Understanding Rational numbers: Definition, Examples, and Operations

rational number

A rational number is a number that can be expressed as a ratio or fraction of two integers, where the denominator is not zero

A rational number is a number that can be expressed as a ratio or fraction of two integers, where the denominator is not zero. Rational numbers can be positive, negative, or zero. Examples of rational numbers include 1/2, -3/4, 0, 2, and -5.

Rational numbers can be represented as terminating decimals or repeating decimals. For example, the fraction 1/5 can be represented as the repeating decimal 0.2, while the fraction 1/3 can be represented as the repeating decimal 0.333…

Rational numbers can be added, subtracted, multiplied, and divided just like whole numbers. When rational numbers are added or subtracted, you need to have a common denominator. To find a common denominator, you multiply the denominators of the fractions together. For example, to add 1/2 and 1/3, you need to find a common denominator, which is 6. Then, convert each fraction to have the common denominator: 1/2 becomes 3/6 and 1/3 becomes 2/6. Add the numerators together: 3/6 + 2/6 = 5/6.

When multiplying or dividing rational numbers, you multiply or divide the numerators together and the denominators together. For example, to multiply 2/3 and 3/4, you multiply the numerators (2 * 3 = 6) and the denominators (3 * 4 = 12), resulting in the fraction 6/12. Simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (which is 6 in this case), yielding the simplified fraction 1/2.

It is important to note that not all real numbers are rational. Numbers like √2 (the square root of 2) and π (pi) are irrational numbers and cannot be expressed as a simple fraction.

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