Fractions (1).notebook
January 28, 2016
Let's review some fractions basics...
Fractions represent parts of a whole.
Equivalent Fractions
Fractions are made up of:
Fractions which are equal. i.e. they
represent the same proportion of a whole.
For example:
The numerator (number on the top)
50 is the same as 1
2
100
4 is the same as 1
2
8
The denominator (number on the bottom)
They are equivalent fractions
Simplifying Fractions
This means reducing fractions to their "lowest terms" In other words,
the smallest equivalent fraction.
For Example 3 can be simplified to 1
4
12
To simplify a fraction, both the numerator and denominator need to be
divided by the same number.
In the above example, 3 and 12 were divided by 3.
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Fractions (1).notebook
Simplify these fractions:
January 28, 2016
Let's get some practice!
Worksheet
Let's sort out some issues regarding fractions, using an example:
Improper Fractions
Our class ordered pizzas for lunch. Each pizza had 6 slices.
This creates what is known as an "improper fraction", where the
numerator is larger than the denominator.
Afterwards, we counted and found that 8 pieces of pizza were left over.
How else could our improper fraction be represented?
How would we represent the remaining pizza as a fraction?
Mixed Numbers
Converting improper fractions to mixed numbers
Our 8 pieces of pizza can also be expressed as being:
In our example, we converted an improper fraction into a mixed number:
1 whole pizza (6 of the pieces)
Here are the steps:
with 2 pieces left over.
(1) Calculate how many times the denominator can go into the numerator
(2) That will be your whole number portion of the mixed number
This gives us what is known as a "mixed number". A whole number and
a fraction together.
(3) The rest that is left over will be your fraction portion of the mixed
number
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Fractions (1).notebook
January 28, 2016
Let's re-do our pizza example with the
steps in mind:
Try some other examples:
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Converting from mixed numbers to improper fractions
25
11
17
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Let's try some more examples:
To convert back the other way, from a mixed number to an improper
fraction, we follow these steps:
(1) Multiply the whole number by the denominator
(2) Add it to the numerator
Example:
(1) 4 x 10 = 40
(2) 40 + 7 = 47
Answer = 47
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It is important that we are comfortable with making these conversions
because we will be using these skills a lot during the next few weeks
Let's get some more practice...
http://www.mathplayground.com/fractions_mixed.html
http://www.mathplayground.com/fractions_improper.html
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Fractions (1).notebook
Adding Fractions
January 28, 2016
Let's try a few more:
Adding fractions with like (the same) denominators is easy.
We simply add the numerators together and leave the denominators
alone.
Once we are done, we
simplify the fraction..
Often, adding fractions will result in improper fractions being created.
We should always reduce these fractions to lowest terms and then
convert them into mixed numbers.
What if we must add fractions which do NOT have a common
denominator?
We MUST change one or both of the fractions into equivalent
fractions so that they have common denominators before we
do the addition.
Here's how we do it:
Step One: Find the Lowest Common Multiple of the denominators
involved.
Step Two: Create equivalent fractions, using that same common
denominator.
Let's try a few more:
We do that by multiplying the numerators by the same amount as we
did for the denominator for each fraction!
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Fractions (1).notebook
January 28, 2016
Let's get some more practice!
Here are the steps!
Step One: Find the Lowest Common Multiple of the denominators
involved.
Step Two: Create equivalent fractions, using that same common
denominator.
We do that by multiplying the numerators by the same amount as we
did for the denominator for each fraction!
Step Three: Add the two numerators together and remember to simplfy
your final answer
To add Mixed Numbers, we simply add the whole numbers together and
then the fractions.
What if the addition of the fractional parts leaves us with an improper
fraction left over?
Let's do another one:
Let's get some more practice!
Worksheet
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Fractions (1).notebook
January 28, 2016
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Subtracting fractions - similar to adding them together.
To subtract mixed numbers, we must first subtract the fractions, then do
the whole numbers:
If they have like denominators, we simply subtract the numerators and
leave the denominators alone:
4 - 2 = 2
6
6
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If they don't have like denominators, we find the Lowest Common
Denominator:
Try this one! See if you can spot the problem....
Sometimes the 2nd fraction is greater than the 1st fraction. In this case, we
need to "borrow" a whole number in the first mixed number to increase
the size of the fractional part.
Watch Carefully!
Let's do another one of those:
Let's try some more!
Watch Carefully!
Worksheet
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Fractions (1).notebook
A world without multiplication...
Let's pretend multiplication didn't exist. If that were the case, how could
I solve 4 x 5?
January 28, 2016
4 x 5 means we have 4 groups of 5. If we set out those 4 groups of 5,
we can add them together.
In other words, how could I think about 4 x 5 in another way so that I
could get the answer without using multiplication?
So, multiplication problems can also be solved by re-thinking
them as addition problems.
So, getting back to fractions, how can we re-think these fractions
questions without using multiplication?
Let's try some more!
worksheet
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