**Locating Rational Numbers On the Number Line**

Winebrenner, William Dunbar Vocational

567-5400

**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.

1. 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).

2. 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.

3. 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.

4 .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.

5. 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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