Class-8 || Rational Numbers || Introduction ||
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Positive and Negative Numbers:
Rational numbers include both positive and negative numbers. A positive rational number is greater than zero, while a negative rational number is less than zero. For example, 3/4 and 5/6 are positive rational numbers, whereas -2/3 and -7/8 are negative rational numbers.
Positive rational numbers are often associated with quantities that represent gains, increases, or values above a reference point. Negative rational numbers, on the other hand, represent losses, decreases, or values below a reference point.
Reciprocals:
The reciprocal of a rational number is obtained by interchanging its numerator and denominator. In other words, if we have a rational number "a/b" (where a and b are integers and b is not zero), its reciprocal is "b/a."
For example, the reciprocal of 2/5 is 5/2, and the reciprocal of -3/7 is -7/3. It's important to note that the reciprocal of a non-zero rational number will always have the opposite sign. If the original number is positive, its reciprocal will be positive, and if the original number is negative, its reciprocal will be negative.
Reciprocals are useful in various mathematical operations, such as dividing fractions or solving equations involving fractions.
Absolute Value:
The absolute value of a rational number represents its distance from zero on the number line, regardless of its sign. The absolute value is always non-negative (greater than or equal to zero).
For positive rational numbers, the absolute value is the same as the number itself. For example, the absolute value of 4/5 is 4/5. For negative rational numbers, the absolute value is obtained by removing the negative sign. For example, the absolute value of -2/3 is 2/3.
Mathematically, we can represent the absolute value of a rational number "a/b" as "|a/b|," where "|" denotes the absolute value symbol.
Absolute value is useful in various situations, such as comparing magnitudes, finding the distance between two numbers, or solving equations involving absolute values.
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