Section 6.1 The Basic Concepts of Fractions and Rational Numbers MTH 231 Section 6.1 The Basic Concepts of Fractions and Rational Numbers

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Applications of Fractions Measurement

Applications of Fractions Music

Applications of Fractions 3. Ratio and Proportion

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Important Interpretations of the Fraction a/b: Agree on the unit (describe, in words, how something is being measured or what one of something is) Understand that the unit is subdivided into b parts of equal size. Understand that we are considering a of those parts of the unit.

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Colored Regions

Number Lines

Strips

Sets

Equivalent Fractions

Fractions in Simplest Form A fraction is in simplest form when the numerator and denominator have no common divisor larger than 1. To reduce a fraction to simplest form (or lowest terms), divide both the numerator and the denominator by the greatest common divisor. Divisibility rules can play an important role in reducing fractions. Two fractions are equivalent if, when reduced to simplest form, they are equal.

Examples

Least Common Denominators As we shall see in a later section, a (least) common denominator is required to add and subtract fractions. Least common denominator = least common multiple.

Examples

Comparing and Ordering Fractions If two fractions have the same denominator, the larger fraction will have a larger numerator. If two fractions have the same numerator, the larger fraction will have a small denominator.

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