Ontario Tech acknowledges the lands and people of the Mississaugas of Scugog Island First Nation.

We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

# Fractions

Let's review some basic functions as well as some basic operations with fractions.

## Understanding Fractions

A fraction is part of an entire object. A fraction is always a rational number. We call the top number the numerator; it is the number of parts you have. We call the bottom number the denominator; it is the number of parts the whole is divided into. There are three different types of fractions; proper, improper, and mixed fractions. The following is a table which provides a brief explanation and example of each:
 Type of Fraction Definition Example Proper The numerator is less than the denominator 5/8  or  11/22 Improper The numerator is greater than (or equal to) the denominator 12/7  or  8/8 Mixed A whole number and proper fraction together 1 1/3  or  2 1/4

## Converting Fractions

Since a mixed fraction is just a whole number and a fraction combined into one "mixed" number, you can use either an improper fraction or a mixed fraction to show the same amount. To convert an improper fraction to a mixed fraction, follow these steps:
• Divide the numerator by the denominator.
• Write down the whole number answer.
• Then write down any remainder above the denominator

Example: Convert the improper fraction 7/4 to a mixed fraction.

Solution:

Divide the numerator by the denominator 7÷4 = 1 with a remainder of 3.

So we write down the 1 as a whole number and then write down the remainder (3) above the denominator (4), like this: 1 3/4

To convert from a mixed fraction to an improper fraction, follow these steps:

• Multiply the whole number part by the fraction denominator,
• Add that to the numerator,
• Then write the result on top of the denominator.

Example: Convert the mixed fraction 5 6/7 to an improper fraction.

Solution:

Multiply the whole number by the denominator: 5 x 7= 35

Add the numerator to that: 35 + 6 = 41

Then write that down above the deonominator (7), like this: 41/7

## Equivalent Fractions

Before doing operations with fractions one must understand equivalent fractions. For example, these fractions are really all the same:

1/2/3/9

They are all the same because any time you multiply or divide both the numerator and denominator by the same number, the fraction keeps its value. For example, ﻿1﻿/﻿7﻿ x ﻿2﻿/﻿2 ﻿= ﻿2﻿/﻿14﻿ means that ﻿1﻿/﻿7 ﻿= ﻿2/14. For equivalent fractions, always remember that what you do to the numerator, you must do to the denominator. This process will help you in understanding how to obtain a common denominator for two fractions.