Fractions Review | Adding, Subtracting, Multiplying, and Dividing Fractions | Math with Mr. J

In this video I'm going to go through a review of adding, subtracting, multiplying, and dividing fractions. Now fractions show up and are important all throughout math, so being familiar with these operations will be very beneficial really no matter where you're at, whether that's in middle school, high school, college, continuing your education as an adult, etc. This video will be helpful for anyone looking for a quick review of how to add, subtract, multiply, and divide fractions and really working with fractions in general. Let's start with adding fractions and jump into number one where we have three-sevenths plus two-sevenths. Now when we add fractions we have to have a common denominator, so we always look to see if our denominators are the same. If they're the same we can add. So in the case of number one we have a seven and a seven for our denominator, so we have a common denominator right away. That means we can add. So we add the numerators. Three plus two is five, so this is going to equal five, and then we keep our denominator the same. Five-sevenths is our answer. We can always look to see if we can simplify. The only common factor between five and seven is one, so we are done. Five-sevenths is in simplest form and our final answer. Again for number one we had a common denominator of seven, so we were able to add right away. Let's move on to number two where we have four-ninths plus one-sixth. So for this one we do not have a common denominator in our original problem, so we need to find a common denominator and then rename both of our fractions with that common denominator before we can add. Now we're going to find a common denominator between nine and six by finding the least common multiple between nine and six, and that's going to be our least common denominator. You may be able to think about what that least common multiple is, but as a review let's write out some multiples of both nine and six in order to find that least common multiple, and again that's going to be our least common denominator. So I'm going to come to the bottom here, so nine and six. Now we can list the multiples of nine and six by just counting up by nine and six. Multiples go on forever, so what we can do we can just start with four or five, see if we have any in common, and then we can go from there. So let's write out four multiples of nine. So nine, 18, 27, 36. Let's write out four multiples of six and then see if we have any in common. So six, 12, 18, 24. It looks like we have 18 in common here, and that's going to be our least common multiple. We're going to use that for our common denominator. So I'm going to rename these fractions underneath the original problem with that denominator of 18. So when we rename we're going to use equivalent fractions, so we're not changing the value of the problem at all. We need to think, how do we get nine to equal 18? Well nine times two is 18. Whatever we do to the bottom, we have to do to the top in order to keep this equivalent. So four times two is eight. Eight eighteenths is equivalent to four ninths, but we renamed that original fraction of four ninths with that common denominator of 18. So again we're not changing the value of the problem at all. We're just renaming with that common denominator so we can add. Let's do one sixth. So how do we get six to equal 18? Six times three is 18. So we need to do the same thing to the top in order to keep this equivalent. One times three is three. Now we have the fractions in our original problem renamed with that common denominator of 18. So we can add. Let's add our numerators. Eight plus three is 11. And then we keep our denominator of 18 the same. Always look to see if you can simplify. Eleven eighteenths, the only common factor between 11 and 18 is one. So we are in simplest form and this is our final simplified answer. Eleven eighteenths. That's how we add fractions. Let's move on to subtraction. Here are our subtraction examples. We'll start with number one where we have eight tenths minus three tenths. Now just like when we add fractions, we need a common denominator in order to subtract fractions. For number one, we have a 10 and a 10 for our denominators. So we have a common denominator in our original problem. So we can go ahead and subtract. For our numerators, we have eight minus three. That gives us five. So this equals five. And then our denominator of 10 stays the same. So we get five tenths. And that's our answer. But we can simplify here. We have a common factor other than one between five and ten that we can divide both of those by. We have a greatest common factor of five. So let's divide both of these by five in order to simplify. Five divided by five is one. And then 10 divided by five is two. So we get one half for our final simplified answer. Let's move on to number two where we have eleven twelfths minus one third. Now for this problem, we do not have a common denominator between our original fractions that we're subtracting. So we need to find a common denominator and then rename these fractions with that common denominator in order to subtract. Now we can find a common denominator by finding the least common multiple between 12 and 3. And that's going to be our least common denominator. Now you may be able to think about what that least common multiple is without writing out lists of multiples for both 12 and 3. But as a review, I'm going to write out some multiples of both 12 and 3 in order to find that least common multiple. So let's come below here and we have 12 and 3. Now my suggestion is to write out four or five multiples for both 12 and 3. See if we have any in common. If not, we can always extend our lists. Multiples go on forever. So again, my suggestion start with four or five and then go from there. So let's start with 12. And we can list the multiples of 12 by just counting up by 12. So let's do 4 here. 12, 24, 36, 48. Now let's do four multiples of 3 and see if we have any in common. So 3, 6, 9, 12. And we have 12 in common. That's our least common multiple. So that's going to be our least common denominator. So let's go back up to the original problem. And underneath here, we're going to rename our original fractions with that denominator of 12. Now 11 twelfths already has that denominator of 12. So we do not need to rename. We can just bring our 11 down. Again, that's because we already have that denominator of 12. Now as far as 1 third, we need to rename that. We're going to use equivalent fractions here. We're not going to change the value of the problem at all. So we need to think, how do we get 3 to equal 12? Well, 3 times 4 is 12. Whatever we do to the bottom, we have to do to the top in order to keep this equivalent. So 1 times 4 is 4. 4 twelfths is equivalent to 1 third. So again, we're not changing the value of the problem at all, because we're working with equivalent fractions. Now we have that common denominator of 12, so we can subtract. 11 minus 4 is 7. And then we keep our denominator of 12. 7 twelfths is our final answer. Always look to see if we can simplify. The only common factor between 7 and 12 is 1. So this is in simplest form. And our final simplified answer, 7 twelfths. That's how we subtract fractions. Let's move on to multiplication. Here are our multiplication examples. We'll start with number 1, where we have 3 eighths times 2 fifths. Now when we multiply fractions, all we need to do is multiply straight across. So numerator times numerator, the top numbers, and then denominator times denominator, the bottom numbers. Once we do that, we can look to simplify if need be. So let's multiply our numerators first. So 3 times 2, that gives us 6. And then 8 times 5, that gives us 40. So we get 6 fortieths. Now 6 fortieths is our answer, but we can simplify here. 6 and 40 have a common factor other than 1 that we can divide both our numerator and denominator by. We can divide both of these by 2. 2 is our greatest common factor. So let's divide both of these by 2. And we get 6 divided by 2 is 3. 40 divided by 2 is 20. So our final simplified answer is 3 twentieths. Let's move on to number 2, where we have 4 times 4 ninths. So we have a whole number times a fraction. Now we need to rewrite that whole number as a fraction before we start. Now in order to put a whole number in fractional form, all we need to do is put it over 1. So let's rewrite this problem. 4 over 1 is 4. It has a value of 4. Again, it's just in fractional form. And we want to do that. That way we have a numerator and a denominator, and we can multiply straight across. Let's bring down our multiplication sign and the 4 ninths. Now we can multiply straight across. 4 times 4 is 16. 1 times 9 is 9. So we get 16 ninths. And that's our answer, but it's in the form of an improper fraction. So we want to convert this to a mixed number. And we do that by dividing our numerator, the top number, by the denominator, the bottom number. So 16 divided by 9. So we need to think, how many whole groups of 9 are in 16? Well, 1. That gets us to 9. And we have a remainder of 7. So that's our numerator of the fractional part. And then we keep our denominator of 9 the same. So 1 and 7 ninths is our final answer. We can always look to see if we can simplify the fractional part of a mixed number. 7 ninths is in simplest form. So we are done. Now, I do want to do a quick recap of how I converted from that improper fraction to the mixed number. And I'm going to write everything out. So let's come below here. I did our numerator, 16, divided by 9. So how many whole groups of 9 in 16? Well, 1. That's our whole number right here. 1 times 9 is 9. We do not hit 16 exactly. We have a remainder of 7. So remainder 7. That remainder goes right here. It's the numerator part of our fraction. And then we keep our denominator of 9 the same. This 9 right here, we keep it the same. So 1 and 7 ninths as our final answer. That's how we multiply fractions. Lastly, let's move on to division. Here are our division examples. We'll start with number 1, where we have 1 half divided by 5 sixths. Now we're going to use the steps keep, switch, flip in order to divide fractions. Now you may also hear keep, change, flip, switch, or change. They both mean the same thing and it's the same process. Now this is also known as multiplying by the reciprocal. So let's rewrite this problem using those steps and see exactly how we divide fractions. So we always keep whatever comes first. So we have 1 half. So let's rewrite 1 half underneath. We keep. Then we switch or change to the opposite of division, which is multiplication. So let's write a multiplication sign. And then for our second fraction, we flip that fraction. That's called the reciprocal. So the bottom number, the denominator, is going to be the numerator. And the numerator is going to be the denominator. So our 6 goes on top and the 5 goes on the bottom. Now we're set up and we can multiply straight across. 1 times 6 is 6. 2 times 5 is 10. So we get 6 tenths. Now 6 tenths is our answer here, but we can simplify. We have a common factor other than 1 that we can divide both 6 and 10 by in order to simplify. And that common factor is 2. So let's divide 6 and 10 by 2 here in order to simplify. 6 divided by 2 is 3. 10 divided by 2 is 5. So our final simplified answer is 3 fifths. So again, keep, switch, flip. Then we can multiply straight across and then look to simplify if necessary. Let's move on to number 2 where we have 3 divided by 4 sevenths. So keep, switch, flip. Now we have a whole number here and we need to rewrite that as a fraction when we keep it. And we do that by putting it over 1. And it's as simple as that. So 3 over 1. That still has a value of 3 wholes. Again, it's just in fractional form. That way we have a top and a bottom and we can go through our steps. Then we switch or change. And then with the second fraction, we flip. So the 7 is our numerator and the 4 is our denominator. So 7 up top, 4 below. Now we can multiply straight across. 3 times 7, 21. And then 1 times 4 is 4. So we get 21 fourths, which is our answer, but it's in the form of an improper fraction. So let's convert this to a mixed number. And we do this by dividing our numerator, 21, by the denominator, 4. So this is going to equal... How many whole groups of 4 can we pull out of 21? Well, 5 whole groups of 4. That gets us to 20. We have a remainder of 1. That's our numerator. And then our denominator of 4 stays the same. So we get 5 and 1 fourth. Now let me go through how I converted that improper fraction to a mixed number one more time. I'm going to write it out. So we do 21 divided by 4. So how many whole groups of 4 in 21? Well, 5. That gets us to 20. 5 times 4 is 20. Subtract. We get a remainder of 1. So this 5 is our whole number. 5 whole groups of 4 in 21. And then our remainder of 1 is the numerator of our fraction. We keep our denominator of 4 the same. Our final answer as a mixed number, 5 and 1 fourth. Now we can always look to see if we can simplify the fractional part of a mixed number. 1 fourth is in simplest form, so we are done. Now one more thing I do want to mention is when we have a fraction that comes first and then a whole number that comes second. So let's do a quick example. And I'll just call this number 3. So we'll come over here where we have some room. And let's do 1 half divided by 4. So keep, switch, flip. Keep the 1 half. Switch to multiplication. And then we need to flip that 4, the reciprocal of 4. So what we do in this case, we put our whole number over 1. We put it in fractional form like we talked about for number 2. And then we flip. So the 1 is our numerator and the 4 is our denominator. So we have 1 fourth for our reciprocal or flipped fraction. Then we can multiply straight across. 1 times 1 is 1. 2 times 4 is 8. 1 eighth is in simplest form, so we are done. So you can see the difference there between whole number divided by a fraction and then a fraction divided by a whole number. It's always keep, switch, flip. Don't worry about if a fraction, whole number, or mixed number comes first or second. It's always those three steps in that order. So something to keep in mind. So there you have it. There's how you add, subtract, multiply, and divide fractions. I hope that helped. Thanks so much for watching. Until next time, peace.