Rational numbers on a number line

The integers p and q written in the form p/q when q>0 are known as rational numbers. Positive, negative, or even zero rational numbers exist. Rational numbers can be represented using the number line. Origin is the number line’s starting point (O). Positive rational numbers are shown on the right side of zero called origin, while negative rational numbers are shown on the left side of origin. The kind of fraction determines how rational numbers are represented on the number line.

The plotting or graphing of positive and negative rational numbers on a number line is known as rational number representation. By increasing the number of divisions, the number line can help us locate an unlimited number of rational numbers between two rational numbers.

Rational numbers on the number line 

Definition:  By simply following a few easy procedures, rational numbers can be represented on a number line. The type of rational fraction to be expressed on the number line affects the number line’s representation. But, before you go to the number line, double-check that the rational number has both a negative and a positive sign. The right side of the zero on the number line is always used to represent positive rational values. Negative rational numbers are always shown on the number line on the left side of zero, whereas positive rational numbers are always represented on the right side of zero.

Proper fractions and improper fractions are two forms of rational numbers.

• Proper fractions: Proper fractions are fractions in which the numerator is less than the denominator. These fractions are more than 0 but less than one.

• Improper fractions: Improper fractions are those in which the numerator is higher than the denominator. After they’ve been transformed to mixed fractions, they’re simple to plot.

To begin, draw a number line and divide it in half. We divide the distance between two successive portions into ‘n’ number of parts to represent rationals. In this example, the distance between 0 and 1, 1 and 2, and so on will be divided into three equal pieces.

Represent Rational Numbers on a Number Line

• On a number line, the representation of rational numbers is very similar to the representation of negative integers or negative fractions.

• On a number line, the left-hand side of ‘0’ represents the negative region, and the right-hand side of ‘0’ represents the positive zone, with ‘0’ as the reference. 

• To appropriately represent the numbers, mark the positive side of the number line, i.e. the right side.

• Set the origin 0 as the number line’s center.

• Create appropriate scales on the number line by dividing two integers into equal sections on both sides of the number line.

• We can’t adjust the scales or keep them in opposite orientations. Scaling should be similar on both sides.

• Mark the scale on the number line once you’ve entered the value to properly denote the point.

Example: On the number line, represent the rational number 6/7.

Solution: First plot rational numbers on a number line to represent- 6/7.

Then we will find the integers that are between – 6/7 and mark them on the number line.

– 6/7 is a number that falls between 0 and 1. We’ll now divide by 7 because the denominator of the supplied rational number is 7,

 Then make 6 moves to the left starting at 0 because the numerator is- 6. 

As a result, as illustrated above, the rational number 6/7 is plotted on the number line.

How do you find rational numbers on a number line

• On a number line, rational numbers are determined by locating the integers between which the rational number lies and then dividing by the denominator of the rational number.

• We shall move to the right or left of 0 on the number line equivalent to the numerator of the rational number, depending on the sign of the rational number. 

• To plot 2/3 on the number line, for example, make three divisions between 0 and 1, then move two steps to the right, retaining 0 as the reference.

Conclusion

We study, Rational numbers on a number line are similar to integers in that they represent positive and negative rational numbers on a number line. Locating rational numbers on a number line aids visual comprehension of arithmetic operations on rational numbers such as adding, subtracting, multiplying, and dividing. It also aids us in comprehending the concepts of comparing and arranging rational numbers.