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Contemporary's GED Mathematics
Jerry Howett

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:

  • addition facts (for adding and subtracting)
  • 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.