# Rational Number Ideas and Symbols

6.1 Rational Number Ideas and Symbols | ||||

6.1.1. Rational Number Uses and Models | ||||

6.1.1.1. Models for rational numbers | ||||

6.1.1.1.1. Used to describe a quantity between 0 and 1 | ||||

6.1.1.1.2. identify the whole representing the numeral 1 | ||||

6.1.1.1.3. separate the whole into equal parts | ||||

6.1.1.1.4. use an ordered pair of integers to describe the portion of the whole under consideration | ||||

6.1.1.2. Identifying the whole and separating it into equal parts | ||||

6.1.1.2.1. Egg carton fractions | ||||

6.1.1.2.1.1. | ||||

6.1.1.2.1.2. | ||||

6.1.1.2.2. Integer Rods | ||||

6.1.1.2.2.1. | ||||

6.1.1.2.2.2. | ||||

6.1.1.2.3. Make your own fraction kit | ||||

6.1.1.2.3.1. | ||||

6.1.1.2.4. | ||||

6.1.1.3. Using two integers to describe part of a whole | ||||

6.1.1.3.1. Need more language to describe part-whole relationship | ||||

6.1.1.3.2. number of pieces of interest vs. number of pieces found in the original whole | ||||

6.1.2. Defining Rational Numbers | ||||

6.1.2.1.
Definition of a rational number: A number is a rational number if and
only if it can be represented by a pair of integers, a/b, where b ≠ 0 and a/b represents the quotient |
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6.1.3. Using Fractions to Represent Rational Numbers | ||||

6.1.3.1. Fractions and Equivalent Fractions | ||||

6.1.3.1.1.
Definition of a fraction: A fraction is a symbol, a/b, where a and b are numbers and b ≠ 0. Here, a is the numerator of the fraction and b is the denominator of the fraction |
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6.1.3.1.2.
Proper fraction: when the numerator of the fraction is less than the denominator of the fraction and both the numerator and the denominator are integers |
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6.1.3.1.3.
Improper fraction: when the numerator of the fraction is greater than
the denominator of the fraction (fractions with non-integers in the numerator or denominators are also improper) |
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6.1.3.1.4.
Definition of equivalent fractions : Two fractions, a/b and c/d, are
equivalent fractions if and only if ad = bc |
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6.1.3.1.5. Paper folding model | ||||

6.1.3.2. Using fractions to represent rational numbers | ||||

6.1.3.2.1.
every rational number can be represented by an integer in the numerator
and the denominator |
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6.1.3.2.2.
sometimes rational numbers are represented by non-integers
in a ratio |
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6.1.3.3. The Fundamental Law of Fractions: Given a fraction a/b and a number c ≠ 0, | ||||

6.1.3.4. Fractions in simplest form | ||||

6.1.3.4.1.
Description of the simplest form of a fraction: a fraction representing
a rational number is in simplest form when the numerator and the denominator are both integers that are relatively prime and the denominator is greater than zero. |
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6.1.3.4.1.1. Finding equivalent fractions on the number line | ||||

6.1.3.4.1.2. Folding paper | ||||

6.1.3.4.1.3. Using a calculator | ||||

6.1.3.4.1.4. Using Integer rods | ||||

6.1.4. Using Decimals to Represent Rational Numbers | ||||

6.1.4.1. Decimals | ||||

6.1.4.1.1.
Description of a decimal: A decimal is a symbol that uses a base-ten
placevalue system with tenths and multiples of tenths to represent rational numbers |
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6.1.4.1.2.
decimal point divides the decimal portion of the number from the whole number portion of the number |
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6.1.4.1.3. Using base ten blocks to explore decimals – see p. 287-8 | ||||

6.1.4.2. Expanded notation | ||||

6.1.4.2.1. | ||||

6.1.4.3. Writing a decimal for a fraction | ||||

6.1.4.3.1. - divide 3 by 4 to get the decimal equivalent | ||||

6.1.4.3.2. - use the Fundamental Law of Fractions | ||||

6.1.4.3.3.
terminating decimals – rational numbers that have a finite number of decimal places when written as decimals: |
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6.1.4.3.4.
repeating decimals – rational numbers that have an infinite number of decimal places filled by the same number or a fixed number of digits repeated over an infinite number of decimal places: |
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6.1.4.3.4.1. | ||||

6.1.4.3.4.2. | ||||

6.1.4.3.4.3.
Generalization about decimals for rational numbers: Every rational number can be expressed as a terminating or a repeating decimal |
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6.1.5. Problems and Exercises p. 311 | ||||

6.1.5.1. Home work: 1-3, 7, 8ac, 9abc, 10c, 11, 12, 14, 19, 20, 22 |