Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online). Mark Zegarelli

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Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online) - Mark  Zegarelli


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math

      3 Use inverse operations and the commutative property to find all three alternative forms for each equation:

      (a) math

      (b) math

      (c) math

      (d) math

      4 Fill in the blanks in each question:

      (a) math

      (b) math

      (c) math

      (d) math

      (e) math

      (f) math

      Remember Parentheses allow you to group operations together, telling you to do any operations inside a set of parentheses before you do operations outside of it. Parentheses can make a big difference in the result you get when solving a problem, especially in a problem with mixed operations. In two important cases, however, moving parentheses doesn’t change the answer to a problem:

       The associative property of addition says that when every operation is addition, you can group numbers however you like and choose which pair of numbers to add first; you can move parentheses without changing the answer.

       The associative property of multiplication says you can choose which pair of numbers to multiply first, so when every operation is multiplication, you can move parentheses without changing the answer.

      In contrast, subtraction and division are non-associative operations. This means that grouping them in different ways changes the result.

      Warning Don’t confuse the commutative property with the associative property. The commutative property tells you that it’s okay to switch two numbers that you’re adding or multiplying. The associative property tells you that it’s okay to regroup three (or more) numbers using parentheses.

      Tip Taken together, the associative property and the commutative property (which I discuss in the preceding section) allow you to completely rearrange all the numbers in any problem that’s either all addition or all multiplication.

      ExampleQ. What’s math What’s math

      A. 5 and 19. To calculate math, first do the operation inside the parentheses — that is, math:

math

      Now finish the problem by dividing math

      To solve math, first do the operation inside the parentheses — that is, math:

math

      Finish up by subtracting math. Notice that the placement of the parentheses changes the answer.

      Q. Solve math.

      A. 12 and 12. To solve math, first do the operation inside the parentheses — that is, math:

math

      Finish up by adding math.

      To solve math, first do the operation inside the parentheses — that is, math:

math

      Finish up by adding math. Notice that the only difference between the two problems is the placement of the parentheses, but because both operations are addition, moving the parentheses doesn’t change the answer.

      Q. Solve math

      A. 24 and 24. To solve math first do the operation inside the parentheses — that is, math

math

      Finish by multiplying math

      To solve math first do the operation inside the parentheses — that is, math

math

      Finish


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