There are different types of numbers that are used in mathematics. One of these is the rational number which can be expressed as a ratio of two integers or fraction forms. The numerator can be positive, negative, or zero but the denominator of a rational number can never be zero. So if x and y are two integers such that y is not equal to zero, then the number x/y is a rational number. It can be said that any number that can be represented in fraction form is a rational number. Any integer is a rational number because it can be written in the form of a fraction. In this case, the integer is taken as the numerator with 1 as the denominator.
Some of the examples of rational numbers are 2/3, -8/21, 0.75, 5/14, 4, -7, 20, etc.
The integers 4, -7, 20 are rational numbers because they can be expressed as 3/1,-7/1, and 20/1 respectively. The decimal number 0.75 is a rational number because it can also be denoted as 3/4.
- A rational number is positive when both the numerators and denominators are positive or negative.
- A rational number becomes negative if one of the numerators or denominators is positive and the other is negative.
- The number 0 is also a rational number as per the definition. Zero can be represented in several fractional forms where the numerator is 0 but the denominator is an integer other than zero.
- The simplest form of a rational number is the fraction form where 1 is the only common factor of the numerator and denominator.
- The addition or subtraction of two rational numbers gives a rational number.
- Two rational numbers when multiplied give a rational number as the product.
- If both the numerator and denominator of a rational number are multiplied or divided by the same non-zero integer, the value remains unchanged.
A number line is nothing but a straight line marked with regular intervals in which the numbers can be placed in sequential order. The use of number lines in mathematics is a very useful concept that provides a visual representation of the position of numbers and helps in analyzing the relationship between numbers. On the number line, the middlemost point is for the value ‘0’. All the other numbers are placed on both sides of zero at specified intervals. All positive numbers are placed on the right side of zero with gradually increasing values from left toward the right. Again, all negative numbers are placed on the left side of zero in a way such that the values decrease as we move from right to left. It also ensures that if we move from left to right on the number line, at any position, a number has a greater value than the number on its left side and vice versa. We can use the number line to represent any type of number, such as whole numbers, integers, fractions, decimals, rational numbers, etc. Learn more about this topic on Cuemath.
The numbers can be plotted on a number line through the steps mentioned as follows:
- Draw a horizontal line.
- Mark zero value at the middle point
- Mark the line with regular intervals according to the scale chosen
- Plot the numbers on the number line following the rule of positive numbers on the right side of zero and negative numbers on the left side of zero.
By plotting the numbers on a number line, we can easily perform basic arithmetic calculations using the numbers. For example, if we need to add 5 and -3, first we start from -3 and move towards right up to five steps. The point we get gives the result which is 2.