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2.7a: Mixed numbers and conversions
A mixed number is merely a whole number plus a fraction,
so this means if I have something like 3 and 5/8.
It is really just meaning 3 + 5/8.
To change a mixed number to a fraction,
we need to multiply the whole number and the denominator
and then add the numerator to that.
Then to change a fraction to a mixed number, we merely divide.
The remainder is going to be our new numerator.
Also, remember that you always keep the same denominator
and this applies to both changing mixed number to fraction
or fraction to mixed number.
The denominator should never change.
Let us look at example 1.
In the first example, we convert 5 and 9/11 to a fraction.
Remember to convert to a fraction, we are going to be working in a clockwise motion
starting at the denominator
and working our way around to the numerator.
Let us re-write it over here to see this a little bit more clearly.
We are going to start by doing 5 x 11 and 5 x 11 is 55,
so that was our first step.
We then work our way around and we add 9,
which means we add 9 to the 55
and this is going to give us 64.
This is our new numerator,
which means we have 64 over 11 because we never change the denominator.
64/11 is the same as 5 and 9/11.
Let us look at example 2 next.
In example 2, we are converting this fraction to a mixed number.
Remember, we simply do this by dividing,
remembering that the fraction bar actually means divide,
so we have 73 ק 12.
Let us write this as a long division problem,
12 goes into 73 six times,
6 x 2 is 12, 6 x 6 is 1 + 1 is 72
and we have a remainder of 1.
Now, we have to determine which of these pieces is which.
The 6 is how many times it went in
so that is how many whole pieces there are.
There are 6 whole pieces.
Next, we look at the remainder.
The remainder was 1.
This is how many pieces were leftover,
so we have 1 out of 12,
12 is the number of whole pieces we had.
Remember, the denominator should never change from the original.
We started with 12 and we ended up with 12,
so our answer is 6 and 1/12.
Remember when converting between mixed numbers and fractions,
you must follow some rules.
Changing a mixed number to a fraction,
you multiply the whole number and the denominator
and then you add in the numerator.
Then if you are changing a fraction to a mixed number,
you simply use long division where the whole number is written,
the remainder becomes the new numerator
and in both cases, the denominator never changes.