[Music] welcome to math with mr j [Music] in this video i'm going to cover how to multiply whole numbers and fractions and we have four examples that we're going to go through together in order to get this down so let's jump into number one where we have three times one-half now the first thing that we want to do we want to rewrite our whole number as a fraction and it's as simple as putting that whole number over 1. so for the 3 we're going to rewrite this and put it over 1. now the point of this we want a numerator and a denominator so a top and a bottom putting that 3 over 1 does not change the value of that 3 or the problem that fraction has a value of 3 it's equivalent to 3 wholes once we have the whole number written as a fraction we bring down the rest of the problem so the multiplication and then the one-half now we're ready to multiply straight across so numerator times numerator and then denominator times denominator as far as the numerators three times one is three the denominators one times two is two so three halves or three over two is our final answer but it's an improper fraction so we don't want to leave it improper we want to convert that to a mixed number so this is the simplifying step we are going to clean up our answer and rewrite it as a mixed number so we do that by dividing the numerator by the denominator so three divided by two now how many whole groups of two can we pull out of three well one one whole group of two so that's our whole number part of our mixed number the remainder which is one is going to be the numerator so if we pull one whole group of two out of three we get a remainder of one and then we keep the denominator of two the same always check to see if you can simplify the fractional part of a mixed number well one-half is simplified so we are done our final answer is one and one-half now before i move on to number two i do want to mention that our answer one and a half is less than the whole number that we started with three normally when we think multiplication we think we are going to increase in value as far as the numbers that we start with well when we multiply by fractions if we multiply by a fraction that is less than a whole we are going to get an answer that's less than the whole number we started with in the original problem so that's something to keep in mind again if we multiply by a fraction that's less than one whole we're going to get an answer that's less than the whole number within our original problem let's move on to number two where we have eight times four-fifths so first thing let's rewrite our whole number as a fraction and we do that by putting it over 1. bring down the rest of the problem here and now we're ready to multiply straight across so 8 times 4 well that's 32. and then 1 times 5 is 5. so we get 32 over 5 that's an improper fraction let's convert it to a mixed number and see if we can simplify further once we have it into mixed number form so we do 32 divided by 5 how many whole groups of 5 out of 32 well 6 that gets us to 30 so we have a remainder of two and then keep the denominator of five the same two-fifths is in simplest form so we are done six and two-fifths moving on to number three we have five-sevenths times five so let's rewrite the problem five-sevenths times put the five over one to put it into fractional form and then multiply straight across so 5 times 5 25 and then 7 times 1 is 7. convert that improper fraction to a mixed number so 25 divided by seven how many whole groups of seven can we pull out of 25 well three that gets us to twenty one so we have a remainder of four keep our denominator of seven the same three and four-sevenths four-sevenths is in simplest form so that's our final answer and lastly number four we have three-fourths times twelve rewrite the problem 3 4 times 12 and multiply straight across so 3 times 12 36 4 times 1 is 4. so we get to an improper fraction here let's convert it to a mixed number so 36 divided by 4 that's 9 and we hit 36 exactly so there's no remainder that means our final answer is going to be a whole number so the final answer for number four is nine so there you have it there's how you multiply whole numbers and fractions make that whole number into a fraction multiply straight across and then simplify your answer i hope that helped thanks so much for watching until next time peace you