Adding and Subtracting integers
Imagine a city. Everyone in the city wears a special bracelet. This bracelet gives points. If you do something good, you get +1 point. If you do something bad, you lose 1 point meaning -1 point.
For example, if you help someone, you get +1 point. But if you make a mess in a library or are rude, you lose 1 point meaning you get -1 point.
Every month, there is a "Check Day". On this day, everyone's points are checked. People with positive points can go to special events in the city. People with negative points can't use some city places, like parks or libraries, for a while.
This system helps people in the city to be kind and good to each other. But some people try to cheat the system. The city checks the bracelets often to make sure they work right.
Good Point, Bad Point ?
Actually, you shouldn't condition yourself to think in terms of "are we adding or subtracting?" Instead, you should set aside the basic knowledge you learned in elementary school and see it purely as a "good point - bad point" calculation.
One negative point cancels out one positive point.
A number always comes with its sign, and the sign is in front of the number.
3-2
Everyone knows this, right? If we subtract 2 from 3, we get 1. However, I want you to forget what you've learned before and focus solely on positive points and negative points. Don't worry about whether subtraction or addition was done; just think about positive points and negative points.
If there's no sign in front of a number, it means the number is positive. Remember, the sign is in front of the number. In this example, there are 3 positive points and 2 negative points.
One negative point neutralizes, or cancels out, one positive point, and I am left with one positive point. We can say the result is +1.
Example : 4+2
I have 4 positive points, and then I gain 2 more positive points. As a result, I have 6 positive points.
4+2 = 6
Example: -3-5
-3-5=-8
Our result is -8.
Example:
-6+5=
I have 6 negative behavior points, and then I gained 5 positive behavior points.
One positive point cancels out one negative point, leaving me with -1 point.
Addition and subtraction involving parentheses
In some cases, operations are in parentheses. We should try to eliminate the parentheses. To do this, the sign in front of the parenthesis is multiplied with each number inside the parenthesis (of course, along with its sign). In other words, it's distributed.
The product of the same signs is positive (like when one is + and the other is also +, or one is - and the other is also -), whereas the product of different signs (when one is positive and the other is negative) is negative.
Example : 2+(+5)= ?
I don't have any operations until I reach the parentheses, so I continue by writing it down as is.
2...
We distributed the sign in front of the parentheses to the inside, meaning we multiplied (+ multiplied by + results in +). This way, we get rid of the parentheses.
Now that we've gotten rid of the parentheses, we can proceed based on the good point bad point calculation.
2+4 = 6
Example : -3 + ( - 5 ) = ?
I have no operations to do with -3, just write it down and move on.
When I get to the front of the parenthesis, I see a '+' sign; the term in front of the parenthesis is in multiplication with what's inside the parenthesis. So, let me distribute the sign in front of the parenthesis into what's inside, in other words, multiply it.
The product of + and - is -, so we've found the sign of our number. It became the sign of -5.
Now that we've gotten rid of the parentheses, we can proceed based on the good point bad point calculation.
-3-5=-8
Example : -6 - ( - 3 ) = ?
Example : 5 - ( 6 + 8 )
The term outside the parenthesis is distributed by multiplying with the term inside the parenthesis.
Let's start the operations;
Step 1:
Step 2:
I need to distribute the term in front of the parenthesis to each term inside the parenthesis individually.
Step 3:
The result is ;
Example : 8 - ( - 3 + 7 )
There's no operation to be done with 8, so I wrote it as it is.
Step 2:
Step 3:
Similarly, I'm doing the same thing to the second term.
We've eliminated the parentheses by distributing the term in front of it throughout the inside. Now, we need to calculate the good and bad scores.
Result is 4 .
Example:
Let's analyze the given example.
Let's start the calculations.
There's no operation to be done with 6, so I wrote it as it is.
I'm distributing the term in front of the parenthesis to my first term inside the parenthesis.
Step 2:
It is essential to determine what is in front of the parentheses;
-3 ( 4+5) and 3- (4+5) will give same result ?
lets look at other example ;
The number is taken with its sign, so in this example, it's not 3 in front of the parentheses but -3. Therefore, -3 will be distributed inside the parentheses.
Therefore, they are not the same things.
Example:
If I subtract 2 from 5, what will be the result? If I subtract -2 from 5, what will be the result? Do these two mean the same thing?
5-2=3
It means subtracting 2 from 5.
5-(-2)= 5+2=7
It means subtracting -2 from 5.
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