hey there it's kaylee today we're going to learn about the distributive property
over addition let's get right to it first we're going to start off with an example i'm sure you
can solve on your own it says evaluate four times six plus five so go ahead and solve this on your
own you can pause the video here great so what answer did you get let's work it out together
i'm sure you used order of operations right so that would mean if we have 4 all times six plus
five we do our addition inside the parentheses first and we would get
four times six plus five is eleven and that would give us an answer of forty four pretty easy right
but this lesson is on the distributive property over addition sometimes use a fancy name for this
called the distributive law of multiplication ooh fancy so let me show you how that works
what we actually do is we take what's outside of the parentheses our 4 and we distribute it to what's
inside our parentheses it goes like this we would take our 4 and we're going to multiply across
what's in our parentheses so if we have this we're going to take this 4. we're going to
multiply it by the 6 and we're going to multiply it by the 5. so this turns into four times six
we keep our addition sign right between our six and our five and we get four times five then we
can do our multiplication four times six that would give me 24 plus 4 times 5 that will give
me 20 and when i add these together i get 44 so same answer and they should match right we're
doing the same thing with two different methods so how does the distributive property actually work
let's imagine that there's three friends all having lunch together and each of them have two
kiwis and four strawberries in their lunch we want to know how many pieces of fruit the friends have
in total and we know that each friend has two plus four pieces of fruit and there's three of
them so we have two kiwis plus four strawberries and we have this three times now let's look at
just the kiwis if we have two kiwis i'm adding that to itself three times that's the same as
right three times two kiwis and for the strawberries if i have four strawberries
and i'm adding them to themselves three times then i have yes three times four strawberries
so this is the same as two plus four being added to itself three times which would look like
yes three times two plus four so this is how the distributive property works if we have three
times two plus four what we're really doing is duplicating the stuff in parentheses three times
like we drew out the three rows of fruit so both the kiwis and the strawberries get multiplied
by three another way of saying it the three gets distributed to the kiwis and the strawberries
nice so we can go ahead and calculate it we have 6 kiwis plus 12 strawberries and
that's just doing our multiplication and if we add those together we get 18 pieces of fruit
in total let's do one more example together this one says evaluate three plus seven multiplied by
eight remember that bullet there that just means multiplication using the distributive property
so this means using our new method and not the order of operations
so to start i'm going to rewrite my expression here in a way that makes more sense remember i can
write multiplication any order like 2 times 6 is the same as 6 times 2 so i'm going to move my 8 to
the front of my parentheses so i'll have 8 times 3 plus 7 but i don't even need this multiplication
sign here i can just cozy my 8 right up to my parentheses so i have 8 times 3 plus 7. now this
expression here is the same as this expression here we're just writing it in different ways
okay so now using the distributive property what do we do first yeah we're going to distribute
what's outside of the parentheses to what's inside the parentheses so i'll have eight times three and
eight times seven and i leave my addition sign right in the middle so this is going to look like
eight times three plus eight times 7 and now i can do my multiplication 8 times 3 that gives me 24
plus 8 times 7 that gives me 56 and if i do my addition 24 plus 56 gives me
80. and that's our solution good job you're ready to practice doing
the distributive property over addition on your own after you do some practice we'll
learn how to use the distributive property over subtraction have fun and remember to always be
clever