How to Divide Fractions | Full Walkthrough + Practice

Welcome to Math with Mr. J. In this video, I'm going to cover how to divide fractions. We'll go through dividing fractions by fractions, dividing whole numbers by fractions, and dividing fractions by whole numbers. Then I'll give you some practice problems that you can try on your own at the end. We'll start with dividing a fraction by a fraction. Let's jump into number one, where we have 5 6ths divided by 1 4th. So basically, we're figuring out how many groups of 1 4th we can make from 5 6ths. Or, in other words, how many 1 4ths are in 5 6ths. Now, whenever we have a division problem involving fractions, we have three steps. Keep, switch, flip. We're actually going to rewrite the division problem as a multiplication problem. So when we rewrite this, we keep our first fraction. We keep 5 6ths as is. Then we switch to the inverse, or opposite, of division, which is multiplication. So we switch to multiplication. And since we switched to the inverse of division, we need to flip our second fraction. So the numerator, 1, is now the denominator. And the denominator, 4, is now the numerator. So 4 is now the numerator, and 1 is now the denominator. When we flip a fraction like this, this is called the reciprocal. So when we rewrite this and keep, switch, flip, we're multiplying by the reciprocal. And now, all we need to do is multiply straight across. So numerator times numerator, and denominator times denominator. Let's start with the numerators. 5 times 4 gives us 20. Now for the denominators. 6 times 1 gives us 6. So we end up with 20 6ths, which is an improper fraction. So let's convert this to a mixed number. Remember, we do this by dividing the numerator, 20, by the denominator, 6. So 20 divided by 6. How many groups of 6 in 20? Well, 3 whole groups of 6 in 20. That gets us to 18. So we have a remainder of 2. That's our numerator of the fractional part. And then we keep that denominator of 6 the same. So we end up with 3 2 6ths. And that's our mixed number. Now 2 6ths can be simplified. We have a common factor other than 1 here that we can divide 2 and 6 by. We have a greatest common factor of 2. So let's divide 2 by 2 and 6 by 2 in order to simplify. We keep our whole number of 3 the same. And then 2 divided by 2 gives us 1. And then 6 divided by 2 gives us 3. The only common factor between 1 and 3 is 1. So this is now in simplest form. Our final simplified mixed number, 3 and 1 3rd. Let's move on to number 2 where we have 3 8ths divided by 2 5ths. So we keep, switch, and then flip. So 2 is now the denominator. And 5 is now the numerator. And now we can multiply straight across. 3 times 5 gives us 15. And then 8 times 2 gives us 16. So we end up with 15 16ths, which is a proper fraction here. And the only common factor between 15 and 16 is 1. So this is in simplest form. We are done. Final answer, 15 16ths. So just remember, when we have division problems involving fractions, we keep, switch, flip. Which in other words, we are multiplying by the reciprocal. Let's move on to dividing whole numbers by fractions. Now we'll take a look at how to divide a whole number by a fraction. Let's jump into number 1 where we have 3 divided by 1 half. So basically, we are figuring out how many groups of 1 half we can make from 3. Or in other words, how many halves are in 3. So let's rewrite this problem using keep, switch, flip, starting with keep. In this case, we have a whole number, 3. So when rewriting this problem, we keep 3. But we are going to write it in fractional form. That way, we have a numerator and a denominator. And remember, we can write whole numbers in fractional form by putting them over 1. And then after we keep whatever comes first, we switch to the inverse of division. The opposite of division, which is multiplication. So let's switch to multiplication here. And since we switched to the inverse of division, we need to flip whatever comes second. In this case, it's a fraction, 1 half. So let's flip 1 half. The numerator, 1, is now the denominator. And then the denominator, 2, is now the numerator. So we have 2 over 1. And now, all we need to do is multiply straight across. Let's start with the numerators. 3 times 2 gives us 6. And then for the denominators, 1 times 1 gives us 1. So we end up with 6 over 1, which is just 6. And this is our final answer. 3 divided by 1 half equals 6. And think about it. If we start with 3 wholes, let's use 3 whole sandwiches, for example, something we can picture, and we divide each sandwich in half, how many halves does that give us? 6. Let's move on to number 2, where we have 8 divided by 3 fourths. So keep, switch, flip. So let's keep 8, and we're going to write it in fractional form. That way, we have a numerator and a denominator. So keep, switch, and now we need to flip 3 fourths. So 3 is now the denominator, and 4 is now the numerator. And now we can multiply straight across. Let's start with the numerators. 8 times 4 gives us 32. Now for the denominators. 1 times 3 gives us 3. So we end up with 32 thirds. And that's our answer. But we have an improper fraction here. So let's convert it to a mixed number by dividing the numerator by the denominator. So 32 divided by 3. How many groups of 3 in 32? Well, 10. That gets us to 30. So 10 whole groups of 3 in 32. Again, that gets us to 30. So we have a remainder of 2. That's the numerator of our fractional part. And then we keep that denominator of 3 the same. So we end up with 10 and 2 thirds. We can always look to simplify the fractional part of a mixed number. The only common factor between 2 and 3 is 1. So this is, in simplest form, our final answer. 10 and 2 thirds. So there you have it. There's how to divide a whole number by a fraction. Let's move on to dividing fractions by whole numbers. Now we'll take a look at how to divide a fraction by a whole number. Let's jump into number 1, where we have 1 fourth divided by 2. So basically, we are taking 1 fourth and dividing it into 2 equal groups, 2 equal parts. So let's rewrite this problem using keep, switch, flip. Starting with keep. So we keep our first fraction here, 1 fourth. So keep 1 fourth as is. And then we switch to multiplication. Then we flip. But we have a whole number here. So how do we flip that whole number? Well, we need to write our whole number in fractional form. And we do that by writing it over 1. So we put 2 over 1. And now 2 is in fractional form. And we flip this fraction. So 2 is now the denominator. And 1 is now the numerator. And now all we need to do is multiply straight across. We'll start with the numerators. 1 times 1 gives us 1. And then for the denominators, 4 times 2 gives us 8. And that's our answer, 1 eighth. The only common factor between 1 and 8 is 1. So this is in simplest form. We are done. 1 fourth divided by 2 equals 1 eighth. Let's move on to number 2, where we have 4 fifths divided by 6. Let's keep, switch. And now we need to flip 6. So we write it in fractional form by putting it over 1. And 6 is now the denominator. And 1 is now the numerator. Now we can multiply straight across. For the numerators, we have 4 times 1. That gives us 4. And then for the denominators, we have 5 times 6. That gives us 30. So we end up with 4 thirtieths, which this can be simplified. We have a greatest common factor of 2 that we can divide 4 and 30 by. 4 divided by 2 gives us 2. And 30 divided by 2 gives us 15. So we end up with 2 fifteenths. The only common factor between 2 and 15 is 1. So this is now in simplest form. Our final answer, 2 fifteenths. So there you have it. There's how to divide a fraction by a whole number. Now that we've gone through some examples together, it's time for you to try some practice problems on your own. So have paper and a pencil ready. So here are your practice problems. I'll give you 5 minutes and then we will go over the answers. Feel free to pause if you need more time or jump ahead to the answers whenever you are ready. Go ahead and start. Okay, so that was 5 minutes. Let's go over the answers. So here are our answers. For number 1, we have 12. For number 2, we have 1 and 1 sixth. For number 3, we have 1 tenth. Moving on to number 4, we have 11 and 1 fifth. For number 5, we have 7 thirty-sixths. And then lastly for number 6, we have 3 fourths. So there you have it. There's how to divide fractions. I hope that helped. Thanks so much for watching. Until next time, peace.