Awesome Operations: Math Fundamentals

In This Chapter

* Reviewing the four arithmetic operations

* Manipulating fractions

* Using charts to convey and understand information

* Strategies to help you solve word problems

Math has basic operations that you need to know. These operations — addition, subtraction, multiplication, and division — make all the other math in this book possible.

The good news is that you most likely learned about basics (like counting) even before you entered school, and you learned about basic arithmetic operations in elementary school. So you've been at it for a long time.

In this chapter, I review counting and the fundamentals of the four basic arithmetic operations. Other important topics I cover here are fractions, percentages, charts and graphs, and word problems. But don't worry: None of these are mysterious.

Numbers You Can Count On

The most fundamental component of math is numbers. The first thing you do with numbers is count, and you probably started counting when you were very young. As soon as you could talk, your mother cajoled you to tell Aunt Lucy how old you were or to count from 1 to 5.

Counting was the first and most useful thing you did with math, and you still use it every day, whether you're buying oranges at the grocery store or checking the number of quarts of motor oil in a case.

TECHNICAL STUFF

Counting has been essential since people first walked the earth. In fact, the Ishango bone is a tally stick (a counting stick), and it's over 20,000 years old!

Several kinds of numbers exist. Over time, mathematicians have given them many names. The two most important kinds are whole numbers and fractions. To see a little bit about how these numbers work, use a number line, a simple display of numbers on a line (see Figure 1-1).

The numbers to the right of 0 are called natural numbers or counting numbers. Of course, they are the numbers you use to count. They're easy for anyone to work with because they represent how many of something someone has (for example, 6 apples or 3 oranges).

Over many centuries and in different cultures, people made up the number 0, which represents the lack of a quantity. The numbers to the left of 0 on the number line, negative numbers, are a harder concept to grasp. You recognize negative number in real life. For example, if your checking account is overdrawn, you have a negative balance. If someone owes you $3.00, you have "negative cash" in your pocket.

Here are the key points to know about the number line:

[check] All the numbers you see in Figure 1-1 are whole numbers, also called integers. An integer is a number with no fraction part. The word comes from Latin, and it means "untouched," so it's the whole deal.

[check] The numbers to the right of zero are positive integers. The numbers to the left of zero are negative integers.

TECHNICAL STUFF

Mathematicians (and I'm not making this up) have trouble with zero. The best they can do is attach it to the positive integers and label the group non-negative integers.

[check] The number line stretches to the left and right, to infinity and beyond (as Buzz Lightyear says).

[check] Decimals (such as 0.75) and regular fractions (such as 3/5) are only a part of a whole number. They all have a place somewhere on the number line. They fit in between the integers. For example 2.75 "fits" between 2 and 3 on the number line, because it's greater than 2 but less than 3.

Reviewing the Four Basic Operations

To do any sort of math, you need to know your math basics. The four basic operations — addition, subtraction, multiplication, and division — let you take care of all kinds of real life math. But what's also very important is that those same basic math operations allow you to handle fractions and percentages, which come up all the time in ordinary math tasks. Later (in Chapter 2), these operations form the basis for managing algebra equations and geometry.

The core operations are addition and subtraction. You very likely know what they are and how they work. Multiplication and division are "one step up" from addition and subtraction. The following sections give you a quick review of these four operations.

Addition

Addition is a math operation in which you combine two or more quantities to get (usually) a larger quantity. Addition was probably the first math you ever did.

You can add numbers (called the operands) in any order. This property (that is, the ability to perform the operation in any order) is called commutativity.

21 + 31 + 41 + 51 = 144

is equal to

51 + 41 + 31 + 21 = 144

No matter in what order you add the operands, the sum still equals 144.

Subtraction

Subtraction is a math operation in which you take away the value of one number from another, resulting in (usually) a smaller quantity.

In subtraction, the order of the operands is important. You can't rearrange the numbers and get the same answer. For example, 77 – 22 (which equals 55) is not the same as 22 – 77 (which equals -55).

Multiplication

Think of multiplication as repeated addition. For example, you likely know that 3 4 = 12, but you can also get there by adding 3 four times:

3 + 3 + 3 + 3 = 12

The technique also works for large numbers. For example, 123 × 7 = 738 is equivalent to this:

123 + 123 + 123 + 123 + 123 + 123 = 738

But who wants to do all that adding?

Here's the best advice for multiplication:

[check] For little numbers, know your multiplication table. It's easy, up to 10 x 10.

[check] For big numbers, use a calculator.

As with addition, you can multiply the numbers in a list in any order. The expression 3 × 4 is the same as the expression 4 × 3. Both equal 12.

Division

Division is essentially "multiple subtraction." In a simple problem such as 12 ÷ 4 = 3, you can get the result by subtracting 3 four times from the number 12.

12 ÷ 3 = 4 with no remainder

is equal to 12 – 3 – 3 – 3 – 3 = 0 (4 subtractions with no remainder)

REMEMBER

In division, the order of the operands is important. You can't rearrange them and end up with the same answer.

Finagling Fractions

Fractions take several forms, but in real life, the forms you deal with are common fractions and decimal fractions.

A common fraction has two parts. The numerator is the top number, and the denominator is the bottom number. You don't have to learn these words, however. Just think "top number" and "bottom number."

numerator/denominator

What do you do with fractions? Arithmetic operations and conversions, that's what.

TECHNICAL STUFF

A common fraction is sometimes called a simple fraction or a vulgar fraction. The vulgar fraction isn't really rude; vulgar is just another word for common (from the Latin vulgus, meaning "common people").

Getting familiar with types of fractions

Like the popular ice cream...