![]() To add numbers whose signs are different, subtract the numerically smaller from. Since a whole number exponent larger than 1 tells us the number of times to multiply the base by itself, it also tells us whether or not we will have a positive or negative result. Addition of numbers with different signs. ![]() When we get an odd number (1,3,5,7,9.) of negative factors the opposite is true and we will get a negative product. Therefore an even (2,4,6,8,10.) number of negative factors produces a positive product. Recall that when multiplying with negative numbers, each pair of negatives yields a positive product. Keeping Track of the Signs Adding a positive number is addition, (e.g., 4 + (+2) 4 + 2 6 Subtracting a negative number is addition, (e.g., 4 - (-2) 4 + 2. When a positive number and a negative number are. The reason here is that our exponent (3) is odd. Every negative number can be thought of as having some positive factors and exactly one negative factor, -1. If we work through the example above, we see that we get the same answer whether or not we use parentheses around the base. Since the negative is wrapped inside of the parentheses, both are now part of the base. The absolute value of a number is the number itself if it is positive and its opposite if. Now let’s think about the other scenario. Rules are often stated using the concept of absolute value. Summary: Adding two positive integers always yields a positive sum adding two negative integers. In this case, we would raise 2 to the 2nd power first, and then multiply the result by -1. Rule: The sum of any integer and its opposite is equal to zero. From the order of operations, we know that we must perform exponent operations before we multiply. We can really think about: -2 2 as -1 x 2 2. It won’t give us a different answer in every scenario, but it’s important to know what’s causing a different answer. A positive number is written with a plus sign in front of the number, or the plus sign may be omitted a negative number is written always with a minus sign in. We can see from the above example that parentheses around a negative base do make a difference. If we are working with a negative number raised to a power, the base does not include the negative part unless we use parentheses: When we work with exponents, we need to be extra cautious when dealing with negative numbers.
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