Converting Improper Fractions and Mixed Numbers | Improper Fractions ⇄ Mixed Numbers

Welcome to Math with Mr. J. In this video, I'm going to cover how to convert between improper fractions and mixed numbers. We'll start with improper fractions to mixed numbers, move to mixed numbers to improper fractions, and then we will end with some practice problems that you can try on your own. So starting with improper fractions to mixed numbers, remember, an improper fraction is a fraction greater than or equal to one. The numerator is greater than or equal to the denominator. So the top is greater than or equal to the bottom. Let's jump into number one where we have 13 over 2, 13 halves. We can see that we have an improper fraction here. The numerator is greater than the denominator. So we're going to write this as a mixed number. So we will have a whole number and a fractional part. We go from an improper fraction to a mixed number by dividing the numerator by the denominator. So the top divided by the bottom. So for number one, we need to do 13 divided by 2. And we will write this off to the side here for number one. So how many whole groups of 2 in 13? How many 2s in 13? Well, 6. That gets us to 12. So 6, this is our whole number of our mixed number. Now we multiply. 6 times 2 is 12. Then we subtract. 13 minus 12 is 1. So we have 6 remainder 1. We use that remainder of 1 for our fractional part of the mixed number. So 6 is our whole number. And then our remainder of 1 is the numerator of our fractional part. And then we keep the denominator the same. So we keep that denominator of 2. So 13 halves equals 6 and a half. We can always look to see if we can simplify that fractional part of our mixed number. But 1 half is in simplest form. So we are done here. Again, 13 halves, 13 over 2 equals 6 and a half. So just keep in mind, all we need to do when going from an improper fraction to a mixed number is divide the numerator by the denominator. Let's move on to number 2 where we have 46 over 8. 46 eighths. Let's write this as a mixed number. So we need to do 46 divided by 8. How many whole groups of 8 in 46? How many eights in 46? Well, 5. That gets us to 40. So 5 whole groups of 8. That gets us to 40. So we have a remainder of 6. That's our numerator. And then we keep our denominator of 8. So we end up with 5 and 6 eighths. Now 6 eighths can be simplified. We have a common factor of 2 that we can divide 6 and 8 by. So let's simplify here. We can divide 6 by 2 and 8 by 2. 6 divided by 2 is 3. And then 8 divided by 2 is 4. So this simplifies to 3 fourths. And we have 5 and 3 fourths now, which is in simplest form. Now for number 2, we did this one without writing the division out off to the side. Either way will work. So use what works best for you. To show number 2 written out, we can do 46 divided by 8. So 46 divided by 8. How many groups of 8 in 46? 5. Multiply. 5 times 8 is 40. Subtract. 46 minus 40 is 6. So we get 5 remainder 6. 5 is our whole number. Then that remainder of 6 is our numerator. Then we keep that denominator of 8. So we end up with 5 and 6 eighths, which we were able to simplify. And we ended up with 5 and 3 fourths. Let's move on to number 3, where we have 35 over 5. 35 fifths. So we need to divide. We need to do 35 divided by 5. Well, how many whole groups of 5 in 35? How many 5s in 35? 7. And that hits 35 exactly. So 7. And again, that hits 35 exactly. We do not have a remainder here. Since we don't have a remainder, we don't have a fractional part. We just have a whole number. And we are done. 35 fifths equals 7. Again, we don't have a remainder. So this works out to be just a whole number. Lastly, let's move on to number 4, where we have 29 over 12. 29 twelfths. So we need to write this as a mixed number. Let's divide. So 29 divided by 12. How many whole groups of 12 in 29? How many 12s in 29? Well, 2. That gets us to 24. So 2 whole groups of 12. That gets us to 24. So we have a remainder of 5. That's our numerator. And then we keep that denominator of 12 the same. So we end up with 2 and 5 twelfths. 5 twelfths is in simplest form. So we are done. 29 twelfths equals 2 and 5 twelfths. So there's how to write an improper fraction as a mixed number. Let's move on to writing a mixed number as an improper fraction. Here's our section on converting mixed numbers to improper fractions. Let's jump into number 1, where we have 2 and 4 fifths. So we need to write this mixed number as an improper fraction. All we need to do here is multiply and then add. We start at the bottom, multiply, then add. So we do 5 times 2, and then add 4. So again, we start at the bottom, and we multiply, then add. So we do 5 times 2, which is 10, plus 4 is 14. That's our numerator. Then we keep our denominator the same. So 5. That gives us our improper fraction. So 2 and 4 fifths equals 14 fifths. Now to break this down a little further and to explain how this works, what we basically do here, when we multiply, that gives us our whole number as a fraction with whatever denominator we have. For example, we did 5 times 2 here, and that gives us 10. And if we write that over our denominator of 5, we have 10 fifths. That's our whole number of 2 written as a fraction. 10 fifths equals 2. Then we add the numerator, which is 4. So we have 10 fifths plus 4 fifths. So we have our whole number as a fraction plus the fractional part of the mixed number. 10 plus 4 gives us 14, and we keep that denominator of 5 the same. So we get 14 fifths. So when we start at the bottom and multiply, then add, it's a quicker way to go through that process of writing the whole number as a fraction and adding the fractional part of the mixed number. Let's move on to number 2, where we have 4 and 1 fourth. So we need to multiply, then add. So multiply, then add. 4 times 4 is 16, plus 1 is 17. So that's our numerator. Then we keep that denominator of 4 the same. So 4 and 1 fourth equals 17 fourths. Moving on to number 3, we have 10 and 5 eighths. So let's write this as an improper fraction. Multiply, then add. 8 times 10 is 80, plus 5 is 85. So 85 is our numerator. Then we keep that denominator of 8 the same. 10 and 5 eighths equals 85 eighths. And then lastly, moving on to number 4, we have 7 and 2 thirds. Let's multiply, then add, in order to convert this to an improper fraction. 3 times 7 is 21, plus 2 is 23. 23 is our numerator. And then we keep that denominator of 3 the same. So 7 and 2 thirds equals 23 thirds. So just remember, when we write mixed numbers as improper fractions, we start at the bottom, and we multiply, then add. 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. For numbers 1, 2, and 3, write each improper fraction as a mixed number. For numbers 4, 5, and 6, write each mixed number as an improper fraction. I'll give you 3 minutes, and then we will go over the answers. Feel free to press pause if you need more time, or jump ahead to the answers whenever you are ready. Go ahead and start. Okay, so that was 3 minutes. Let's go over the answers. So here are our answers. For number 1, 11 thirds equals 3 and 2 thirds. For number 2, 77 tenths equals 7 and 7 tenths. For number 3, 38 fourths equals 9 and 2 fourths, which can be simplified to 9 and a half. For number 4, 2 and 3 eighths equals 19 eighths. For number 5, 8 and 5 sixths equals 53 sixths. And then lastly, for number 6, 5 and 1 fifth equals 26 fifths. So there you have it. There's how to convert between improper fractions and mixed numbers. I hope that helped. Thanks so much for watching. Until next time, peace.