5th Grade Math

hello welcome to this lesson and

mastering fifth grade math here in this

lesson we're going to talk about the

topic of order of operations so as we go

through this lesson we'll be working

examples step by step to teach you the

concepts of what we call order of

operations in math and then we'll also

be going on through all of the other

lessons in this batch in the series here

taking every single concept step by step

so let's follow on through here the one

thing I want to make sure and let you

know is that after you finish watching

this lesson and you understand

everything I want you to work all of

these problems on a separate sheet of

paper yourself and then I would like you

to get the workbook the worksheets out

and walk all of those problems when

you're confident that you understand

everything and you're doing well then

you can move on to the next topic that's

the way to succeed in math so we have

this concept called the order of

operations what it basically means is up

till now you really have gotten good at

adding and subtracting numbers and

multiplying and dividing numbers we've

also done quite a bit of work with

fractions but it turns out that there's

a specific order that we are supposed to

do adding and subtracting and

multiplying and dividing when we have a

bigger problem so let me tell you what

that order is I'll just write it on the

board and then you'll have it here and

then as we work a lot of problems you'll

see very quickly it is very very simple

so this whole concept concept is called

the order of operations and basically as

I said before it just tells you how you

should solve your problems what order

you should solve your problems so number

one the number one thing you do when

you're solving a problem that involves

you know adding subtracting multiplying

dividing is we have the concept of

parentheses in math so I'll get to that

a little bit later we'll talk about it

when we do our problems but number one

you want to always do inside whatever is

inside the parentheses first does it

matter what else is happening in your

problem if you see any parentheses in

your problem you have to do what's

inside of those guys first number two

the next thing and the order is you want

to

you multiplication and division and what

I when I say do multiplication and

division I'm talking about doing it left

to right what this means is if you have

two times 2 divided by 6 times 5 then

you're doing multiplication and division

as you read left to right across the

page all right and then the last thing

is and there's only three rules so this

is the third one the final thing you

want to do is you want to do adding and

subtract you want to add subtract left

to right all right so that's the basic

idea as you get higher and higher into

math there are a few additional rules

and order of operations we'll get to

those as you get higher in math but

right now at this level what we're

trying to do is we're trying to show you

that sometimes you run into these things

called parentheses when you're solving

problems I'm going to show you exactly

what that is in just a minute don't

worry about it it's very simple and also

we're trying to show you the rule that

you follow when you're solving these

problems when you're calculating the

number one thing you do very first thing

you do is you always do whatever is

inside of the parentheses first

all right after you've done that then

you do multiplication and division next

and you do it left to right just like

you read a book and then after that you

do adding and subtracting left to right

just like you read a book so these are

the three rules we're going to use these

over and over and over again so let's

just get started by solving a real

problem because you know a lot of times

you talk about these things but until

you see it you don't really know what

I'm talking about so let's say we have

the problem 5 times 6 minus 4 and I ask

you I want you to calculate what 5 times

6 minus 4 is so a lot of students would

take 5 times 6 and then we get the

answer of that and then they would

subtract 4 all right but also some other

students might say well let me take 6

minus 4 and then multiply by 5 what is

going to give me the correct answer well

let's follow the order of operations you

have to do it in a specific order other

you get the wrong answer so let's show

you what that is first it says do what's

inside of the parentheses first

there are no parentheses in this problem

so you don't even worry about number one

it doesn't apply alright number two do

multiplication and division left to

right so multiplication division comes

before adding and subtracting that means

that this multiplication here has to be

done before the subtraction because we

go down the order here this is the most

important this is the next thing we do

and this is the last thing we do so

adding and subtracting basically is

always going to be last in every problem

you do so since we have multiplication

here that step or order number two or

step number two five times six the way

we write this down as we say this is 30

now we still have the minus four so we

just carry it along for the ride so we

see exactly what we did and your teacher

will see exactly what you did five times

six gives you 30 the minus four has not

been done yet because multiplication

came first all right and then now we

look at this line and we see what do we

have left to do the only thing left is a

subtraction we've done everything else

adding and subtracting comes last so we

go ahead and do this so the answer here

30 minus 4 is 26 and this is what you

would circle on your test this guy is

the correct answer if you put this in a

calculator or a computer or doing it by

hand as we've done here 26 is the

correct answer now I want to show you

how a lot of students get into trouble

if you don't follow order of operations

so I'm going to change colors and I'm

going to change colors to kind of this

pink color here so let's say we have 5

times 6 minus 4 the way we were supposed

to do is we multiplied first then we did

the subtraction but let's say somebody

doesn't know this very well and they

decide to do the subtraction first now

this is clearly wrong because the

subtraction is the very last thing we do

but let's say somebody does it so 6

minus 4 gives you 2 that comes from this

and then let's say you still chose you

used to put the 5 out to be multiplied

as the last step so let's go ahead and

see what happens here 5 times 2 the only

thing left to do and the problem would

be 10 so one student who did it

correctly gets the answer of 20

another student who does the answer

incorrectly gets ten so who's going to

get the right answer well not the guy

who did this because he did it wrong or

she did it wrong

6 minus 4 is 2 & 5 times 2 is 10 but the

way that you do it here is backwards of

how you're supposed to do it you always

do parentheses first

then you do multiplication and division

and then you do adding and subtracting

here we did everything out of order so

just to make sure you know this is wrong

I'm going to put a big X through this

that is wrong I'm not going to show you

in every problem the wrong way to do it

but I want to just show you that the

order matters if you don't do the order

correctly you're going to get the total

wrong answer and just not do it right so

let's go ahead and continue on here and

get some more practice we're just going

to do a lot of these things what if I

have 36 divided by 6 minus 4 again some

students might look here and say well

I've got subtraction I've got division

what do i do first well you go your

order of operations we check for

parentheses first there are no

parentheses here then we do

multiplication and division well here's

some division so 36 minus 6 I'll switch

colors 36 I should say divided by 6 is

going to be 6 and then we still have the

minus 4 so this is equal to 6 minus 4

now the only thing remaining to do and

the problem is subtraction that comes

dead last 6 minus 4 is 2 so the answer

is 2 all right so as we work these

problems I just want you to remember

three things they're very easy

do parentheses first then do multiplying

and dividing then do adding and

subtracting you're adding and

subtracting should always come last so

as we continue to work these problems I

want you to kind of keep that in mind

because those rules are never going to

change in math you're always going to be

using these rules now what if you have

the problem 10 plus 7 times 4 right now

here's the correct way to do it the

first thing you look and see is do I

have any parentheses in this problem and

I don't so I don't even worry about

parentheses the next thing I do is I

look do I have any multiplication or

division because that is the next thing

in the list and I see that I have 7

times 4 now I also have an addition here

but we know that we always do addition

and subtraction

last so we don't do that first we always

do the multiplication or division first

so I know it seems a little weird but

what you're going to do is skip over

here and say 7 times 4 is 28 now don't

forget you still have to add the 10 to

it so you write it just like this for

your next steps 10 plus 28 and now to do

the final part of the problem you know

that 10 plus 28 is 38 and there's

nothing else left to do because that

addition was the last thing and the

problem so notice we followed our order

of operations first we did

multiplication we did it right here and

then we did the addition we get an

answer of 38 a lot of students will get

the wrong answer because they'll do this

addition first 10 plus 7 is 17 right and

then they'll multiply the 17 that they

got times 4 that's going to give you the

wrong answer 17 times 4 is not 38 all

right so you have to do it right you do

parentheses first then multiply divide

then addition and subtraction and I keep

saying it over and over again because

it's honestly one of the most important

things you can learn in math is order of

operations now for this problem we're

going to introduce this idea of a

parentheses 18 divided by 2 times 6

divided by 3 now here if you've never

seen parentheses in math before it looks

a little bit weird but the way you read

parentheses in math is just in terms of

the order of operations all parentheses

mean the only reason we have parentheses

is because we want to force what's

inside of the parentheses to happen

first

because parentheses are always number 1

on the list all right so we can't do

this multiplication that's in the middle

first because we have to handle what's

inside the parentheses first so the way

you handle this is you say well inside

this parentheses is 18 divided by 2 and

18 divided by 2 is 9 so we put a 9 here

and you can kind of keep the parentheses

here for now we'll keep the

multiplication for now and inside this

parentheses is 6 divided by 3 and you

know that that is equal to 2 so here we

have parentheses 9 parentheses 2 since

there's only one number inside of these

parentheses in this step

here we can kind of remove the

parentheses we don't really need them

anymore I'm going to leave them here for

this problem parentheses only makes

sense when you have multiple things

going on inside if you do everything and

you just get one number then you can

drop the parentheses I don't even matter

anymore okay so we've done everything

inside the parentheses and now the only

thing that we have left to do is this

operation the multiplication because we

go through the order of operations we've

done the parentheses now we look for

addition and subtraction we don't have

any next we look for multiplying a

division and we do that like this

so nine times two is 18 18 is the final

answer to that problem all right so you

don't want to accidentally be doing

things like two times six first you know

or anything like that because you want

to handle what's inside this parentheses

what's inside this parentheses once you

have those then you handle the other

operations and we always do adding and

subtracting before multiplying and

dividing all right let's go into the

next problem our gonna do quite a few of

these what if we have something like

five times twenty minus three plus eight

okay

so now the problems are getting a little

bit bigger this looks a little bit

complicated at first if you get confused

at what to do just go back to your order

of operations first thing check for

parentheses then multiplying and

dividing then adding and subtracting but

notice in this case that we have a

parentheses here so we know we have to

do what's inside the parentheses now

here's the catch whenever I showed you

the order of operations I said do the

parentheses first then do multiplication

division then do adding and subtracting

if you're working inside of the

parentheses whatever is inside of there

you still need to follow this order so

we first look inside of the parentheses

and we look for any multiplying or

dividing inside of the parentheses first

and we don't see any so in this case we

can do the subtraction first because

it's inside the parentheses and inside

the parentheses we always look for

adding it's a multiplication and

division first and then adding and

subtracting so everything outside the

parentheses of we're not able to touch

right now but inside of here 20 minus 3

is 17 so we put a 17 here that comes

from that now the times

that's on the front end and the +8

that's on the back end that all stays

the same now I could put a parenthesis

around 17 because you know there was

parentheses here but once I solved

everything inside of the parentheses and

it's just one number left from that I

can drop the parentheses the parentheses

really only only make any sense when

there's multiple things happening

because you're trying to group

operations once you've done it all then

you can just drop it so what we have now

is five times seventeen plus eight and

I'm going to ask you how do we solve

that well we've already done parentheses

that's done so then we look for

multiplying and dividing and we do that

left to right so here we see five times

seventeen we're going to do that first

we're not going to do any plus eight

because that comes last so what we'll

have then five times 17 is going to give

you 85 and then we carry the plus eight

down because we have to do that in the

very last step the only thing remaining

is addition and we know adding

subtracting does come last so 85 plus

eight is 93 and that is the final answer

you need to make sure you understand the

concept of what we're doing here because

a lot of students will get confused if

you don't know the order of operations

you might try to multiply 5 times 20

first or you might try to do this

something with it's three plus 1/8 first

and you can't there's a specific way of

doing it you do inside the parentheses

once you're zoomed inside the

parentheses you always look for

multiplication of division first then

adding and subtracting inside the

parentheses once we did that then you

bounce out of it and you go left to

right multiplying and dividing and then

left to right adding and subtracting so

this whole process becomes a whole lot

more comfortable to you the more and

more of these things we do so let's say

we have 7 times 7 minus 3 inside of some

parentheses how do we handle this one

okay well first we check for parentheses

and we see we have parentheses now

inside of here we only have one thing to

do 7 minus 3 there's no multiplying or

dividing in here so we don't worry about

that we just go to the subtraction 7

minus 3 is 4 we can drop the parentheses

now because we've tackled what's inside

of there the times 7 remains because we

haven't done

that yet and then the very last thing

that we do is 7 times 4 is 28 and that

is the final answer you know if you want

to keep parentheses around here I mean

you can just to remind yourself that

this 4 came from the parentheses that's

okay but still you're just going to

multiply 7 times 4 at the end of the day

because that is what's going to give you

the final answer there there's nothing

else left to do after you handle the

parentheses in this case all right let's

do 10 plus 10 divided by 2 divided by 5

all right so here's a problem first

thing we do is we look for parentheses

we see that we have parentheses so we

know we have to do what's inside here

first but once we're inside of there

first we look for multiplying and

dividing we do those first and we look

for adding and subtracting so we see

that we have a division here 10 divided

by 2 is 5 and just to remind you I'll

keep the parentheses around the 5 to

show you that we've handled it the plus

10 remains in the / 5 also remains okay

there's no adding or subtracting them

here we've done everything that we need

to do we've done the division first so

if we have a 5 here now we go to the

next step we look at this we've done the

parentheses the next thing we do is we

look for multiplying and dividing it's a

very next step after parentheses well we

have addition here but we have division

over here so we need to do this first 5

divided by 5 is 1 we still have our plus

10 that we have it handled yet okay and

the very last thing there's nothing else

to do 10 plus 1 is 11 so addition and

subtraction come last another way to

think about it is the only time addition

and subtraction don't come last as if

they're inside parentheses because then

you have to do them first so you just

kind of have to keep an eye on on the

ordering and there's only three rules at

this level that you need to know okay

now let's go ahead and switch this over

and do a couple more additional problems

just to give you some extra practice

what if you have 8 times 8 minus 9 times

2 how do we handle something like that

first we look for parentheses and we see

that we don't have any parentheses so we

forget about that

then we look for multiplying and

dividing now we do multiplying and

dividing left to right we do multiplying

and dividing left to right this

subtraction is not going to happen until

the very very end so just forget about

trying to subtract anything but we see

that we have a multiplication here we're

going to go left to right 8 times 8 is

64 right 9 times 2 is 18 so we can do

all this at once and they're linked by

the subtraction that has to come later

you see what I mean so we do this to

make 64 we do this to make 18 because

we're reading left to right and we're

doing the multiplication or division but

the any subtraction or anything like

that that's happening we wait till later

and the final answer 64 minus 18 if you

forget how to do that 64 18 you can just

subtract to the side we can borrow here

make this a 5 this 14 minus 8 is going

to give me 6 5 minus 1 is going to give

me 4 so the answer is 46 46 just like

that so you need to do the

multiplication and division first left

to right that's what we mean by left to

right we do it like this and then we do

addition and subtraction for the very

last step now what if we have 24 divided

by 4 divided by 2 times 3 now here's

where left to right is going to become

even more important ok we first look for

parentheses we don't see any parentheses

so the next thing to do is look for

multiplication and division and we do it

left to right all right left to right so

we see we have a bunch of stuff going on

here we have division here web division

here we have multiplication here and

these are all linked together so you

can't really do them all at once so what

you really should do is do them left to

right okay so what we have is in the

first step in the first step we have 24

divided by 4 what is that equal 6 now

let's just carry the divided by 2

multiplied by 3 from this let's just

carry that to the next problem this

became a 6 now we go left to right

multiplication and division 6 divided by

2 is 3 now we have the times 3 we'll

just leave that along for the ride and

then finally 3 times 3

is nine so the answer to that problem is

nine this is what we really mean when we

say multiply and divide left to right

okay when you look at that you you can

do the first multiplication or division

then bring the problem down then do the

next multiplication or division bring

the problem down and do the final

multiplication or division bring the

problem down since we didn't have any

addition or subtraction in that problem

then we didn't have to worry about it we

just did the multiplying and dividing

left to right if you start doing things

out of order then you're not going to

get the right answer now I want to

contrast that to what we had up here we

could have done this also in more of a

left-to-right kind of way in fact I'll

do this again for you just to show you I

showed you the first time that we kind

of do both of these separate and link

them with the subtraction let me just

show you really quickly how you would do

that a little bit with a little bit more

steps to show since we see that we have

multiplication in two places and we want

to go left to right another way to do

this

it's really the same thing you can say 8

times 8 is 64 then you just carry the

rest of the problem - 9 times 2 so we

just did the first multiplication down

below and then in the very next step we

see well this is a subtraction we can't

do that we're going to do this

multiplication so 64 minus the 9 times 2

becomes the 18 right and then we already

figured out the 64 minus 18 is 46 so

that's a way to break it down into even

more steps do the very first

multiplication left to right then you're

scanning to the right then you do that

next multiplication because we're going

to the right we do that one and then the

very last thing we do that subtraction

notice addition subtractions always last

in all of our problems unless and sits

inside of parentheses that's the only

exception alright now the next thing we

want to do just to gain some extra

practice is what about 4 times 8 plus 19

minus 3 what do we do first well the

first thing we do is we say way we have

parentheses so we're going to do that

now inside the parentheses is

subtraction now I've been saying

subtraction comes last but the only

exception remember is if it's inside of

parentheses then we can do it first we

have to handle the parentheses first so

19 minus 3

if you remember is 16 so that becomes 16

now this stuff has to remain in the

problem untouched very first thing we do

is we handle the parenthesis making the

16 now you can keep the parenthesis

there or you can drop them either way

once you've evaluated the parenthesis

then the number you have is just going

to carry down through the problem now

we've done the parenthesis now we look

for multiplication and division left to

right now we see in the problem there's

a plus here we don't do that first we do

this multiplication 4 times 8 30 to the

plus 16 is just going to hang on for the

ride and then what we have 32 plus 16

the only thing left to do is the

addition 48 this is the final answer

that's the final answer all right now so

far we've been doing problems and

they've been you know increasing

complexity but here I want to do one

last one just to flex your muscles a

little bit and give you a little bit of

extra practice this will be our last

problem for this lesson and in order to

do that problem I'm going to go off to

the next board here what if we have

parenthesis 20 minus 3 times 6 divided

by parenthesis 2 times 2 minus 3 so

here's a little more complicated because

we have two sets of parenthesis right

they're linked by division but inside of

each parenthesis we have a mixture of

addition of subtraction in this case

with multiplication subtraction with

multiplication so students sometimes

look at that and they don't know what to

do you just follow the rules step by

step so the first thing is you look and

say well I have parenthesis I have to do

what's inside of those parentheses first

I have to write once I'm inside of the

parenthesis I still follow the same

rules add subtract first I'm sorry

multiply and divide first then add and

subtract last that's what I follow when

I'm inside of the parenthesis so when

I'm working inside of this parentheses

I'll carry it down with a parenthesis

like this I can't do this subtraction

first I have to handle the

multiplication first so 3 times 6 is 18

I close that parenthesis off so you see

I can't do it all in one step I have to

do the multiplication first because that

comes first then the division carries

over inside of this parentheses I'll

look inside and I say do I have

multiplication

vision and I do so I do this first two

times two is four

let me just carry the minus three for

the later step in the problem again I'm

still working inside of these

parentheses here because I have to

follow the order of operations inside of

them so what I have here is 20 minus 18

the only thing left to do is to and then

over here 4 minus 3 you only left to do

thing and left to do in there so I have

to do it as one so I have my parentheses

here I'm free to drop these parentheses

now because they don't they don't serve

any purpose to sort of just have go

around one number and 2 divided by 1 is

2 so the answer to this whole entire

thing is 2 now if you start doing crazy

things like 6 divided by 2 first like

don't do the parentheses first you're

not going to get the right answer so

what of operations is one of those

things that trips up a lot of students

but once you understand the rules every

problem can be broken down into very

very similar things the very first thing

we want to always do is do the inside of

the parentheses first and I think by now

you've seen that once we get inside the

parentheses we still have to follow

multiply and divide first and subtract

secondly even inside the parentheses

right but first we look for parentheses

then outside of that we do

multiplication division left to right

first then adding and subtracting left

to right and by left to right I mean

literally you have to go like in this

problem like in this one right here we

had a whole string of divisions and

multiplications on the same level the

way you evaluate it is do the first one

then do the second one then do the last

when you read like reading a book left

to right so make sure you understand

these guys watch all of these again

practice every one of these problems

again until you feel like you're doing

pretty well and then go off into the

worksheets solve all of those get your

skills really really sharp with this

because order of operations comes up a

great deal in math so you want to make

sure you really and truly are good at it

the good news is once you understand it

you can get all of these problems and

questions correct and so it's just

something you have to practice so make

sure you go get that practice right now