![]() ![]() As such, we can begin our calculations as if both integers were positive, compute what the result would be in that case, and only then fix the sign accordingly. On the other hand, the result's value itself, be it positive or negative, doesn't care much about the signs. To be precise, the result's sign depends on those of the factors or of the dividend and divisor for multiplication and division, respectively. The only thing we have to keep in mind is the sign. In essence, the negative and positive number rules for multiplying integers and integer division are almost the same. The first one doesn't really happen here, but it'll come in handy in the next section. Furthermore, it's possible to reduce the two into one in such case according to the following rules: Observe how whenever we had two signs next to each other, we have to put the negative number in brackets. See a few examples of adding and subtracting integers below: To find a - b, move b positions from a:.To find a + b, move b positions from a:.Look for a on the negative and positive number line.Suppose that we have integers a and b, and let's explain how we can find a + b and a - b. When adding and subtracting integers, it's a good idea to keep the negative and positive number line from the above section in mind. Given a positive integer, we can also find the sum of digits in order to determine the divisibility of the number. The differences in negative and positive number rules are small, and we point them out in each section below. In particular, we can add, subtract, multiply, divide, raise to a power, take the root, calculate the logarithm, etc., using those numbers. This way, a number and its opposite are at the same distance from 0 but to the opposite sides (this distance is called the number's absolute value).Īrithmetic and algebraic properties apply to all the values on the negative and positive number line. ![]() ![]() On the other hand, if we go left, we meet the same numbers but with minuses: -1, then -2, -3, and so on. In other words, if we start at zero and go right, we'll visit 1, then 2, 3, and so on. Negative numbers are the mirror image of positive ones with the mirror put at 0. If you want it written correctly, it will look like this.ĭo you get the same answer if we write it this way?Ĭan you see how -5 is the same value as 0-5? We just placed some zeros in the empty spaces of the problem.In essence, the line tells us where one number lies with respect to the others: is it larger (to the right) or smaller (to the left) of something else? When they introduce us to mathematics, we count to ten on our fingers, so we know that, for example, 2 comes after 1 but before 3. Mathematicians like to keep things organized. No real math problem would ever be written like that, but it might be a final test question. With five minus signs in a row, you have a negative sign. Since there are ten minus signs in a row, you can switch it to a plus sign. An extra credit problem on a test might look like this. If you have an odd number of dashes, you keep a minus/negative sign. If you have an even number of dashes together, you change to a plus sign. The overall pattern is about odds and evens. Just remember that two dashes make a plus sign. Look at the way two dashes became a plus symbol. Do you see how there is a minus sign and a negative sign next to each other? In math, when you get two negative signs in a row, the value becomes positive, or, in our case, a plus sign. When you subtract a negative number you are actually doing this… 5 - (-2). ![]() What about subtracting negative numbers? Your next big step is to understand the idea of combining signs before numbers. You can already subtract a positive from a positive (4 - 2) and a positive from a negative (-2 – 4). We have one more type of number to subtract. Work these examples out on your own to see if you get the correct answers. The negative values had us moving to the left. See how we switched it over to an addition problem? You can see how we did it on the number line too. ![]()
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