Uploaded by videosbyjulieharland on 03.03.2010

Transcript:

>> I'm going to cover consecutive integer problems

so let's start off with examples of two consecutive integers.

Consecutive means just one after the next

so if the first one is 5, the next number would be 6,

those are two numbers in a row right?

How about let's say 10 and 11,

those are 2 consecutive integers.

You could also have a negative number so like you could have -8

and the next number after -8 would be -7,

think of a number line etc. So these are some examples

of 2 consecutive integers so let's say instead

of a specific integer that you know you're gonna have

to use variables.

You don't know what the first one is

but let's say the first one is N what would be the next integer?

So we don't know what N stands for what would be the next one?

Well see what I did on each of these

if I knew what the first one is to get

to the second one you add one

so if the first number is N the second number would be M+1.

So to define two consecutive integers you would say the first

one is N and then you would say the second one would be N+1,

that's how you could define 2 consecutive integers.

What if you were asked to define 3 consecutive integers?

Well again let's just think of some examples first.

So examples might be 5, 6, and 7 right,

or how about 22, 23, and 24.

Or let's say we have some negative numbers like -10,

then the next one would be -9 and -8

so hopefully you're getting the idea

so if I were gonna define 3 consecutive integers I'm gonna

say the first number, let's call it this way, the first,

the second, and the third number.

Alright we always want to start off with the first one

and what would the next consecutive integer be?

Add 1 but how would I get the third number?

You add one again so that's how you would define 3

consecutive integers.

I'm gonna do a problem were we have

to define consecutive integers and then we'll go onto what

if it's talking about consecutive odd integers,

or consecutive even integers.

We'll start off with just consecutive integer problem.

Find 3 consecutive integers whose sum is negative 81.

Alright so we know we're looking for 3 consecutive integers

so that's how we want to start off defining our variables

so we've got the first number let's remember to call that N

and since they're consecutive it's easy M+1 is the next one

and the third number is M+2 not it says their sum is -81

so basically we're adding the first number

to the second number, to the third number,

and we should get -81.

I get the idea I'm gonna end

up having some negative numbers here

so that's how we're gonna do our equation

so the first number is just N plus the second number is N+1,

I'm gonna use a different color so it's easier to see it,

and the third number is M+2

so those are our 3 consecutive integers and that equals -81

so there's our equation.

Now we're going to go ahead and solve this equation

so we're gonna add the like terms on the left side,

3N+3 is -81, subtract 3 from both sides and be careful

with your positive and negative signs here.

We have 3N is -84 and then we need to divide both sides

by 3 so that N equals -28.

Alright now the question is find 3 consecutive integers so now

that we know what N is that stands for the first one

so the first number must be -28

and then what would the next one be?

Add one to that and add one to that, now let's add those up.

They're all gonna be negative so I could just put a negative sign

and if I add that up I get 81 which is right.

Not used to adding negatives up and down you might want

to show your check this way.

-28+-27+-26= - 81 ok that's the check and now of course we have

to answer the question that's being asked.

Find 3 consecutive integers so we say the integers are -28,

-27, and -26 and that's an example

of the consecutive integer problem.

Alright here's another consecutive integer problem.

Find 2 consecutive integers

if 3 times the smaller integer is 12 more

than twice the larger integer.

Alright so we have to begin by defining our variables

and we've got a first and second but I'm gonna write that instead

as the smaller and the larger number this time,

since it happens to use the word smaller and larger,

but these are consecutive integers

so if the first one's N,

the second one will be 1 more which is M+1.

Alright so what's it say?

3 times the smaller is 12 more than twice the larger

so we can do a little bit of English

and algebra together here.

What it's saying here I'm gonna do 3 times whatever

that smaller number is right?

That's gonna be the same is 12 more.

That means I'm gonna add 12 right to something, to what?

Twice the larger, twice the larger number alright

so let's do that.

3 times the smaller will be 3 and the smaller one is N

so I'm gonna put in N for the smaller, that's the same

as 2 times the larger number.

Now the larger number is N+1 so you need to put

that in parenthesis N+1 right and then add 12

and there's our equation.

Alright so let's go ahead and solve it, 3N is 2N+2+12

and I'm gonna subtract 2N from both sides

and then I'm also going to also add the 2 and 12

on the right side of the equal side so I get N =14

so I know what N is and what's N stand for?

The small, the first number so M+1,

the next number is gonna be 15 right?

So it looks like the numbers are 14 and 15

but let's make sure this all checks out.

Alright so it says 3 times the smaller number,

3 times 14 is 42 ok.

Is that the same thing?

Is 12 more than twice the larger?

Well if you got 15 what's twice 15?

That means 2 times 15, 30 if I add 12 to that I also get 42.

So you could check to see that makes sense that 14

and 15 are the two numbers we're looking for.

Yeah and so that will be the answer here.

The numbers are 14 and 15

[ pause in speaking ]

that's how to do a consecutive integer problem.

Now I'm not gonna have time to do a problem

about consecutive even and odd integers

but I'm gonna do a little introduction here.

Let's start out with some examples

of 3 consecutive even integers.

Alright you know like 4, 6, and 8,

those are 3 consecutive even integers or how about 14,

16 and 18 and of course you might have some negative numbers

like -20, -18 and -16 so if you look

at the first integer how would you get to the next integer?

You add 2 so if the first integer is N what would the next

one be?

M+2 and what would the one after that be?

So this is 2 consecutive integers.

If I wanted 3 the next one would be M+4.

So instead of adding 1 we're gonna go by 2s.

Now let's look at examples of 3 consecutive odd integers.

Alright let's do some odd integers.

How about 7, 9 and 11, or 23, 25, 27,

etc. Well what happens here?

If you know what the first one is let's say its N how would you

get to the next odd integer?

You don't' want to add one because you'd be

at an even integer so you have to add 2

to get another odd integer and then to get

to the next odd integer you'd have to add 2 again.

So check this out whether you're talking about even

or odd integers they're both defined as N and M+2 and M+4

if you're doing it for 3 in a row and we'll work on those

in another video, problems with those.

so let's start off with examples of two consecutive integers.

Consecutive means just one after the next

so if the first one is 5, the next number would be 6,

those are two numbers in a row right?

How about let's say 10 and 11,

those are 2 consecutive integers.

You could also have a negative number so like you could have -8

and the next number after -8 would be -7,

think of a number line etc. So these are some examples

of 2 consecutive integers so let's say instead

of a specific integer that you know you're gonna have

to use variables.

You don't know what the first one is

but let's say the first one is N what would be the next integer?

So we don't know what N stands for what would be the next one?

Well see what I did on each of these

if I knew what the first one is to get

to the second one you add one

so if the first number is N the second number would be M+1.

So to define two consecutive integers you would say the first

one is N and then you would say the second one would be N+1,

that's how you could define 2 consecutive integers.

What if you were asked to define 3 consecutive integers?

Well again let's just think of some examples first.

So examples might be 5, 6, and 7 right,

or how about 22, 23, and 24.

Or let's say we have some negative numbers like -10,

then the next one would be -9 and -8

so hopefully you're getting the idea

so if I were gonna define 3 consecutive integers I'm gonna

say the first number, let's call it this way, the first,

the second, and the third number.

Alright we always want to start off with the first one

and what would the next consecutive integer be?

Add 1 but how would I get the third number?

You add one again so that's how you would define 3

consecutive integers.

I'm gonna do a problem were we have

to define consecutive integers and then we'll go onto what

if it's talking about consecutive odd integers,

or consecutive even integers.

We'll start off with just consecutive integer problem.

Find 3 consecutive integers whose sum is negative 81.

Alright so we know we're looking for 3 consecutive integers

so that's how we want to start off defining our variables

so we've got the first number let's remember to call that N

and since they're consecutive it's easy M+1 is the next one

and the third number is M+2 not it says their sum is -81

so basically we're adding the first number

to the second number, to the third number,

and we should get -81.

I get the idea I'm gonna end

up having some negative numbers here

so that's how we're gonna do our equation

so the first number is just N plus the second number is N+1,

I'm gonna use a different color so it's easier to see it,

and the third number is M+2

so those are our 3 consecutive integers and that equals -81

so there's our equation.

Now we're going to go ahead and solve this equation

so we're gonna add the like terms on the left side,

3N+3 is -81, subtract 3 from both sides and be careful

with your positive and negative signs here.

We have 3N is -84 and then we need to divide both sides

by 3 so that N equals -28.

Alright now the question is find 3 consecutive integers so now

that we know what N is that stands for the first one

so the first number must be -28

and then what would the next one be?

Add one to that and add one to that, now let's add those up.

They're all gonna be negative so I could just put a negative sign

and if I add that up I get 81 which is right.

Not used to adding negatives up and down you might want

to show your check this way.

-28+-27+-26= - 81 ok that's the check and now of course we have

to answer the question that's being asked.

Find 3 consecutive integers so we say the integers are -28,

-27, and -26 and that's an example

of the consecutive integer problem.

Alright here's another consecutive integer problem.

Find 2 consecutive integers

if 3 times the smaller integer is 12 more

than twice the larger integer.

Alright so we have to begin by defining our variables

and we've got a first and second but I'm gonna write that instead

as the smaller and the larger number this time,

since it happens to use the word smaller and larger,

but these are consecutive integers

so if the first one's N,

the second one will be 1 more which is M+1.

Alright so what's it say?

3 times the smaller is 12 more than twice the larger

so we can do a little bit of English

and algebra together here.

What it's saying here I'm gonna do 3 times whatever

that smaller number is right?

That's gonna be the same is 12 more.

That means I'm gonna add 12 right to something, to what?

Twice the larger, twice the larger number alright

so let's do that.

3 times the smaller will be 3 and the smaller one is N

so I'm gonna put in N for the smaller, that's the same

as 2 times the larger number.

Now the larger number is N+1 so you need to put

that in parenthesis N+1 right and then add 12

and there's our equation.

Alright so let's go ahead and solve it, 3N is 2N+2+12

and I'm gonna subtract 2N from both sides

and then I'm also going to also add the 2 and 12

on the right side of the equal side so I get N =14

so I know what N is and what's N stand for?

The small, the first number so M+1,

the next number is gonna be 15 right?

So it looks like the numbers are 14 and 15

but let's make sure this all checks out.

Alright so it says 3 times the smaller number,

3 times 14 is 42 ok.

Is that the same thing?

Is 12 more than twice the larger?

Well if you got 15 what's twice 15?

That means 2 times 15, 30 if I add 12 to that I also get 42.

So you could check to see that makes sense that 14

and 15 are the two numbers we're looking for.

Yeah and so that will be the answer here.

The numbers are 14 and 15

[ pause in speaking ]

that's how to do a consecutive integer problem.

Now I'm not gonna have time to do a problem

about consecutive even and odd integers

but I'm gonna do a little introduction here.

Let's start out with some examples

of 3 consecutive even integers.

Alright you know like 4, 6, and 8,

those are 3 consecutive even integers or how about 14,

16 and 18 and of course you might have some negative numbers

like -20, -18 and -16 so if you look

at the first integer how would you get to the next integer?

You add 2 so if the first integer is N what would the next

one be?

M+2 and what would the one after that be?

So this is 2 consecutive integers.

If I wanted 3 the next one would be M+4.

So instead of adding 1 we're gonna go by 2s.

Now let's look at examples of 3 consecutive odd integers.

Alright let's do some odd integers.

How about 7, 9 and 11, or 23, 25, 27,

etc. Well what happens here?

If you know what the first one is let's say its N how would you

get to the next odd integer?

You don't' want to add one because you'd be

at an even integer so you have to add 2

to get another odd integer and then to get

to the next odd integer you'd have to add 2 again.

So check this out whether you're talking about even

or odd integers they're both defined as N and M+2 and M+4

if you're doing it for 3 in a row and we'll work on those

in another video, problems with those.