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.

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Adding and Subtracting Fractions

It is easiest to work with proper or improper fractions when adding or subtracting fractions. If the fraction is mixed, simply convert it to an improper fraction before you start. There are three simple steps to adding or subtracting fractions.

Step 1: Make sure the denominators are the same (lowest common denominator).
Step 2: Add or subtract the numerators and put the answers over the same deonominator
Step 3: Simplify the fraction (if needed).

Example: \(\frac{3}{4}-\frac{1}{4}\)

Solution:

Since both deonominators are the same, go to step 2:

\(\frac{3}{4}-\frac{1}{4}=\frac{3-1}{4}=\frac{2}{4}\)

Now, simplify the fraction:

\(\frac{2}{4}=\frac{1}{2}\)

As stated in step 1, before you can add or subtract fractions, the fractions need to have a common denominator. If the denominators are not the same, you can either use the least common denominator method to make them the same, or you can multiply both parts of each fraction by the denominator of the other.

This latter method always works, but you will often need to simplify the fraction afterwards.

Now, take a look at the fractions \(\frac{1}{3} \text{ and } \frac{1}{6}\).If we wanted to add or subtract these two fractions, we would need a common denominator. As stated above, we could multiply both parts of each fraction by the denominator of the other:

\(\frac{1}{3}\times\frac{6}{6} = \frac{6}{18}\) and \(\frac{1}{6}\times\frac{3}{3}=\frac{3}{18}\)

Now we can add or subract these two fraction. However, this is not the lowest common denominator. To find the lowest common denominator for the two fractions \(\frac{1}{3}\) and \(\frac{1}{6}\),we would have to list the mulitples of 3 and the multiples of 6:

\(\frac{1}{3}\) has multiples of 3: 3, 6, 9, 12, 15, 18, 21,...

has multiples of 6: 6, 12, 18, 24, 30, 36,...

Notice that the smallest number that is the same is the numer 6, so the lowest common denominator for \(\frac{1}{3}\) and \(\frac{1}{6}\) is 6. Now, the fraction \(\frac{1}{3}\) can be written as \(\frac{2}{6}\) by using equivalent fractions, and we can now add/subtract the two fractions \(\frac{2}{6}\) and \(\frac{1}{6}\).

Example: Find the lowest common denominator and equivalent fractions for \(\frac{3}{4}\) and \(\frac{5}{12}\).

Solution:

\(\frac{3}{4}\) has multiples of 4: 4,8,12,16,20,24,28,....

\(\frac{5}{12}\) has multiples of 12: 12, 24, 36, 48, 60, 72,....

The lowest common denominator for \(\frac{3}{4}\) and \(\frac{5}{12}\) is 12. The equivalent fractions would be:

\(\frac{3}{4}\times\frac{3}{3}=\frac{9}{12}\) and \(\frac{5}{12}\times \frac{1}{1}=\frac{5}{12} \)

Example: \(\frac{1}{5}-4\frac{5}{7}\)

Solution:

First convert the mixed fraction into an improper fraction: \(\frac{4 \times 7+5}{7}=\frac{33}{7} \).

Now, what we really want is \(\frac{1}{5}-\frac{33}{7}\).

Notice that the the denominators are different. The lowest common denominator would be 35. The equivalent fractions are:

\(\frac{1}{7} \times \frac{7}{7}=\frac{7}{35}\) and \(\frac{33}{5}\times\frac{5}{5}=\frac{165}{35}\)

Therefore, \(\frac{7}{35}-\frac{165}{35}=\frac{158}{35}\)