![]() ![]() Subtracting a positive number is subtraction, (e.g., 4 - (+2) = 4 - 2 = 6.Adding a negative number is subtraction, (e.g., 4 + (-2) = 4 - 2 = 2.Subtracting a negative number is addition, (e.g., 4 - (-2) = 4 + 2 = 6.Adding a positive number is addition, (e.g., 4 + (+2) = 4 + 2= 6.Here are the rules for adding or subtracting negative numbers: With negative numbers, this is often wrong. We learn our subtraction facts and become conditioned to that minus symbol immediately meaning to take the second number away from the right. Part of the challenge with adding and subtracting negative numbers is figuring out what to do with the signs. Working with a number line is another great strategy for visualizing how subtracting can create negative integers in a more abstract context. A good example is temperature, where values can fall below zero (This is especially good if Celcius temperatures are understood as zero has a very clear meaning there.) Another good choice would be altitude above or below sea level. Instead, introduce the concept of negative numbers using measurements that might convincingly have negative results. ![]() So in summary, because the we only allow the log’s base to be a positive number not equal to 1, that means the argument of the logarithm can only be a positive number.Worksheet 4 Tricks for Adding and Subtracting Negative NumbersĪdding and subtracting numbers can be confusing at first because the idea of a negative quantity of something can be a strange concept, even to a 6th grader. Then what we know is that, if the base of our power function is positive, it doesn’t matter what exponent we put on that base (it could be a positive number, a negative number, or 0), that power function is going to come out as a positive number. And if those numbers can’t reliably be the base of a power function, then they also can’t reliably be the base of a logarithm.įor that reason, we only allow positive numbers other than 1 as the base of the logarithm. So 0, 1, and every negative number presents a potential problem as the base of a power function. And as you know, unless we’re getting into imaginary numbers, we can’t deal with a negative number underneath a square root. If you raise a negative number to a positive number that’s not an integer, but instead a fraction or a decimal, you might end up with a negative number underneath a square root. In the same way, 1 raised to anything is always still 1. Or, put a different way, 0 raised to anything is always still 0. In other words, there’s no exponent you can put on 0 that won’t give you back a value of 0. When you have a power function with base 0, the result of that power function is always going to be 0. To understand why, we have to understand that logarithms are actually like exponents: the base of a logarithm is also the base of a power function. The reason has more to do with the base of the logarithm than with the argument of the logarithm. Negative numbers, and the number 0, aren’t acceptable arguments to plug into a logarithm, but why? In other words, the only numbers you can plug into a log function are positive numbers. The argument of a log function can only take positive arguments. While the value of a logarithm itself can be positive or negative, the base of the log function and the argument of the log function are a different story. ![]()
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