Sets of Rational Numbers

Set

A collection of "things" (objects or numbers, etc). Each member is called an element of the set. There should be only one of each member (all members are unique). Example: {1,2,3,4} is the set of counting numbers less than 5. [Note: Each number is listed once. Sets in math do not have any duplicates (extra copies).]

Element

A member of a set (like a member of a family). For example, here's a SET of my family: {me, my husband, Mom, Sister Pat, Brother Jerry, Stanley the Cat}. My Sister Pat is an ELEMENT of the SET of my family. Math example: The number 2 is an ELEMENT of the SET {1,2,3}

Whole Numbers

All the Counting Numbers plus Zero

Integers

All the Whole Numbers with their opposites {-1, -2, -3, ...} and Zero

-12 is an element of which set(s)?

Integer and Rational Numbers

Name this set: {....-3,-2,-1,0,1,2,3...}

Integers

The natural numbers and their opposites plus zero

Integers

Mixed Numbers, such as 3½ or -2¼, are elements of which set(s)?

Mixed Numbers are elements of the Rational Numbers set. This statement is true because every Mixed Number can be written as an Improper Fraction. Fractions are elements of the Rational Numbers.

Name this set: {1,2,3,.....}

Natural Numbers (also called Counting Numbers)

The number 5 is an element of which set(s)?

Natural, Whole, Integer, and Rational Numbers sets

Rational Numbers

Numbers that can be written as a fraction

5/6 is an element of which set(s)?

Rational Numbers

Numbers that can be written as a fraction are part of the set of __________________ .

Rational Numbers The word Rational has the word RATIO within it. A Ratio compares one number to another. A Fraction is a type of RATIO. A Fraction often compares a "part" to a "whole." The part is the numerator and the "whole" is the denominator.

1.333... is an element of which set(s)?

Rational Numbers. Terminating and repeating decimals can be written as fractions of RATIOs (RATIOnal Numbers). 1.333... can also be written as 4/3. Note: A bar drawn above the repeating numbers or "..." are two ways used to show the repeating pattern of digits.

0.7625 is an element of which set(s)?

Rational Numbers. Terminating and repeating decimals can be written as fractions or RATIOs (Rational Numbers). 0.7625 is a terminating decimal.

Numbers like 1/2, .6, .3333... belong to the set of ______ numbers

Rational Numbers: Integers, fractions, and most decimal numbers

What does the VENN Diagram of the SETS of Rational Numbers look like?

The VENN diagram shows the different types of numbers as SUBSETS of the Rational Numbers set. All elements (every member) of the Natural Numbers subset are also Whole Numbers. All elements of the Whole Numbers subset (including the Natural Numbers subset) are part of the Integers set. All elements of the Integers subset (including the Natural Numbers and Whole Numbers subsets) are part of the Rational Numbers set.

Can a Fraction also be a Whole Number or an Integer?

This is not always true, but can be true sometimes. Some Improper Fractions can be reduced (or "simplified") to Whole Numbers or Integers (when negative, -40/10).

Name this set: The natural numbers plus 0

Whole Numbers

Name this set: {0,1,2,3...}

Whole Numbers

Zero is an element of which set(s)?

Whole, Integer, and Rational Numbers

Natural Numbers or Counting Numbers

{1,2,3,.....} The numbers you learned in kindergarten when you started to count