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Locating Rational Numbers On the Number Line Return to Mathematics Index Winebrenner, William Dunbar Vocational Objective: 1: The learner will use the name RATIONAL NUMBER when referring to locations on the number line. 2: The learner will write rational numbers as the ratio of two integers. 3: The learner will convert each rational number to a mixed number. 4: The learner will divide any given length into n equal parts. Apparatus Needed: Number line, straight edge, compass, pencil, paper. Recommended Strategy: Once the student is comfortable with the concept that integers, positive and negative, can be located on the number line, proceed to identifying all rational numbers as a ratio of two integers. If the rational number is an improper fraction, convert it into a mixed number. It will then become obvious between which two integers is this rational number. For fractional parts of the next integer, such as divisions of 5ths or 7ths, for example, the problem is how to divide the line segment into n equal parts. This lesson is about how to locate the rational number on the number line which is a fractional part of the next integer. Teach the student that to divide any given length into n equal parts write the fractional part in the form a/b where a and b are positive integers (a rational number). Change improper fractions to mixed numbers so that a/b = k+(m/n) where k is a positive number and the fraction m/n is converted to lowest terms. Divide the line segment between k and the k+1 position into n equal parts, which can always be done by straight edge and compass construction, by marking off n equal parts on a y-axis and marking off the length of the line segment on the x-axis. The two axis do not even have to be at right angles to each other. Connect the last nth position with a straight line to the end of the line segment on the x-axis and proceed to construct n similar triangles. You will see that the line segment is now divided into n equal parts. Physically place this divided line segment on k and k+1 of the number line and count off m divisions. This is the location of the a/b rational number. For negative rational numbers teach the same strategy and instruct the student that this rational number is on the left side of the zero number.
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Uspoređivanje racionalnih brojeva Zbrajanje i oduzimanje racionalnih brojeva Dijeljenje racionalnih brojeva Racionalni brojevi - uvod Racionalni brojevi su svi negativni razlomci, nula i pozitivni razlomci. Skup racionalnih brojeva označava se s Q. Svaki razlomak možemo zapisati u obliku , gdje je a cijeli broj, a b prirodni broj. Oblik razlomka je standardni oblik racionalnog broja. Za svaki racionalni broj r vrijedi: Racionalne brojeve možemo pridruživati točkama pravca. Racionalni brojevi su suprotni brojevi. Modul racionalnog broja (apsolutna vrijednost) je racionalni broj koji za brojnik ima modul brojnika, a za nazivnik modul nazivnika zadanog racionalnog broja. Primjer: Racionalni brojevi mogu se proširivati i skraćivat, a pri tom vrijedi: