Dividing Fractions | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to divide whole numbers by fractions fractions by whole numbers and then fractions by fractions let's start with dividing whole numbers by fractions now when working with fractions and division we need to remember three steps keep switch flip we can also think multiply by the reciprocal when we flip a fraction that's called the reciprocal so this means we're going to use multiplication to solve these this actually makes the process simpler now how and why this works is a topic for another video i'll drop that link down in the description let's jump into number one where we have two divided by one fourth now we can think of this as how many one-fourths are in two or how many one-fourths can we make out of two we are dividing two by one fourth let's rewrite our problem using keep switch flip also known as multiplying by the reciprocal so we start with keep we always keep the first number or fraction in the case of number one we have a whole two so we need to keep that as two but we're going to rewrite it as a fraction whenever you rewrite a whole number and put it in fractional form all you need to do is put it over 1. now the purpose of this we want to have a numerator and a denominator so we kept the value of 2 there we just put it in fractional form then we switch from division to multiplication and since we switched to the inverse or opposite of division we're going to need to flip the second number or fraction in the case of number one here we have a fraction so the denominator is now going to be the numerator and the numerator is now going to be the denominator so we have 4 over 1. once we get to this point we have a multiplying fractions problem which we just multiply straight across when we multiply fractions so two times four is eight and one times one is one so we get to the answer of eight over one which is an improper fraction so we do not want to leave it like that this is going to be 8. our final answer is 8. 2 divided by 1 4 equals 8. let's move on to number 2 where we have seven divided by two fifths so we are finding out how many two-fifths are in seven so to speak so keep switch flip we will keep our seven but put it in fractional form by putting it over 1 switch to multiplication and then flip our second number or fraction now we can multiply straight across 7 times 5 is 35 and 1 times 2 equals 2. so our answer is 35 over 2. now we don't want to leave it improper we want to convert this to a mixed number so we do 35 divided by two how many whole groups of two are in 35 well 17. so that's our whole number of our mixed number now we didn't hit 35 exactly we had a remainder of 1 so that's our numerator of the fractional part and then we keep our denominator of 2 the same so 17 and a half always look to see if you can simplify the fractional part one half is in simplest form so we are done our final answer 17 and a half so that's how we divide a whole number by a fraction let's move on to dividing fractions by whole numbers so here are our examples for dividing fractions by whole numbers let's jump into number one where we have one-half divided by three so we are taking one-half and dividing it into three equal groups or parts let's rewrite the problem using keep switch flip in order to solve this so always keep the first fraction or number so let's rewrite the problem so one half we are going to keep then we switch to the opposite or inverse of division which is multiplication and since we switched to multiplication we need to flip the second number or fraction in the case of number one we have a whole 3 here so how do we flip this well let's put that whole number over 1 that way we have a numerator and a denominator that does not change the value of the problem that still has a value of 3. so now we can flip so the 1 is going to go up to the top and be our numerator and the 3 is going to be the denominator so we flipped that second number once we get to this point we have a multiplying fractions problem so we can multiply straight across 1 times 1 is 1 and 2 times 3 is 6. so 1 6 is our final answer always check to see if you can simplify 1 6 is in simplest form so we are done one half divided by 3 equals one-sixth let's move on to number two where we have four-sevenths divided by six keep switch flip so let's rewrite the problem keep four-sevenths switch to multiplication and then we need to flip so we can write that 6 in fractional form and now we can flip so the 1 is now our numerator and the 6 is now our denominator and we can multiply straight across 4 times 1 is 4 7 times 6 is 42 so we get 4 over 42 which can be simplified 4 and 42 have a greatest common factor of 2. so let's divide each of these by 2 and we get 2 over 21 for our final simplified answer and that's how we divide a fraction by a whole number lastly we have fractions divided by fractions so let's move on to that here are our two examples for dividing fractions by fractions let's jump into number one where we have three-fourths divided by one-seventh so we are seeing how many one-sevenths we can make out of three-fourths or how many one-sevenths are in three-fourths so to speak so let's start by rewriting this problem using keep switch flip so we always keep the first fraction or number so we keep three fourths as is we switch to the opposite or inverse of division which is multiplication and since we switch to the opposite or inverse of division we're going to flip the second fraction so the seven is going to be our numerator and the one is going to be our denominator so we end up with seven over one once we get to this point it's a multiplying fractions problem so we can multiply straight across 3 times 7 is 21 and then 4 times 1 is 4 and we end up with 21 fourths now that's an improper fraction so we do not want to leave it we need to divide our numerator of 21 by 4. how many whole groups of 4 are in 21 well 5 that gets us to 20. so 5 whole groups of 4 that's our whole number of the mixed number here now that doesn't hit 21 exactly we have a remainder of 1 so that's our numerator in our fractional part of the mixed number and we keep our denominator of 4 the same always look to see if you can simplify the fractional part of a mixed number 1 4 is in simplest form so we are done five and one fourth is our answer for number one so three-fourths divided by one-seventh equals five and one-fourth let's move on to number two where we have two-thirds divided by two-fifths keep switch flip so keep two-thirds here switch to multiplication and then flip that second fraction so five over two and now we can multiply straight across two times five is ten three times two is six so we get ten sixths so that's an improper fraction we need to convert to a mixed number so ten divided by six how many whole groups of six out of 10 well 1 and we get a remainder of 4 keep our denominator of 6 the same we can simplify 4 6. we have a common factor of 2 so let's divide each of these by two here and we get one and two thirds so our answer for number two is one and two two-thirds two-thirds divided by two-fifths equals one and two-thirds so there you have it there's how you divide whole numbers by fractions fractions by whole numbers and then fractions by fractions i hope that helped thanks so much for watching until next time peace [Music]