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Contemporary's GED Mathematics

Whole Numbers

# Chapter Outline

#### Whole Numbers

(See page 17)

Whole numbers are written with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

#### Number Values and Facts

(See pages 17–20)

Place value means that the position of each digit in a number determines its value:

• billions
• hundred millions
• ten millions
• millions
• hundred thousands
• ten thousands
• thousands
• hundreds
• tens
• units or ones

The building blocks of mathematics are the arithmetic facts:

• multiplication facts (for multiplying and dividing)

There are many different types of whole numbers:

• odd number—not evenly divisible by 2
• even number—evenly divisible by 2
• consecutive numbers—follow one after the other
• prime number—evenly divisible by only itself and 1
• factor—divides evenly into another number

#### The Basic Operations

(See pages 20–24)

The four basic arithmetic operations are addition, subtraction, multiplication, and division.

• The answer to an addition problem is called the sum or total.
• The answer to a subtraction problem is called the difference.
• The answer to a multiplication problem is called the product.
• The answer to a division problem is called the quotient.

#### GED Test-Taking Shortcuts

(See pages 24–29)

A round whole number ends with a zero. To round a whole number, follow these steps:

• Underline the digit in the place to which you are rounding.
• If the digit to the right of the underlined digit is greater than or equal to 5, add 1 to the underlined digit.
• If the digit to the right of the underlined digit is less than 5, leave the underlined digit as it is.
• Change the digits to the right of the underlined digit to zeros.

Estimating means finding an approximate answer.

• Front-end estimation means rounding each number in a problem to the left-most place.

The Casio ƒx-260 solar calculator can be used for Part I of the GED Mathematics Test.

#### Special Topics with Whole Numbers

(See pages 30–38)

A mean, or average, is a number that represents a set of numbers. To find the mean of a set of numbers, follow these steps:

• Add the numbers in the set.
• Divide by the number of numbers in the set.

A median is a number in the middle of a group of numbers. To find a median, follow these steps:

• Arrange the numbers in order from smallest to largest.
• The number in the middle is the median.

When two numbers are in the middle of a group, the median is the mean, or average, of these two numbers.

The mathematical expression 52 means "5 to the second power."

• The 5 is called the base.
• The 2 is called the exponent.
• The exponent tells how many times to write the base in a multiplication problem.

To find a power, follow these steps:

• Write the base as many times as the exponent indicates.
• Multiply the base by itself.
• On a Casio ƒx-260 calculator, use the x2 key.

The opposite of raising a number to the second power is finding the square root of a number. The symbol ÷ means "square root."

• To find the square root of a number, ask yourself, "What number multiplied by itself equals this number?"
• To find a square root on a Casio ƒx-260 calculator, use the √ key.

A number sequence, or number series, is a list of numbers in a special order.

• To find the missing number in a number sequence, find the pattern that changes the numbers from left to right.

#### Properties of Numbers

(See pages 39–43)

Properties of numbers describe the ways arithmetic operations can be performed:

• The commutative property for addition is a + b = b + a.
• The commutative property for multiplication is a × b = b × a.
• The associative property for addition is (a + b) + c = a + (b + c).
• The associative property for multiplication is (a × b) × c = a × (b × c).
• The distributive property for addition is a(b + c) = ab + ac.
• The distributive property for subtraction is a(b - c) = ab - ac.

#### Order of Operations

(See pages 43–45)

When a math problem requires more than one operation, use the correct order of operations:

• Do operations in grouping symbols.
• Do powers from left to right.
• Do multiplication from left to right.
• Do addition and subtraction from left to right.

#### Using a Number Grid

(See pages 45 and 46)

A number grid is an alternate format for marking answers on the GED test. Each grid has five blanks above a column of numbers and symbols. To mark an answer on a number grid, follow these steps:

• Write the answer in the blank boxes at the top of each column.
• Below each column fill in one circle that corresponds to the digit you wrote at the top.