Welcome to Math with Mr. J. In this video, I'm going to cover how to multiply mixed numbers. Now, I'll go through one example, which should be helpful for anyone looking for a quick review or refresher, whether you learned this recently or years ago. If you need more help or examples, I dropped links to other videos on this topic down in the description. Let's jump into our example where we have 4 and a half times 2 and 3 fifths. Now the first thing that we want to do is to convert our mixed numbers to improper fractions.
That way we have a numerator and a denominator and we can multiply straight across. So in order to do this we start at the bottom. So let's start at the bottom here and we work our way to the top. We multiply. then add.
So we do 2 times 4, our denominator times the whole number. So 2 times 4 is 8 plus our numerator of 1. That gives us 9. So again, 2 times 4 is 8 plus 1 gives us 9. That's the numerator of our improper fraction. We keep our denominator of 2 the same. Now that improper fraction is equivalent to our mixed number.
They're just in different forms. We're not changing the value of the problem at all when we convert to an improper fraction. Let's bring our multiplication sign down and then convert our other mixed number.
So we multiply, then add. So 5 times 2 is 10, plus 3 gives us 13. That's our numerator. And then keep our denominator of 5 the same.
Once we have our mixed numbers converted to improper fractions, we can multiply straight across. So numerator times numerator and denominator times denominator. Let's start with the numerators. So 9 times 13, that gives us 117. And then 2 times 5 gives us 10. So that's our answer as an improper fraction.
117 tenths. Now let's convert that to a mixed number. We do that by dividing our numerator, 117, by 10. Now we can either do this using mental math or writing out the division problem to the side.
I'll do both here. So 117 divided by 10, how many whole groups of 10 can we pull out of 117? Well, 11. That gets us to 110. We don't hit 117 exactly, so we have something left over, a remainder.
So the difference between 110 and 117 is 7. That's what's left over. That's our numerator. And then keep our denominator of 10 the same.
Now, if you're unable to do that using mental math, you can always come to the side and write out the division problem. So, for example, we'll start with... How many whole groups of 10 out of 11? 1. 1 times 10 is 10. Subtract. We get 1. Bring down the 7. So how many whole groups of 10 out of 17?
1. 1 times 10 is 10. Subtract. And we get a remainder of 7. So we get the same thing either way. Sometimes problems are a little more friendly and we can do them using mental math.
Sometimes we may need to write out the division problem. Either way works. So just to recap how we converted from an improper fraction to that mixed number, we did 117, the numerator, divided by 10, the denominator. So how many whole groups of 10 out of 117?
11. Then we have a remainder of 7, which is our numerator, and we keep our denominator of 10 the same. Always check to see if you can simplify the fractional part of a mixed number. number?
Well, 7 tenths is in simplest form. The only common factor between 7 and 10 is 1. So this is in simplest form. And we are done. 11 and 7 tenths. So there you have it.
There's how you multiply mixed numbers. I hope that helped. Thanks so much for watching.
Until next time, peace.