![]() ![]() As with multiplication, it doesn’t matter which order the positive and negative numbers are in, the answer is always a negative number. In those terms, the exponent (“E” in PEMDAS) comes before multiplication by -1 (“M” in PEMDAS) unless we make the multiplication by -1 come first by putting it in parentheses (“P” in PEMDAS). When you divide a negative number by a positive number, your answer is a negative number. This difference is explained by “order of operations,” which is covered in an upcoming chapter. We get a different result without parentheses, Order of OperationsĪs we saw above, parentheses are important when dealing with exponents of negative powers. When the exponent is odd, there’s always one of them left over, making the overall product negative. The -1’s cancel out to become positive 1’s in pairs. Taking a negative number to an odd power generates a negative number every time. ![]() In this case, writing the -3 in parentheses is required to communicate that we are squaring the negative number, not multiplying the squared number by -1. It is basically the same thing as multiplying and dividing normally. Taking a negative number to an even power generates a positive number. Today, we are going to learn how to multiply and divide by positive and negative integers. Multiplying a negative number by a negative number makes the answer positive. In this book, we will follow printed convention and often use the symbol, but you should make a habit of writing on your scratch paper (and ultimately your noteboard in the testing center) in this fashion: For example, 2-3 can be written as 1/2 3. ![]() In other words, we can convert a negative exponent to a positive one by writing the reciprocal of the given term and then we can solve it like a positive term. It’s a good idea to omit the multiplication symbol, because in a handwritten context, it is too easily confused with the variable x. Negative Exponents tell us how many times we need to multiply the reciprocal of the base. Also, writing parentheses allows you to convey multiplication without using the multiplication symbol. Doing so helps reduce preventable errors. It’s a good habit to write parentheses around negative numbers, as above. Multiplying a negative number by a positive number, or a positive number by a negative number, makes the answer negative. Subtracting a negative number is the same as adding a positive number. This is similar to the rule for adding and subtracting: two. Arithmetic with Negative Numbers Adding and SubtractingĪdding a negative number is the same as subtracting a positive number. When you multiply two negative numbers or two positive numbers then the product is always positive. ![]()
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