Rational numbers on a number line
Choose a numerator p and a denominator q, positive or negative, and see where p/q sits on the number line: split each unit into q equal parts and count p of them. Find its decimal, the integers it lies between, and fractions equal to it.
Core concept
A rational number is p/q with q ≠ 0; to place it, cut each unit into q equal parts and count p parts from 0, to the right if p/q is positive and to the left if it is negative; equivalent fractions such as 1/2 and 2/4 share one point
Topic: Rational numbers
A rational number can be written as p/q, where p and q are integer: A whole number that can be positive, negative or zero, like −3, 0 or 7. All key words and q is not 0. 3/4, −7/3 and 5 (which is 5/1) are all rational. Every rational number has its own point on the number line. To find it, cut each unit into q equal parts. Then count p parts from 0: to the right if p/q is positive, to the left if it is negative. So 3/4 is three quarter-steps right of 0, and −7/3 is seven third-steps left: past −2 but not yet −3. Dividing p by q gives its decimal: A number with a point, like 2.5, where the digits after the point are tenths, hundredths … All key words, 3/4 = 0.75. fraction: A part of a whole, written like ¾: the bottom number says how many equal parts, the top how many you take. All key words such as 1/2 and 2/4 are equivalent: they land on the same point.
What you will learn
- Place positive and negative rational numbers on a number line.
- Write a rational number as a decimal.
- Find the two integers a rational number lies between.
- Recognise equivalent rational numbers.
Before you start
- Know integers on a number line and what a fraction means.
Materials
- A strip of paper, a ruler and a pencil to draw a number line
Equipment
- None
Procedure
- Record 3/4.
- Change it to −7/3 and record.
- Record 1/2, then 2/4.
How this simulation is simplified
- The number line runs from −5 to 5; q is always positive and the sign is carried by p.