Algebra Know-It-ALL

{3^3 , 5, 7^2 }. That’s okay if you can remember that 3^3 does not literally mean 27 in this context, and 7^2 does not literally ...

46 Natural Numbers and Integers account, they have a claim to $49 of your money. If you think of it as your account, you’re $49 ...

natural numbers as being attached to a ray that stands straight up above the “number reflec- tor,” and their negatives as being ...

48 Natural Numbers and Integers to 2, down four units to −2, up five units to 3, down six units to −3, and so on. Keep hop- ping ...

If we remember the basic multiplication sign rules, we can see that − 100 =− 5 × 5 × 2 × 2 This same technique can be applied to ...

50 Natural Numbers and Integers Find out whether or not 901 is a prime number. Break down 1,081 into a product of primes. Break ...

Let’s take a close look at the processes, also called operations, known as addition and subtrac- tion. Much of this material wil ...

you have a numeral that represents a negative integer, you can get the numeral representing its absolute value by removing the m ...

What if we reverse the order of this sum? We start with 2 and travel upward −3 units. We’re talking about displacement here, not ...

54 Addition and Subtraction Boulevard to be displaced by −4 miles. This means the jam has been displaced to the east by 4 miles. ...

Identity, Grouping, and Signs Let’s review the mechanics of addition and subtraction, and make sure you understand how the signs ...

56 Addition and Subtraction Grouping with parentheses A couple of minutes ago, you saw some expressions containing parentheses a ...

not done so well. The group leader asks, “How much did you cut back? Go on, don’t be afraid to tell us.” You blush, clear your t ...

58 Addition and Subtraction but 5 − 3 = 2 In formal terms we would say that for any two integers a and b, it is not always true ...

Here’s a challenge! Suppose you have bought a new car and you want to go for a test drive. You live on a flat plain that seems t ...

60 Addition and Subtraction This works whether the numbers are positive, negative, or 0. It also works if there are four or more ...

Add, then subtract The associative law can work indirectly when subtraction is involved, if you change every sub- traction into ...

62 Addition and Subtraction We can use the associative law for addition to get a+ [(−b)+ (−c)] We can simplify this to a+ (−b−c) ...

Practice Exercises This is an open-book quiz. You may (and should) refer to the text as you solve these problems. Don’t hurry! Y ...

64 Addition and Subtraction compared to the same month in the previous year. You look at the records for January and find out th ...