Subtraction and addition with whole numbers

The addition of whole numbers is when

these have the same sign, not only when

one of them has the plus sign, so

since this is the first number, then it's understood that

if not indicates it's

positive and here we can see that both

have the same sign

so both move to the same side of the number line

or an amount is being added, for instance,

here we have 5 apples

it means that they're given to you

and the +7

it means that they're giving

another 7 apples

so as a whole we have

12 apples or as mentioned in the number line

using 0 as a reference

+5 means that you move 5 units to the right

ok?

and the +7 means that here are 7 more

so, it would be: 1,2,3,4

5,6,7

in total it moved from 0 twelve spaces or leaps

another example that's an addition and in general sometimes

it's not considered

it's when we have two negative numbers, for example -6 and -3

the same sign, they move towards the same way

or making an analogy with oranges, here they took

six oranges and here they're taking away other 3

so in total they took from me 9 oranges

it's an additon, but only of negatives

and it can also be solves through the number line

here we have 0, but in this case

let's go to the negative side

it would obviously be -6

1,2,3,4,5,6

remember that negatives move to the left

and other -3 mean that while being here

1,2,3

due that we move to the same way

the scale has to be added

if there's uncertainty on how to perform

an addition of negative signs

I recommend to think about a money situation

for it's what we use on a daily basis

let's assume that someone asks for 6 pesos

and then this same person asks you for other 3 pesos

we're going to interpret negative as taking money away

so as a whole that person owes you 9 pesos

or the positive can be associated with money that someone is giving you

then, it'd be: I was given 5 pesos

and then they gave me 7, as a whole, I was given 12

solving other exercises, here we have

several numbers and all are positive

well, let's remember that the first one if not indicated is also positive

it's an addition

here we can add either by pairs

or to this one, I add an amount and so on

until we simplify all this in one amount

it's easier for me to group by pairs

put multiples together or every ten or close to it

in this case. it's a 20, this and this give me 10, so it's 30

and adding a 14 it turns into 44, so the answer is +44

here all numbers have the same sign, in other words, minus

so here we have a negative addition and by grouping here

it's easier this one and this other one, it'd be a 30 and a 6, it'd be a 36 negative

so when we have the numbers without parenthesis

double signs, only when all numbers are all the same

then it'll be an addition of either positives or negatives

in the case of the subtraction with whole numbers

it's always when we have a pair of numbers and these have different signs

well here the first one, this one is positive

here we see that it's positive and this one negative

so by looking for the difference between 9 and 4

that we know it's 5 and due to this one being greater

than the 4, the answer should be

positive, this is just like having 9 apples and they ask you for 4, or lost them and you end up with

5 since you had more that what it was taken away

the answer is positive

this can also be shown in the number line

putting the 0 here, if we have 9 units 3,4,5,6,7,8,9

and they take away 4, then this was going one way and now

minus 4 means that you go back 4,3...4 then this

amount would be 5 positive

it must be taken into account that his same operation

can be done the following way where -4

stays in the first position and the +9 in the second due to the fact that is remains

with the same sign, then the answer must be the same

this subtraction has different signs

the difference between 9 and 4 is that 5 units separate them

since this one is greather than this other one, the answer remains positive

or if you want ti use the numeric table

or you can aldo make an analogy with money, if you lost 4 pesos

that you borrowed and they give you back 9, it means that what you owed is covered

and you still have 5 pesos

solving other exercises where you apply subtraction

here we have two numbers with different signs, so

looking for their difference, you take 2 from 8, you get 6, that's the distance that separates them

these numbers and because the 8 is greater

than 2 the answer should be negative, in this other one

the signs are different, so looking for the difference

it's 4, 15 is greater than 11 so

the answer is positive

if by doing the subtraction this way

you get confused or don't fully understand, think what was mentioned in the money analogy

which is used on a daily basis

if you have 2 pesos and someone asks you for 8 pesos

you'd be short by 6, since they're missing, it means they're negative

in this case, let's assume that they asked you for 11 pesos and then give you 15, it means that they paid and that

you have 4 left

it also works with

the number line, it represents poditive numbers that move to the right

negatives move to the left and the answer as you can see

is 6 and here +4, another thing that you must take into account is that

this didn't become negative by multiplication

positive times negative and apply the law of signs and the answer is negative, if you see

here when applying the law of signs it won´t be positive

it won't be positive, it'd be negative, so

here we don't apply the law of signs, if and when we don´t have a parenthesis here

it'd be a multiplication, then when we have numbers

without parenthesis or square brackets

or keys, it'll always be a subtraction

and it'll be solved this way

to finish solving this exercise, here we have several numbers where some

are positive and others negative so we have several ways to

come up with the answer, I reccomend to add

the same signs first for example the 6

9 and 8, then it would be a positive addition

here 9+8=17

and then 17+6=+23

and the others are also of the same sign, then it's a negative addition

so here it'd be 5 and 11=16 and 20=36

but negative

to finish, since we have 2 numbers and they have different signs, then it's a subtraction

looking for the difference between them or 36-23 gives us 13

and due to the fact that 36 is greater than 23

the answer is negative

you can also solve by pairs, in other words,

you start on this side, subtract and between these two numbers you get +1

and then +1-11 you get -10 and then

here -10+9 you get -1

-21 adding 20 and -21+8 you get -13

either way you get the same answer

Subtitled by Mali Reyna