Welcome to my video on subtracting mixed numbers.
Here we have 3 and 3/4ths being subtracted by 1 and 7/8ths.
And the first thing I like to do.
I wrote this for you in green.
I like to convert the mixed numbers to improper fractions.
And then subtract.
And I do realize there are quicker ways to subtract mix numbers.
However, this method which I am teaching is guaranteed to work the same way for every
single problem.
Where as the other methods that might be a little quicker are not guaranteed to work
the same way for every single problem.
So let's just get started right away.
Let's convert our mixed numbers into improper fractions.
We'll start first with 3 and 3/4ths.
Since this mixed number has a 4 in the denominator.
Our improper fraction is also going to have a four in the denominator.
And in the numerator, we have to multiply the denominator of 4 with the whole number
of 3.
4 times 3 is equal to 12.
And then we have to add that with our numerator of 3.
And this is all being subtracted with 1 and 7/8ths.
So let's do the same thing with this mixed number.
Let's change it into a improper fraction.
since it has a denominator of 8, the improper fraction is also going to have a denominator
of 8.
And in the numerator we multiply the 8 by the whole number of 1.
8 times 1 is 8.
And then we add all that to the numerator of 7.
So let's simplify these two fractions.
In the first fraction we have 12 plus 3 in the numerator. 12 plus 3 is equal to 15.
And our denominator stays the same.
And this is all being subtracted by our second fraction which has a numerator of 8 plus 7,
which is just 15 as well.
And our denominator of 8 stays the same.
So now when you subtract or add two fractions, you have to have a common denominator.
That means that both denominators have to be the same.
So since we have one denominator which is a 4 and another denominator which is an 8.
We have to make them both the same.
So I'm going to multiply the 4 by 2.
Which gives us 2 times 4 which is 8.
And then both denominators will be the same.
And you have to remember whatever you do to the bottom of a fraction you have to do to
the top of a fraction.
So since we multiplied the bottom by 2, we have to multiply the top by 2 as well.
So now let's simplify the first fraction.
In the numerator we have 2 times 15.
2 times 15 is 30.
and in the denominator we have 2 times 4 which is 8.
And our second fraction stays the same.
And now since we have common denominators of 8 we can subtract these fractions really
easily.
Whenever you're subtracting fractions the denominator stays the same.
Since we have a denominator of 8, our answer is also going to have a denominator of 8.
And in the numerator we are just going to subtract the two numerators.
So we have 30 minus 15.
so now we can simplify this even further.
In our numerator we have 30 minus 15 which is just 15.
And our denominator of 8 stays the same.
So now we have an improper fraction of 15 over 8 as our answer.
However, since we are subtracting mixed numbers, our final answer should also be a mixed number.
So I am going to change 15 over 8 into a mixed number.
This can be done using long division.
I'm going to divide 15 by 8.
8 goes into 15 one time.
1 times 8 is 8.
And then if you subtract 15 minus 8, we have a remainder of 7.
Since 8 goes into 15 one whole time, our mixed numbers is also going to have a whole number
of 1.
Since we have 7 leftover in our remainder, our numerator is also going to have a 7 in
our mixed number.
Since we have an 8 in the denominator of the fraction, we are also going to have an 8 in
the denominator of the mixed number.
So 15 over 8 is exactly the same as 1 and 7/8ths.
And this is our final answer.
So here are some more videos with some more example problems related to the video you
just watched.
I really hope you are finding my tutorials helpful.
So until my next video, I will see you later.