welcome to working with fractions today we'll be going over multiplying
fractions remember in our very first video operations overview we mention
that regardless of whether the denominators were the same or not
fractions can always be multiplied multiplication with fractions isn't that
hard samy multiply 1/2 by 2 well that equals
1 and intuitively this makes sense two halves make a whole
now if we were to write this whole problem out it would look like 1/2 times
2 over 1 and in order to get 1 as our answer we would multiply across the top
and across the bottom to give us 2 over 2 which reduces down to 1 over 1 and
this in turn is just basically equal to 1 now let's use another example with
some more complicated fractions say that a recipe needed 2/3 a cup of water for
one person but we wanted to feed three people now remember that with whole
numbers if you wanted to multiply say 4 times 3 we would basically add 4 3 times
2 4 plus 4 plus 4 it's the same idea with 2/3 times 3 so you add 2/3 plus 2/3
plus 2/3 and if you remember our addition video this is going to go to 6
over 3 which reduces to 2 so you might notice a pattern by now the numerator
the top number multiplies the other numerator and the denominator multiplies
the other denominator it's that simple so to use an example with just numbers
if we were to multiply 3/5 by 2/3 what we would do is do 3 times 2 gives us 6
and 5 times 3 gives us 15 and this reduces down to 2 over 5
and there you go so if you were to have a mixed number that is something like
one and one thirds or two and four fifths all you need to do is convert
that into an improper fraction something that's bigger on the top and the bottom
before multiplying say if we wanted to multiply 2 and 4/5 by 3/7 now 2 and 4/5
is really 2 plus 4/5 and if you remember your addition from our previous video to
convert this we would find the common denominator of 5 multiply 2 by 5 over 5
skips us 10 over 5 then we can add 10 over 5 plus 4 over 5 giving us 14 over 5
so to think of this visually imagine that we had two whole pizzas plus 4/5 of
a pizza what we can do is cut up the whole pizzas into fifths
and then we can just count up the sections and everything gives us 14
fifths now multiplying 14 fifths by 3/7 we get 3 times 14 gives us 42 5 times 7
gives us 35 so we have this really ugly fraction 42 over 35 and if you have
sharp eyes you might notice that 42 and 35 are both products of the number 7 so
this means that this fraction can be simplified now if you don't know how to
reduce fractions don't freak out there's another video that will help you out
with that in this series but in the meantime let's fill a 7 out of here and
you can see that this can be written as 7 times 6 over 7 times 5 now crossing
out the sevens we know that this fraction over here is equal to 6 over 5
and again this is an improper fraction so we have to rewrite this once more as
1 & 1 ok so you might notice that if we add a little foresight in our previous
steps we may have seen that when multiplying 14 fifths by 3/7 14 fifths
could be written as 7 times 2/5 times 3/7 and we could have cancelled out the
7 on top and a 7 on bottom leaving us with 2/5 times 3 over 1 which is you can
clearly see is just six fifths or 1 and 1/5
and there you have it you now know how its multiply fractions think of the
fraction bars the kind of wall the numerators do their thing and the
denominators do their thing no mixing you're also prepared for tricky
situations like if you get a mixed number or if you have to reduce things
at the end all in all thank you for watching and be sure to check out the
games on always ice cream and clever dragons to test your knowledge on this
and other topics see you next time