I am trying to start again with math, giving it a second shot after i completly gave up on math for about 10y. I looked up multiple cheet sheets and rules, but they all say different things. My problem especially +29 – +59. The rule thing i got from the internet says + – + = larger integer’s sign, but then another tutorial said well if you reverse + and -, then you can get the answer that way, but they are 2 different answers. And i’m confused too about what, like what’s the point of doing the operations if we can just change whatever symbols we want, but then we do but nothing matches as the result so i’m just confused.
I just don’t get it, none of the rules match and in my head none of it even makes any sense. So i feel like i need to memorize the rules, but there are no rules. Pls help, i started crying due to the fustration because now i remembered why i despised math so much.
Update: I started being able to complete operations, even of 5 in a row. Thank you all! Ended up dropping tje unecessary + and just – – = + idk, but i’m doing it.
In: 2
I teach remedial math to high schoolers, so this is my wheelhouse (though much harder to do thru text).
> The rule thing i got from the internet says + – + = larger integer’s sign,
Best to not look at any of that stuff. Use common sense.
• If you were 10ft above sea level and went down 3ft, you are now 7ft above sea level.
• If you were 10ft above sea level and went down 10ft, you are now 0ft above sea level (you are at sea level, 0ft).
• If you were 10ft above sea level and went down 13ft, you are now below sea level due to an excess of 3ft, so -3ft or 3ft below sea level.
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If you want, you can think of there never ever being such a thing as subtracting (at least for this level of math), just adding negatives.
5-2 = 3
5+(-2) = 3
5-(-2) = 7
5+2 = 7
Adding positive numbers move right on the number line.
Adding negative numbers move left on the number line.
Subtracting positive numbers move left on the number line.
Subtracting negative numbers move right on the number line.
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Think of positive integers as objects you own, and negative integers as objects you owe somebody.
Your +29 – +59 would usually be written as 29 – 59. But you can think of it as 29 + -59. Here you are adding your 29 objects you own, and your debt you owe of 59 objects. If you paid your debt as much you could, you would have 0 objects and 30 objects still owed (59 – 29). Because they are owed it is negative still, so it would be -30.
I would think about it like this:
You’re standing on a very long, straight race track. You’re standing on a solid line that we’ll call the starting line. Ahead of you, way past the horizon, is a brilliant sunset.
When you have positive (+) numbers, what you should do is face toward the sunset, and take that many steps toward it. So if you had, say, “29” (which you seem to be writing as “+29”, kinda odd but not wrong, if it helps you keep track then go for it), then what you’d do is face toward the sun, and take 29 steps toward it.
When you have negative numbers, what you should do is face *away* from the sunset, and take the given number of steps in that direction. (Or, you can think of it like walking backwards, you’ll get to the same place either way.) So if you had “-59”, you turn away from the sunset and take 59 steps.
Addition would be like doing this for several numbers in sequence. So if you had “29 + 59”, you’d face toward the sunset, take 29 steps, then immediately take 59 more steps. If you then asked yourself, “how many steps away am I from that starting line?” you’d have your answer. 29 + 59 would be 88 steps in total. If you turned around and walked 88 steps, you’d get back to the starting line.
Subtraction is weird. It’s kind of a roundabout way to say, “add, but do the opposite of the thing after this”. So, “+59 – +29”, for example, is actually the same as “+59 + -29”. You can convert the subtraction to addition and flip the sign of whatever came after it. After you do this, we’re left with only addition. That’s something we already know how to handle. We can now do the same procedure: walk 59 steps toward the sunset, then turn around and walk 29 steps away from the sunset. How many steps are we away from the starting line? 59 – 29 = 30 steps away.
So, now the thing you asked about. Subtraction but when the second number is “bigger”. Say, for something like “+29 – +59”. We can do what we did last time, and convert that subtraction into addition: “+29 + -59”. Now, we walk. Face to the sunset, walk 29 steps. Then, turn around, and walk 59 steps. How far away from the starting line are we now? Well, if you walk 29 steps away, then turn around, and walk 59 steps, you’ll actually come back to the starting line on your 29th return step. But you still have 30 steps to go, right? You keep walking those 30 extra steps. But this time you’re behind the line instead of in front of it. So, in a sense, you’re still “30 steps away” from the starting line, but the fact that you’re *behind* the line this time is special. That’s actually what it means to get a negative answer: you returned to the 0 mark and went past it in the direction opposite the way you usually go. Or, looking at it another way, it would take that many steps in your normal direction just to get back to the 0 mark. So 29 – 59 = -30. If you faced toward the sunset again, walked 30 steps, you’d get back to the starting line.
For addition, the order of the numbers doesn’t matter. (+29) + (+59) is the same as (+59) + (+29). The sign of the larger integer will carry through. But for subtraction, the order is important. This is because the – changes the sign of the second number only.
It may help you to think of subtraction problems as addition problems where the sign of the second number is the opposite of what it was in the original problem. So in the case of (+29) – (+59), change the problem to (+29) + (-59). Then the rule of the largest integer still works.
Look at it this way: + is what you have, – what you owe. Addition is adding to your pocket, substraction is paying, but a substraction is just an addition where one of the numbers is negative and the other is not, so you can write a substraction like an addition changing + by -. That’s it:
So, 29 + -59 = you have $29, you pay $59. Now you owe $30, cause you paid with more money than what you had. Like someone else’s money that you had in your pocket. So, 29 + -59= -30.
70 – +64 = 70 – 64 = 6. $6 *you still have*, cause you had 70 and paid $64.
70+ -80 + 100 = you had $70 then you paid $80 and collected $100 (or collected $100 and then paid $80, it doesn’t matter). That’s $170- $80 or -$10 +$100 = $90. Positive, so obviously *you still have* because you *collected more than what you paid*.
Think of all numbers as having a bracket around them that preserves their sign. So
1 + 1 is really (+1) + (+1)
1 – 1 is (+1) – (+1) or (+1) + (-1)
To remove the brackets, you find the product of the operands (multiplication) using the following rules
(+x+ = +)
(- x – = +)
(+ x – = -)
Now if they have a negative sign, -1 – 1, this is( -1) + ( -1) or (-1) – (+1) because the final value of the operand is the same
(+ x -) = (- x +) = –
So -1 + 1 is -1 + +1
1 – -1 is (+1) – (-1) = +1 + 1
>The rule thing i got from the internet says + – + = larger integer’s sign
Would be extremely interested to know what planet this specific piece of math knowledge came from lmao.
First, we don’t sign positive integers. It’s 56, not +56.
Second, do not differentiate between +/- being a sign (positive and negative), and +/- being an **operation** (addition/substraction). For all intents and purposes, **it is the exact same thing**.
Once you understand that, you being to understand why 56-38 can be read two ways: 58 minus 38, or, 58 added to minus 38.
56-38 = 56 + (-38). Yet we never write the latter.
So a long list of additions and subtractions would just look like -15+72+23-41-2+8. You will **never** see two signs one after the other.
If you’re adding a negative number: 5+(-8), you’re just subtracting: 5-8.
If you’re subtracting a positive number: 5-(+8), you’re just, once again, subtracting: 5-8.
Once you know that, the rest is trivial. Take -2+38-56. You can start from either side, so let’s do the latter:
38-56 is a negative number since 56 is larger than 38. Result is -18.
That leaves -2-18. That’s -20. Subtracting two negative numbers is the same as adding them. Just think of someone taking 2 apples away then 18 more. The total number of apples you’re missing is 20.
Imagine a tall building with infinite floors and infinite basements. You’ll be entering the building at the street level. For reference or as starting point, call it ‘0’ level or just ‘0’. All floors above ground level are designated as +1, +2, +3… or simply 1, 2, 3…. from ground up. Similarly, all basement floors which are below ground floor are designated as -1, -2, -3,… from ground down.
The sign + or – gives you a sense of direction from your starting point. If it is, say, +4 floors, it means you climb UP 4 floors from where you currently are. + is for climbing up. If it is, say, -2 floors, it means that you should climb DOWN 2 floors from where you currently are.
Please visualize first and then draw this building on a piece of paper. Start with simple examples.
– You’re on ground floor (0) and you climb up 7 floors. This is 0 +7 = 7. So you’ll end up on Floor #7.
– You’re on ground floor (0) and you climb down 3 floors. This is 0 – 3 = -3. So you’ll end up on Floor# -3 or 3rd basement.
– You’re on Floor #10 and you’re asked to climb down 4 floors. This is 10 – 4 = 6. You’ll end up on Floor #6.
– You’re on Floor #7. You’re asked to climb down 7 floors. This is 7 – 7 = 0. You’ll end on ground level or street level.
– Now if you’re on Floor #4 and are asked to climb down 6 floors. This is 4 – 6. Go back to your drawing and visualize this movement. You’ll land on Floor # -2 or 2nd basement. So, 4 – 6 = -2.
Do you see the pattern? When you’ve to subract large number from small number, do the reverse operation (6 – 4) and then change sign of the result (-2).
For all other iterations, visualize the building and floors again.
+, + = +
-, – = –
etc.
Hey OP, you need to realise is that the “negative sign” is different from the “subtraction operator”. They’re the same symbol, but they’re actually different things. A negative sign in front of a number means it’s a negative number. A subtraction operator between two numbers is telling you to subtract one number from the other. Both are denoted by the symbol – but you need to realise what you’re dealing with.
Think of it in terms of money. The sign in front of the number denotes whether it’s a credit or a debt.
If there’s a positive+ sign, its a credit (someone gives you money). +9 means a credit of 9.
If there’s a negative- sign, it’s a debt (you have to lose some money). -8 means a debt of 8.
So, you just need to think about the total amount of money you’ll get in these situations:
– Credit plus credit
– Credit subtract credit
– Debt plus debt
– Debt subtract debt
– Credit plus debt
– Credit subtract debt
– Debt plus credit
– Debt subtract credit.
Give it a go! Thinking in terms of money often helps adults understand more abstract mathematical concepts.
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