# Real Numbers

**REAL NUMBER LINE:**

Draw a straight line and mark a convenient point as zero,
0, then mark equally

spaced distances. Label these as integers → positive to the right and negative
to

the left. To indicate that there are more positive integers to the left and to
the right

we use the symbol “…” which is understood to mean “ and so on” in the pattern

set.

Numbers associated with points on the real number line are
called coordinates of

the points.

Real numbers include whole numbers, fractions, decimals,
and other numbers that

we will see in Section 1.8.

If a and b are real numbers then the expression a/b

is called a fraction. The top number a is called the
numerator and the bottom number b is

called the denominator. Division by zero is not allowed, so b ≠ 0 or the result
is undefined.

Equivalent Fractions: If the numerator and denominator are
multiplied by a common factor ,n,

the resulting expression is an equivalent fraction that has the same numerical
value.

If the numerator and denominator contain a common factor
the expression can be reduced to an

equivalent fraction that has the same numerical value. Answers containing
fraction expressions

must always be left in the “simplest form”.

Equivalent Fractions

-> Fractions can also be written as decimals if they are
terminating or repeating.

In algebra we write fractions with a larger numerator than denominator in
improper form.

**Examples:**

Terminating:

Repeating

-> Fractions are sometimes integers when reduced to simplest form:

Examples :

**SPECIAL TERMS:**

English words | Math symbols . |

ABSOLUTE VALUE unsigned number | |

OPPOSITES equal value, opposite sign | |

RECIPROCALS numbers with product of 1 |

**ABSOLUTE VALUE: Examples:**

Perform inner operations first. | |

Do not drop absolute value symbols here | |

Replace absolute values with unsigned numbers and perform resulting operation. |

Perform inner operations first. | |

Do not drop absolute value symbols here. | |

Do not drop absolute value symbols here. | |

Do not drop absolute value symbols here. | |

Replace absolute values with unsigned number and perform resulting operation. |

**CAUTION: **Do not “drop” the absolute value “bars”
without performing all operations inside and

do not “drop” them without replacing the resulting number with an unsigned
number.

**Equivalent Fractions:**

If the numerator and denominator contain a common factor
the expression can be

reduced to an equivalent fraction that has the same numerical value. Answers

containing fraction expressions must always be left in the “simplest form”.

**Multiply fractions:** Multiply numerators times
numerators and denominators times

denominators.

Check the result to see if it will reduce to

[If numerators have common factors with denominators,
factor them out and reduce

before you multiply.]

**Example: Multiply fractions.**

Leave answer as improper fraction.

Raise (power) both the numerator and denominator.

**Geometry:**

A Square:

Perimeter = 4 s

Area = s^2

A Rectangle:

Perimeter = 2L + 2W

Area = L W

A Triangle

Perimeter = a + b + c