Understanding Rational Numbers: Definition, Representations, and Operations

Rational number

A rational number is a number that can be expressed as a fraction, where both the numerator and the denominator are integers

A rational number is a number that can be expressed as a fraction, where both the numerator and the denominator are integers. In other words, a rational number can be written in the form a/b, where a and b are integers and b is not equal to zero.

Rational numbers can be positive, negative, or zero. Examples of rational numbers include 1/2, -3/4, 5, and 0.

Rational numbers can be easily represented on the number line. For example, the fraction 1/2 represents the point exactly halfway between zero and one on the number line. Similarly, -3/4 represents the point three-quarters of the way left from zero.

Rational numbers can be added, subtracted, multiplied, and divided just like whole numbers. When adding or subtracting rational numbers, you need to find a common denominator and then perform the operation. When multiplying rational numbers, multiply the numerators together and the denominators together. When dividing rational numbers, multiply the first number by the reciprocal of the second number.

It is important to note that some rational numbers have repeating or terminating decimal representations. For example, 1/3 is equal to 0.333…, where the threes repeat infinitely. On the other hand, some rational numbers have non-repeating, non-terminating decimal representations. For example, 1/7 is equal to 0.142857142857…, where the digits 142857 repeat indefinitely.

In summary, a rational number is a number that can be represented as a fraction a/b, where a and b are integers and b is not equal to zero. Rational numbers can be positive, negative, or zero, and they can be added, subtracted, multiplied, and divided. Some rational numbers have repeating or terminating decimal representations, while others have non-repeating, non-terminating decimal representations.

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