(25\) beats/minute.

Proportions compare the equality of two ratios or fractions. There may be an unknown variable (e.g., \(x\)) to solve in a proportion.

**Solve for the unknown variable in each proportion.**

`Example 1`

\[\frac{6.3}{0.9}=\frac{0.7}{n}\]

To solve the proportion, cross multiply (multiply the denominator to the other side of the equation).

Now solve for the unknown by dividing the coefficient (number in front of the variable) back to the other side of the equation.

\begin{align} \frac{n \times 6.3}{6.3}&=\frac{0.7\times 0.9}{6.3} \\ n&= \frac{0.7\times 0.9}{6.3} \\ n &=0.1\end{align}

`Example 2`

\[\frac{y}{\frac{3}{5}}=\frac{\frac{7}{12}}{\frac{14}{15}}\]

cross multiply

\begin{align} \frac{y}{\frac{3}{5}} \times \frac{14}{15}&=\frac{7}{12} \\ y\times \frac{14}{15}&=\frac{7}{12}\times \frac{3}{5} \end{align}

Now solve for the unknown y by dividing the coefficient (number in front of the variable) back to the other side of the equation.

\begin{align} \frac{y\times \frac{14}{15}}{\frac{14}{15}}&=\frac{\frac{7}{12}\times \frac{3}{5}}{\frac{14}{15}} \\y&=\frac{\frac{7}{12}\times \frac{3}{5}}{\frac{14}{15}} \\ y &=\frac{3}{8}\end{align}

`Example 3`

A serving of fish steak (cross section) is generally \(\frac{1}{2}\) lb. How many servings can be prepared from a cleaned \(18\frac{3}{4}\)-lb tuna?

Solution:

\begin{align}\frac{1\,serving}{\frac{1}{2}\,lb}=\frac{x\,servings}{18\frac{3}{4}lb}\\ 37\frac{1}{2}\,servings=x\end{align}

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

- Last Updated: Jul 17, 2024 3:24 PM
- URL: https://libraryguides.centennialcollege.ca/mathhelp
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