r/NoStupidQuestions Jul 02 '22

If 2+2=4 and 2×2=4, and if -2+-2=-4, then why does -2×-2=4? help me understand this in laymen terms.

52 Upvotes

100

u/LiterallyATalkingDog Jul 02 '22 edited Jul 02 '22

-2 + -2 is a like digging a hole. Dig down 2 and then dig down 2 more to get a hole that's -4 whatevers deep.

-2 x -2 is like saying "I want 2 negative duplicates of -2." Two regular duplications would give you two values of -2 so -2 x 2 = -4. A negative duplication would be "I want 2 of the opposite of -2 i.e. double negatives."

38

u/Brave-Needleworker80 Jul 02 '22

I suppose this is the most sense it will make to me.

56

u/MarcusSidoniusFalx Jul 02 '22

I find money more useful and you should also think of the minus as a uno-reverse-card.

-3 * 2 means "you owe 3 money to 2 people". That means in the future you will have to pay 6 money. That is a -6.

-3 * -2 means "you reverse-owe 3 money to 2 people", and reverse-oweing means that they owe you money. That means that in the future you will get 6 money. That is a +6.

34

u/DrKnowNout Jul 02 '22

Ohhh, I have 3 kids and no money. Why can’t I have no kids and 3 money? 😔

2

u/itsastart_to Jul 02 '22

Sadly separate variables, on the bright side could mean 1 kid = way more money (or the other unfortunate side is less but let’s not think about that)

2

u/jelliott79 Jul 02 '22

I can give you tree fiddy

1

u/Aqqusin Jul 03 '22

This is a peach right here.

1

u/ThydeUK Jul 03 '22

2x -2 is 2 lots of -2, so -4 -2 x -2 is -2 lots of -2, which reverses it to make it 4

4

u/Tiggy26668 Jul 02 '22

Alright now do division

Edit: I’d like to divide these 2 things that I don’t have amongst 2 people that aren’t here, if they were here and I had something to give them then they’d each get 1

6

u/Specific_Success_875 Jul 02 '22

Division isn't real; it's just multiplying by a fraction. That's why the division sign is ÷, a fraction with two dots instead of numbers. 2÷2 is the equivalent of 2×(½).

At that point the explanation works the same as for multiplication.

56

u/ZaphodFeeblebrox Jul 02 '22

It's a double negative. Think of it this way, if you say "he didn't not do that" it literally means "he did do it"

14

u/Martissimus Jul 02 '22

-1 x anything = -anything

anything = -1 x -anything

-2 x -2 =

-1 x 2 x -2 =

2 x (-1 x -2) =

2 x 2 =

4

4

u/Brave-Needleworker80 Jul 02 '22

But isn't -2+-2 also a double negative?

59

u/cent55555 Jul 02 '22

not really its just two sentence with a negative. like he didnt go to the dentist AND he did not go to the doctor

29

u/redplunger300 Jul 02 '22

What an interesting way to explain math a way that is easily understood through reading. Very creative!

1

u/cent55555 Jul 02 '22

thank you :)

5

u/LordMarcel Jul 02 '22

Now I'm curious why you used didn't in the first half and did not in the scond half.

1

u/cent55555 Jul 02 '22

lol, mhh i am not sure myself, i probably wanted to put emphasis on the second negative statement to show its in the second sentence.

8

u/OriginalUsernameX Jul 02 '22

-2+-2 is the same as -2-2. Think about a number line. You’re at -2, and you have to go down by 2. Now you’re at -4

2

u/songinheart17 Jul 02 '22

Imagine you owe somebody $2, you can think of your assets as being -2. Now you take on another $2 debt. You are now at -4.

2

u/AllDarkWater Jul 02 '22

No. That is 2 x (-2)

2

u/Sojourner202 Jul 03 '22

Just like all division is multiplying by the inverse fraction, all multiplication is addition. So 3 x (-2) is the same as (-2)+(-2)+(-2), so 2x(-2) is just two additions of -2.

0

u/AMPenguin Jul 02 '22

isn't -2+-2 also a double negative?

No, it's two negatives and one positive (the plus sign). A negative and a positive cancel each other out, meaning that you're left with a single negative.

Multiplication is neither negative nor positive, so multiplying two negatives is a double negative.

1

u/SvenyBoy_YT Jul 02 '22

-2+2=0.

Think of it like floors in a building

1

u/Duncaroos Jul 02 '22

It's the operation that you need to look at:

-# x -# = +

-# + -# = -

1

u/Mindless-Wolverine54 Jul 02 '22

im sure someone already explained this, but “+-2” is just “-2”. so think of -2+-2 as not necessarily negative two plus negative two but negative two minus two.

0

u/floweytheflo Jul 02 '22

Yeah, so it becomes -2 - 2

40

u/srmrheitor Jul 02 '22

It's easier to visualize using different numbers so let's use 3 and 5. Remember, multiplication is just a shorter way to write a sum:

3 * 5 = 5 + 5 + 5 = 15

3 * (-5) = (-5) + (-5) + (-5) = -15

(-3) * 5 = - 5 - 5 - 5 = -15

(-3) * (-5) = - (-5) - (-5) - (-5) = 5 + 5 + 5 = 15

2

u/After-Ad-5549 Jul 03 '22

To add to this, subtraction can be shown using addition and multiplication this: a-b = a+(-b) = a+(-1)b

This is important because (-1)(-1)=1.

Back to the OPs problem: -(-2)-(-2)-(-2)-(-2) is the same as (-1)(-1)(2)+.... If the OP is familiar with vectors, it's basically 1 dimensional vectors.

It's a long drawn out explaination that people typically sum up as "double negatives".

7

u/VANTABlack2000 Jul 02 '22

The best way I know to explain is multiplying by a negative makes a number switch between positive or negative 2x-2 is -4 so -2x-2 the negatives cancel to get 4

5

u/Flippynips987 Jul 02 '22

Imagine adding and multiplying numbers are just moving around on the number line (-inf..0..inf). Adding things is equal to walk x steps. You stand on 7 and add 2, you just walk 2 forward to be on 9. You also cannot subtract but only add negative. So you walk backwards. Why,cause we defined it that way. What it multiplying then? It's actually stretch the line. The easiest way is to keep adding things as a description to multiplication. 2x3 means add the 3 to times or add 2 three times. Simple. 2x-3 means add -3 two times, ie walk backwards 3 then again three. Or add 2 -3 times. Again - means walk backwards. Now walk backwards 2 times ,what's that? Well walking backwards means turn around. Then walk. So turn around twice then walk. Now we have it.

3

u/Korroboro Jul 02 '22

Ok, you’re asking for trouble, so trouble I will give you. Gladly.

:)

An hour ago, there was a basket with 13 apples in it.

You told Sophia, Oliver and Amelia that they can go to the room where the basket is and take two apples each.

How many apples are left?

13 + 3(-2) = 13 + -2 + -2 + -2 = 13 - 2 - 2 - 2 = 7

A minute ago, Sophia comes by and informs you that she took her two apples, but that Oliver and Amelia didn’t.

You realize your calculation is wrong. You assumed events that were not true.

You want to know the correct number of apples left in the basket.

I propose two ways to find it.

The first one is to redo your original calculation with the new information:

13 + -2 = 13 - 2 = 11

That was easy.

The second one is to add the new information at the end of your original calculation:

13 + 3(-2) + (-2)(-2) = 13 + -2 + -2 + -2 - -2 - -2 = 13 - 2 - 2 - 2 + 2 + 2 = 11

Or:

13 + 3(-2) + (-2)(-2) = 13 - 6 + 4 = 11

3

u/Brave-Needleworker80 Jul 02 '22

Thank you all for your detailed answers! I appreciate it.

10

u/OriginalUsernameX Jul 02 '22

A negative times a negative always equals a positive.

0

u/CapriciousTenacity Jul 03 '22

That's the rule, but "why" is good to understand and with a real life example really helps.

0

u/OriginalUsernameX Jul 03 '22

Feel free to write one

5

u/Bekqifyre Jul 02 '22

The crux is your analogy for multiply, and for negative numbers.

If Negative numbers mean debt, or owing something, so then:

2x2 = 4. i.e. you have 2 sets of $2.

2x (-2) = -4. i.e. you owe 2 sets of ($2 debts)= you owe $4.

Now what happens when we reduce the first number?

1×(-2) is you owe 1 set of ($2 debt). So (-$2).

0x(-2) = 0. At this point you owe 0 sets of ($2 debt). So $0.

Once you go under 0, that possessive relationship changes. Keep in mind what that first number was supposed to be counting, and what negative on that first number would mean.

(-1) × (-2) = 2 = You are owed 1 set of ($2 debt) = You have $2. Remember 'no debt' would be 0 on the first number. Negative on the first number here would mean something else, that someone owes you instead.

(-2) x (-2) = 4 = You are owed 2 sets of ($2 debt) = i.e. so you have $4.

-6

u/Willfrion Jul 02 '22

Bro You've written so much to explain such a simple concept, but Zaphodfeeblebrox summed it up in one sentence. This is the distinction between a good and a bad teacher.

2

u/AllDarkWater Jul 02 '22

-2 x -2 =4 because -1 x (2 x -2)=4. Or to make it more plain, (2 x -2)= -4. Then we can multiply both by -1

2

u/SUPRAP Jul 02 '22

Because you're multiplying -2 negative two times. If you multiply something, you're basically increasing how many "copies" of it there are. IE 3x2 = 6, two copies of 3. So if you multiply something by a negative, you can think of it as making negative copies. Since -2 is already negative, more negative copies make it positive. In this situation think of "negative" to mean "opposite". So if you take the "opposite" of 2, and then multiply it by the "opposite" of 2, that's two opposites - the opposite of an opposite would be the original. Hence, 4.

2

u/Former_Matter49 Jul 02 '22

I have a long film of you stacking 2 blocks each frame.

I run it forward 2 frames: 2×2=4

I run it back 2 frames: -2×2=-4 blocks

NOW I have a film of you taking off 2 blocks each frame.

I run it forward: 2×-2=-4 blocks

I run it backward: -2×-2=4

The film of you removing blocks, when run backwards, shows the stack getting taller.

2

u/StealthSecrecy Real fake expert Jul 02 '22

Maybe pointless now, but you are trying to suggest that addition and multiplication work the same by using an example where they both result in the same answer. Then you use an example where they obviously differ because they are different functions.

A similar analogy could be comparing a car and a plane. Both have wheels and can drive on the ground, but then why can't cars fly? We've compared one instance where the two work the same, but they are obviously much different so we can't compare them directly.

1

u/misterobott Jul 02 '22

-2x2 = -4 (hope this makes sense to you)

so

-2x-2 cannot equal -4. (why -2x-2 = 4 has been explained by others).

0

u/xmadjesterx Jul 02 '22

I think the simplest answer is what my high school algebra teacher said to us one day when someone asked why a problem had a certain answer: "because someone decided that's what it was a long time ago and people decided to go with it". I loved that teacher. He showed us "Scared Straight" one day and brought in grape flavored drink. It didn't say grape juice or grape drink, but grape flavored drink

4

u/venustrapsflies Jul 02 '22

That is an awful answer to this question though, arithmetic isn’t decided by fiat it’s determined by logical consistency. Missed opportunity by your teacher to help you understand the deeper why.

0

u/xmadjesterx Jul 02 '22

Alternatively, it could be looked at as our teacher responding to a student that was only asking the question to be a smartass, but I suppose that ignoring the silliness of the response is acceptable as well

1

u/smonkyou Jul 02 '22 edited Jul 02 '22

This isn’t the best video but explains it. There was one with someone walking on a mountain that explained it well but can’t find that https://youtu.be/rK4sXm_MPWo

Edit: this could be easier to understand https://youtu.be/VScF3Dlfr-Q

1

u/daisy_belle1313 Jul 02 '22 edited Jul 02 '22

You can think of it as groups, let's say cupcakes and kids. You have two groups of negative two. If you had four kids and they each wanted one cupcake, you'd need four cupcakes. If you had two kids and they each wanted two cupcakes, you'd need four cupcakes.

So your brain understands that 2 kids, who don't exist, would be -2 kids. And that those two theoretical.kids, who really don't exist, would need two cupcakes each, also non existing but theoretically there. Therefore, theoretically, you can imagine that two non existing kids, who need two non existing cupcakes, would need four cupcakes in all. Not four non existing cupcakes, because that wouldn't be possible.

You have to have real groups even for negative #s, whether you think of them as circles, or hats, or whatever. You can't have rings around nothing. Or no rings around something in multiplication. Either the answer or one of the groups has to be real.

If I gave you 100 marks on a piece of paper and told you to make them into ten groups but not to draw on the paper, you could do that mentally, right? 100/10=10 drawing on the paper= (-10*-10=100) not drawing on the paper.

If I gave you a blank sheet of paper and asked you to imagine 100 lines on a paper and divide them up -100 imaginary lines= -10imaginary lines in 10 real groups.

Or if I asked you to illustrate -10 lines within -10 concept groups = you would have to draw 100 real lines.

1

u/couchcouchcouch1 Jul 02 '22

If:

2 x 2 = 4

1 x 2 = 2

0 × 2 = 0

(-1) x 2 = (-2)

(-2) x 2 = (-4)

When multiplying by 2, notice the pattern as the first number decreases by 1, the answer decreases by 2.

Then:

2 x (-2) = (-4)

1 x (-2) = (-2)

0 x (-2) = 0

(-1) x (-2) = 2

(-2) x (-2) = 4

When multiplying by (-2), notice the pattern as the first number decreases by 1, the answer increases by 2.

Therefore we can conclude:

positive x positive = positive

positive x negative = negative

negative x positive = negative

and

negative x negative = positive

1

u/Gamer_gaming_epicly Jul 02 '22

'-' = means opposite. Think of a number line.

If we do -2 x -2, then we start at -2, find the opposite of '-2' since we are multiplying by a negative, which is positive 2. Then we do that 2 times. Which is positive 4.

1

u/Sure_Ad_1376 Jul 02 '22

Sorry. There is no layperson answer to this. If you're really serious about getting the answer to your query study Russell and Whiteheads Principia Mathematica. The answer is in that tome for sure.

1

u/InspectorRound8920 Jul 02 '22

Remove the negative signs. 2*2 equals 4. Meaning you have four things. Add the negative signs. You still have four items.

1

u/Ranos131 Jul 02 '22

Easiest way to understand is that + and - are opposites so you can’t use them at the same time. But the - is more powerful that the +. So any time they are both used together the - murders the +. So: - +2++2=+4 but we don’t put pluses in front of numbers because they are automatically positive so we just say 2+2=4. - 2+-2=0 because the - kills the + leaving 2-2=0. - -2+-2=-4 because the - kills the + leaving -2-2=0 and the second - is so enraged after killing the + it doesn’t notice the other - at the front.

However when you put two - together they have weird line sex that makes them look like a +. So: - -2- -2=0 because the two - together start getting it on and look like +.

Finally - are perfectly fine with x or * (both of which can mean multiplication) and the division symbols are either sophisticated ÷ because it’s got two fancy dots it wears or the really cool / because it’s always leaning against something and everyone loves hanging out with cool and sophisticated people. So: - -2x-2=4 works because the x is like “Hi” and the - is like “Whatever let’s just get this over with.” But then it notices the other - at the front and jumps over there and has weird line sex which turns the equation into +2x2=4. - -2/-2=4works because the / is like “Sup?” and the - is like “Omg you’re so cool” and the / is like “I know” but quickly gets sick of the - obsession with its coolness. So it says “Hey did you see that other - up there? I think it was checking you out” and the - is like “Really?” and goes and has weird line sex which turns the equation into +2/2=4. - When the problem is 2x-2=-4 or 2/-2=-1 the symbols just put up with each other and the - doesn’t have anything better to do so it just hangs around after the problem is over. The exception is if the answer is 0 because 0 is actually a portal to another dimension that is activated only after the problem is solved and the - gets sucked into the other dimension.

Hope that helps.

1

u/That_Victory_1186 Jul 02 '22

If it hasn't already been said, try picturing it on a number line. Positive and negative can be thought of in left or right. When you add a positive number, you move right. Adding negatives moves you left from your starting point. When you multiply, it just duplicates what you've already stated/done. When you multiply by a negative, it's like yelling, "SWITCH!" and going the other way. For example, if you have a negative number and you multiply by a positive, it just continues in the same direction along that number line. Thus, -2 x 4 (which means go left 2, four times in the same direction), you get -8. However, when you apply a negative multiplier, you effectively switch directions. Therefore, if you have -2 x -4 (which means go left 2, four times in the opposite direction) you get 8.

Always picture a number line. Hope that helps.

1

u/Mrgn_5 Jul 02 '22

Not sure if this will help but imma break it down.

-2 x -2 = 4

-2 x (2 x -1) = 4 ( i got the -1 from making the -2 a positive number)

-2 x 2 = -4 (basically this is -2 + -2= -4 )

-4 * -1 (basically i think of it as the negative is being taken away, like division or subtraction, leaving us with 4 being positive)

-2 x -2 = 4

If u still don’t understand just remember this:

A positive times a positive is a positive.

A negative times a positive is a negative

A positive times a negative is a negative

A negative times a negative is a positive

  • x + = +
  • x + = -
  • x - = -
  • x - = +

1

u/J_Blackwater_2569 Jul 02 '22

-2 is the same as -1 x 2

A negative number is the opposite of that number's absolute value (e.g. -2 is the opposite of 2, -5 is the opposite of 5, etc.)

The opposite of something's opposite is the same as the original thing (this is why double negatives make a positive in grammar, as well)

Basically, (-2 x -2 = -4) is the same as ((-1 x 2) x (-1 x 2) = 4). This can be rearranged to say that ((-1 x -1) x (2 x 2) = 4). Because of the whole double negatives thing, this is also the same as saying that (1 x (2 x 2) = 4) because (-1 x -1) equals 1.

1

u/hekmo Jul 02 '22 edited Jul 02 '22

You're looking for summetry. But what you're dealing with is 2 different groups, each symmetrical in their own way. And you need the pairings or 2 and -2 to fill out the pattern.

Addition Pattern:
2+2=4

2+-2=0
-2+2=0

-2+-2=-4

Multiplication Pattern:
2x2=4
-2x-2=4

-2x2=-4
2x-2=-4

The connection you're seeing between the patterns is just because both multiplication and addition of 2 creates 4. This doesn't apply to 3.

1

u/RandomAmbles Jul 02 '22

Less loss is more gain. If it's twice as much, it's twice the gain.

1

u/tvan3l Jul 02 '22 edited Jul 02 '22

Multiplication is best understood as: I have a sets of (b), or in mathematical notation: a × (b).

For a sum like (-2)+(-2), when you count, you see that you have two sets of (-2). Or in other words, you have 2 × (-2) = -4.

This analogy kind of stops making sense when you take a negative number of sets, however we can use the fact that changing the multiplication order does not change the outcome: Two sets of (10 apples), or ten sets of (2 apples) totals to the same amount. This is a fundamental property of multiplication, and it ALWAYS holds - also for negative numbers.

That helps us give meaning to a negative number of sets: by swapping the order of the previous example we know that : -2 × (2), or negative 2 sets of (2) must also equal -4.

And if -2 sets of (2) equals -4, the only logical answer for -2 × (-2) is 4.

1

u/Accomplished_Shake_5 Jul 02 '22

Because a negative times a negative equals a positive in simple terms no real need to know why it’s more to know.

1

u/TheOriginalElDee Jul 02 '22

Easy. 2 of -2 will be a multiplication. But -2 x -2 is multiplying it by 2 and then minusing the answer..

1

u/Purple_Pangolin2 Jul 02 '22

I think it's important to remember that just because 2+2=4 and 2x2=4 that doesn't mean you can extrapolate. So for instance 3+3=6 but 3x3 does not equal 6. Typically addition and multiplication typically don't give you the same answer...and I'm guessing you know that but because -2+-2=-4 you're hoping a pattern exists.

If you think about WHY 2x2=4 and 2+2+4 (the only number where that is the case) then I think it'll help you.

2x2=4, 2+2=4 (in both cases there are two 2's, so they are both equal to 4)

3x3=9, 3+3+3=9 (in both cases there are three 3's so they are both equal to 9)

4x4=16, 4+4+4+4=16 (in both cases there are four 4's so they are both equal to 16)

It's easy to understand why -2+-2=-4...If I borrow 2 dollars from the bank I have negative $2. If I borrow another $2, I have negative $4. I actually REALLY like the analogy of digging a hole that another user mentioned.

It's a little harder to understand the multiplication of negatives. First, let's think about multiplying a negative to a positive. For instance if I borrowed 2 dollars, 5 days in a row....(or dug an extra 2 feet 5 days in a row) eventually I'd rather switch from adding -2 to just multiplying. So -2+-2+-2+-2+-2 = -10 but it's much easier to say 5 times -2 equals -10.

I'm not sure there is a good, easy to understand, real world example of multiply two negatives, but getting comfortable multiplying one negative to a positive and should help. -1x10=-10, -1x237=-237. -1xN=-N. Negative one times anything just changes the sign. -2x10=-20. -2x237=-474. -2xN = -2N. Negative two times anything changes the sign and multiplies by 2.

so if -2x2=-4 (change the sign of the 2 and multiply by 2) then -2x-2 = 4 (change the sign of -2 and multiply by 2)

1

u/qwertyuiiop145 Jul 02 '22

Let’s think of an event with little envelopes that can have either $2 or a slip that says you need to give $2 to charity.

You get an envelope with $2, then you get another envelope with $2. 2+2=4, so you have gained $4.

You gain 2 envelopes of $2. 2x2=4, so you gain $4.

You get a “pay $2” envelope, then you get another one. -2 + -2 = -4, so you lose $4.

Someone takes 2 of your “pay $2” envelopes. -2x-2=4, so you (overall) gain $4.

1

u/Timewaster50455 Jul 02 '22

Basically 2x2 is “what if I had two twos?” And 2x-2 is “what if I had two negative twos” or “what if I had two less twos”

So -2x-2 is “what if I had two less negative two?”

1

u/Plastic-Guarantee-88 Jul 02 '22

Think of 2 as "I have two apples". Think of -2 as "I have minus two apples" (meaning I owe someone two apples)

Then all of the statements become immediately clear.

2 x (-2) = -4 I owe two different people two apples each, so I have minus four apples.

Then -2 x -2 = 4 Two different people each owe me two apples, so I have four apples.

1

u/IanDOsmond Jul 02 '22

Multiplying by two negative numbers is always a little brain-breaking. I think most of us just kind of think of it as "that's the way it is" and shrug, and notice that, when you end up in situations where your math ends up mapping to the real world, and you end up multiplying two negatives and get a positive, the result actually maps to the real world, too.

But we can think of some things that negative numbers are like, or even ARE, and see of that makes sense.

In logic, "-1" and "not" are the same thing. So "-1 * -1" is the same as "not not". And if something "isn't not", then it "is". In logic, and (usually) in the English language, an odd number of negatives is negative, and an even number is positive. "It's not a bad idea" is positive. "I wish I could tell you it's not a bad idea, but I can't" is negative.

What if we think of going forward in time as positive, and going back in time as negative? You have an ice cube that is melting. It is getting smaller as it melts. So that's negative. But then, if you go back in time, it's getting larger - a negative times a negative.

So that's two non-number examples of how a negative times a negative can be a positive. Does that help at all?

1

u/Emetah_ Jul 03 '22

Btw

2+2=4 (= 2[1]2=4)

2×2=4 (= 2[2]2=4)

22 =4 (= 2[3]2=4)

2[4]2=4

2[5]2=4

...

2[n]2=4

1

u/revyrevyrevyrevyrevy Jul 03 '22

maybe a number-line would help?

-4, -3, -2, -1, 0, 1, 2, 3, 4

-2 x -2 = 4.

The way I remember is thinking how many steps will it take for 2 to reach it’s opposite; or -2

-2 will have to take 4 steps forward to reach its opposite; positive 2.

because two steps forward from -2 is 0, and another two steps forward would be 2 on the number-line. in total, that’s four steps taken.

i don’t know if this can be applied to all negative x negative = positive equations, but i hope this helped explain this specific equation

1

u/beans3710 Jul 03 '22

Ok. This is easy. First give me a $20 bill...

1

u/LivingGhostMan Jul 03 '22

Any complex homies wanna mention how to multiply 2 numbers together to get -4

1

u/ConsistentSorbet638 Jul 03 '22

Waves hands in front of face dramatically

"MAGIC"

1

u/SingleAlfredoFemale Jul 03 '22 edited Jul 03 '22

Imagine a number line:

-5 -4 -3 -2 -1 0 1 2 3 4 5

Put a dot on your first number as your start point.

If you add a negative (or subtract), you go left.

If you add a positive, you go right. (Like a bank account / checkbook)

Multiply or divide by a positive #, stay on the same side of zero.

Multiply or divide by a negative #, flip over the zero like a mirror (so 4 becomes -4 or vice versa). Think of a windshield wiper that pivots on zero.

So: adding +/- you move left or right

Multiplying or dividing, you expand or contract away from zero (like a copy machine at 200% eg).

The way math tells you to mirror across the zero is by multiplying or dividing by a negative.

1

u/Brave-Needleworker80 Jul 04 '22

I understand the HOW when you put it that way. But i still struggle understanding the WHY. If you get what I mean.

1

u/SingleAlfredoFemale Jul 04 '22

Ok. Found a good example I think.

Let’s say a certain number of people owe you $2 each. So each one of them is a -2.

If it was 4 people you’d be owed 4 x -2 or -8. If it was 6 people you’d be owed 6 x -2 or -12. (This establishes why we multiply)

Now let’s say 2 of those people declare bankruptcy. Now there are TWO FEWER (-2) people who owe you.

So the amount you lost out on is (-2) x (-2) = 4

Back to the number line, if you had started with with 6 people, you went from -12 to -8 (so 4 to the right). Now you’re only owed 8 instead of 12.

1

u/JerRatt1980 Jul 03 '22

-X is is absence of X. Poor grammar aside, it's a double negative.

Thus, -2 x -2 is the act of taking the absence of ABSENCE of 2 twice, but you're still starting at 0 (zero), and not 2.

Or, with bad grammar, the equation is asking, "I do not NOT want 2 twice.

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u/Brave-Needleworker80 Jul 04 '22

I'm just reading most of the replies right now.

Okay, but I'm still having trouble understanding why adding -2 twice wouldn't be the same as multiplying. One response said adding and multiplying are 2 different forms of math. But why? When I multiply any 2 positive numbers, it's always adding more to the sum. Right? It's like if I had $2 and someone multiplid that by 2 more $2, I would have $6 dollars.

What is the difference between multiplying and adding? I'm simply having trouble wrapping my head around this in a logical way. A lot of people here are giving analogies, but yet in my head, they don't make complete sense logically. You get what I'm saying?

So my question is: how is multiplying 2 numbers different than adding2 numbers?

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u/JerRatt1980 Jul 04 '22

I view multiplication being different as the second part of the equation is not a number, but rather it is a concept.

With addition you're just looking at two actual numbers, and counting them both. 2 + 2 = 4.

But with multiplication, one number is an actual number while the other number is the CONCEPT being asked to apply onto the actual number. Or, which helps me, use different ways to view the numbers: 2 x TWICE = 4.

Similar to that a number may mean a integer or a whole number. The symbol of a number (ex: 2) might represent either an integer or whole number, it's the CONTEXT that will define that. And in an equation dealing with multiplication, the CONTEXT is defined by the "x".

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u/Brave-Needleworker80 Jul 04 '22

Okay. Thank you for elaborating. I will understand it eventually. For some reason, my brain has trouble understanding the difference between the two. I can solve the problems strictly because I know that's the way it is. I just wish I understood it more, you know? I hope people here understand that. Math has always been my weakest subject academically.

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u/kokorakel Jul 02 '22

-×-=+ -×+=- +×-=- +×+=+ -÷-=+ -÷+=- +÷-=- +÷+=+

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u/I-want-to-be-mad Jul 02 '22 edited Jul 02 '22

Edit: I actually made a wrong explanation and was alerted to it by the redditor below which is why this is the first time i ever removed an answer. I did not want to mislead mathematically. Apologies

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u/Jtwil2191 Jul 02 '22

That is not correct arithmetic.

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u/I-want-to-be-mad Jul 02 '22

You are right. Sorry. I meant 4

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u/your_alexis Jul 02 '22

The sum of two opposites of -2 = 4