[Music] welcome to math with mr j [Music] in this video i'm going to cover how to divide mixed numbers and whole numbers we have two examples that we're going to go through together in order to get this down now in this video we have one problem where we have a mixed number divided by a whole number and then one example where we have a whole number divided by a mixed number the steps that we're going to use to solve these are the top of the screen so let's jump into number one the mixed number divided by the whole number so we have eight and two-thirds divided by two the first thing we want to do is change any mixed numbers or whole numbers to improper fractions that way we have a numerator and a denominator and we're able to continue on through our steps so let's start with our mixed number here we'll start at the bottom and work our way to the top so we multiply and then add we do 3 times 8 which is 24 plus 2 which is 26 that's our numerator we keep our denominator of 3 the same so we get 26 over 3 so that's our equivalent improper fraction there let's bring our division sign down now for any whole number in order to put it in fractional form all we need to do is put it over one it's as simple as that so now we're ready for the next step which is ksf keep switch and flip those are the steps of dividing fractions so the k keep that means we keep our first fraction so 26 over 3 we keep we switch to the opposite of division which is multiplication the f flip that means since we switched to multiplication we need to flip the second fraction so the two is now the denominator and the one is the numerator so we end up with one half 1 over 2. now we're ready to multiply straight across and get our final answer but before doing so we can always check to see if we can use cancellation you can think of cancellation as simplifying the problem before multiplying straight across you need to look for common factors between our numerators and denominators so for example number one we see that we have a 26 and a 2 there so we have a common factor of 2 between those two numbers so we can divide 26 by 2 and 2 by 2. so 26 divided by 2 is 13 and 2 divided by 2 is 1. so cancellation actually gives us simpler numbers to work with and then also helps us cut down on simplifying at the end so we have 13 times 1 we're ready to multiply straight across so 13 times 1 is 13 and 3 times 1 is 3 so we end up with 13 over 3 which is an improper fraction that is our answer but we don't want to leave it improper we want to change it to a mixed number so we do that by doing our numerator 13 divided by our denominator three so let's write it out to better understand what we're doing here so 13 divided by three how many whole groups of three out of thirteen well four that gets us to twelve four times three is twelve subtract we get a remainder of one so four is going to be our whole number portion we could do 4 whole groups of 3 out of that 13 with a remainder of 1 so that's our numerator and we keep our denominator of 3 the same so we get 4 and 1 3. always check to see if you can simplify the fractional part but 1 3 is simplified so we are done 4 and 1 3. i do want to show you what answer or i'm sorry compare our answers if we did not use cancellation to see how that would work out so let me rewrite we had 26 over 3 times one half here so 26 times 1 is 26 3 times 2 is 6. so we end up with 26 over 6 so looking a little different here but let's see how it ends up once we simplify so 26 divided by 6 how many whole groups of 6 out of 26 4 that gets us to 24 right so 4 and we would have a remainder of 2 and keep our denominator of 6 the same so 4 and 2 6 now the fractional part there can be simplified because 2 and 6 have a common factor a greatest common factor of 2. so let's divide each by 2 and see what we get we keep our whole number 4 the same 2 divided by 2 is 1 6 divided by 2 is 3. so we end up with the same answer 4 and 1 3. so in the case of cancellation we simplified before multiplying straight across and when we didn't use cancellation we had more simplifying at the end so you can see the difference there two paths but we ended up with the same correct answer no matter which way we worked it out there so on the number two where we have seven divided by three and three fifths so again first thing we need to do is change any mixed numbers or whole numbers to improper fractions seven is a whole number so we can just put it over one divided by three and three-fifths we start at the bottom work our way up we multiply let's make that an arrow we multiply and then add so 5 times 3 is 15 plus 3 is 18. keep our denominator of 5 the same so now we're ready for the dividing fraction steps keep switch flip so always keep your first fraction switch to multiplication and then we flip so we have 5 18. now we're ready to multiply straight across but we can look for cancellation in the case of number two the only common factor between our numerators and denominators is one so we can't use cancellation so we go right to multiplying straight across 7 times 5 is 35 1 times 18 is 18. so our answer is 35 over 18 but we do not want to leave it improper let's change it to a mixed number so we need to do 35 divided by 18 how many whole groups of 18 well 18 times 2 is 36 so we don't quite have enough for 2 is going to be 1 whole group of 18 and that's going to give us a remainder of 17 keep our denominator of 18 the same the only common factor between 17 and 18 is 1 so that is in simplest form and we are done our final answer is 1 and 17 over 18. so there you have it there's how you divide mixed numbers and whole numbers i hope that helped thanks so much for watching until next time peace