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.

# Ratio and Proportion

A ratio is the relationship between one amount and another. Ratios occur whenever comparisons are being made. The ratio of a to b can be written a : b or as the fraction a/b. Ratios are usually reduced to lowest terms for simplicity. This can be done by dividing both terms by the greatest common factor.

Example:

Reduce the ratio 28:12 to lowest terms.

Solution:

In this case, the greatest common factor (the largest number both terms can be evenly divided by) is 4.

28/4  :  12/4

7 : 3

Example:

Determine the ratio of hydrogen to nitrogen in ammonia provided that when you have 18 hydrogen atoms you have 6 nitrogen atoms.

Solution:

If ammonia has 18 hydrogen atoms and 6 nitrogen atoms, then the ratio is 18:6. In simplest form, the ratio of hydrogen to nitrogen is 3:1.

## SOLVING FOR AN UNKNOWN QUANTITY

When two ratios are set equal to each other, the resulting equation is called a proportion. If the ratio

A : B and the ration C : D are proportionate to one another they can be rewritten as the equation

A/B  =  C/D

An unknown variable in a proportion can be solved for using basic algebra.

Example:

If 4 : 3 is proportionate to 20 : x, solve for x.

$$\displaylines{ \frac{3}{4} &=& \frac{x}{20} \\ \frac{3\cdot20}{4} &=& x \\ x &=& 15}$$

In chemical reactions, the amount of products produced is proportionate to the amount of reactants used.

Example:

Given that 3 moles of carbon dioxide are produced for every mole of propane burned, determine the number of moles of propane required to produce 18 moles of carbon dioxide.

Solution:

1:3 and $$\displaylines{x:18 \\ \frac{1}{3}=\frac{x}{18} \\ \frac{18}{3}=x \\ x=6}$$

Ratio and Proportion Example 1:

Ratio and Proportion Example 2 - Similar Triangle:

Ratio and Proportion Example 3 - Concentration:

Ratio and Proportion Example 4 - Chemical Reaction:
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