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

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alt="Bullet"/> Adding larger numbers with and without carrying

       Subtracting larger numbers with and without borrowing

       Multiplying with one-digit and multiple-digit multipliers

       Knowing how to do long division step by step

      The operations of addition, subtraction, multiplication, and division are at the heart of arithmetic. I call them the Big Four operations.

      In this chapter, the focus is exclusively on these four operations. To begin, I discuss each of the Big Four operations in turn. Then, I show you how to add, subtract, multiply, and divide larger numbers.

      Even if this information isn’t new to you, make sure that you know it before moving on to the chapters that follow. In Chapter 4, I discuss negative numbers, which depend heavily on the operation of subtraction. And then in Chapter 5, you discover a variety of more advanced Big Four topics that I expand upon in later chapters of the book.

The Big Four Operations

      When most folks think of math, the first thing that comes to mind is four little (or not-so-little) words: addition, subtraction, multiplication, and division. I call these operations the Big Four all through the book.

In this chapter, I introduce you (or reintroduce you) to these little gems. Although I assume you’re already familiar with the Big Four, this chapter reviews these operations, taking you from what you may have missed to what you need to succeed as you move onward and upward in math.

      Adding things up: Addition

      Addition is the first operation you find out about, and it’s almost everybody’s favorite. It’s simple, friendly, and straightforward. No matter how much you worry about math, you’ve probably never lost a minute of sleep over addition. Addition is all about bringing things together, which is a positive goal. For example, suppose you and I are standing in line to buy tickets for a movie. I have $25 and you have only $5. I could lord it over you and make you feel crummy that I can go to the movies and you can’t. Or instead, you and I can join forces, adding together my $25 and your $5 to make $30. Now, not only can we both see the movie, but we may even be able to buy some popcorn, too.

      Addition uses only one sign — the plus sign (+): Your equation may read or but the plus sign always means the same thing.

       When you add two numbers together, those two numbers are called addends, and the result is called the sum. So in the first example, the addends are 2 and 3, and the sum is 5.

      Take it away: Subtraction

      Subtraction is usually the second operation you discover, and it’s not much harder than addition. Still, there’s something negative about subtraction — it’s all about who has more and who has less. Suppose you and I have been running on treadmills at the gym. I’m happy because I ran 3 miles, but then you start bragging that you ran 10 miles. You subtract and tell me that I should be very impressed that you ran 7 miles farther than I did. (But with an attitude like that, don’t be surprised if you come back from the showers to find your running shoes filled with liquid soap!)

      As with addition, subtraction has only one sign: the minus sign (−). You end up with equations such as .

       When you subtract one number from another, the result is called the difference. This term makes sense when you think about it: When you subtract, you find the difference between a higher number and a lower one.

      One of the first facts you probably heard about subtraction is that you can’t take away more than you start with. In that case, the second number can’t be larger than the first. And if the two numbers are the same, the result is always 0. For example, . Later, someone breaks the news that you can take away more than you have. When you do, though, you need to place a negative sign in front of the difference to show that you have a negative number, a number below 0:

       When subtracting a larger number from a smaller number, remember the words switch and negate: You switch the order of the two numbers and do the subtraction as you normally would, but at the end, you negate the result by attaching a negative sign. For example, to find 10 − 13, you switch the order of these two numbers, giving you 13 − 10, which equals 3; then you negate this result to get −3. That’s why 10 − 13 = −3.

       The negative sign does double duty, so don’t get confused. When you stick a negative sign between two numbers, it means the first number minus the second number. But when you attach it to the front of a number, it means that this number is a negative number.

      A sign of the times: Multiplication

      Multiplication is often described as a sort of shorthand for repeated addition. For example,

      Although multiplication isn’t as warm and fuzzy as addition, it’s a great timesaver. For example, suppose you coach a Little League baseball team, and you’ve just won a game against the toughest team in the league. As a reward, you promised to buy three hot dogs for each of the nine players on the team. To find out how many hot dogs you need, you can add 3 together 9 times. Or you can save time by multiplying 3 times 9, which gives you 27. Therefore, you need 27 hot dogs (plus a whole lot of mustard and sauerkraut).

       When you multiply two numbers, the two numbers that you’re multiplying are called factors, and the result is the product.

      When you’re first introduced to multiplication, you use the times sign (×). As you move onward and upward on your math journey, you need to be aware of the conventions I discuss in the following sections.

       The symbol · is sometimes used to replace the symbol ×. For example,

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