Exploring Rational Numbers: Definition, Examples, and Mathematical Operations

Rational numbers

Rational numbers are numbers that can be expressed as a ratio, or a fraction, of two integers

Rational numbers are numbers that can be expressed as a ratio, or a fraction, of two integers. In other words, a rational number can be written in the form p/q, where p and q are integers and q is not equal to zero.

Examples of rational numbers include:

1. 1/2: This is the fraction one-half, where the numerator (p) is 1 and the denominator (q) is 2.

2. -3/4: This is the fraction negative three-fourths. The numerator (p) is -3 and the denominator (q) is 4.

3. 2: This is also a rational number. Whole numbers can be written as fractions with a denominator of 1. So, 2 can be written as 2/1.

Rational numbers can be positive, negative, or zero. They can also be finite decimals, such as 0.25 (which is 1/4) or 3.5. Infinite decimals that repeat or terminate are also rational numbers. For example, 0.333… (with the threes repeating indefinitely) is a rational number because it can be expressed as 1/3.

Rational numbers can be operated on using the four basic mathematical operations: addition, subtraction, multiplication, and division. When adding or subtracting rational numbers, you need to find a common denominator in order to combine them. When multiplying or dividing rational numbers, you can simply multiply or divide the numerators and denominators.

It is important to note that not all numbers are rational. For example, the square root of 2 (√2) is a non-repeating, non-terminating decimal, and thus, it is an example of an irrational number.

Understanding rational numbers is essential in various areas of mathematics, such as fractions, decimals, and algebra. It is useful in practical applications, including measurements, money, and ratios.

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