A rational number is a real number that can be expressed as a fraction p/qâ€‹, where q is not zero. Examples include 1/2â€‹, 1/5â€‹, and 3/4â€‹. The number “0” is also a rational number because it can be written as 0/1â€‹, 0/2â€‹, etc. However, fractions like 1/0â€‹ are not rational since they are undefined.

**What is a Rational Number?**

In math, a rational number is any number that can be written as p/qâ€‹, where qâ‰ 0q. Both the numerator p and the denominator q are integers. When you divide the fraction, the result will be a decimal that either terminates or repeats.

**Identifying Rational Numbers**

To determine if a number is rational, check if it:

- Can be written as p/q, with qâ‰ 0.
- Can be simplified to a decimal form.

**Examples of Rational Numbers**

p | q | qp/q |

10 | 2 | 10/2 = 5 |

1 | 1000 | 1/1000 = 0.001 |

50 | 10 | 50/10 = 5 |

**Types of Rational Numbers**

Rational numbers include positive, negative numbers, and zero. They can all be written as fractions.

- Real numbers (R) include all the rational numbers (Q).
- Real numbers include the integers (Z).
- Integers involve natural numbers(N).
- Every whole number is a rational number because every whole number can be expressed as a fraction.

**Standard Form of Rational Numbers**

A rational number is in standard form when the numerator and denominator have no common factors other than 1, and the denominator is positive. For example, 12/36â€‹ simplifies to 1/3.

**Positive and Negative Rational Numbers**

Rational numbers can be positive or negative. If both numerator and denominator are positive, the number is positive. If one is negative, the number is negative.

Positive Rational Numbers | Negative Rational Numbers |

Same sign for numerator and denominator | Opposite signs for numerator and denominator |

Greater than 0 | Less than 0 |

Examples: 12/17, 9/11, 3/5 | Examples: -2/17, 9/-11, -1/5â€‹ |

**Arithmetic Operations on Rational Numbers**

**Addition**:- Example:

**Subtraction**:- Example:

**Multiplication**:- Example:

**Division**:- Example:

**Multiplicative Inverse of Rational Numbers**

The multiplicative inverse of p/q is q/pâ€‹. For example, the inverse of 4/7â€‹ is 7/4â€‹.

**Properties of Rational Numbers**

- Adding, subtracting, or multiplying two rational numbers always gives a rational number.
- A rational number stays the same if both numerator and denominator are multiplied or divided by the same factor.
- Adding zero to a rational number keeps it the same.
- Rational numbers are closed under addition, subtraction, and multiplication.

**Rational vs. Irrational Numbers**

A rational number can be written as a fraction with a non-zero denominator. An irrational number cannot be expressed as a simple fraction and has an endless, non-repeating decimal. Examples of irrational numbers include:

- Pi (Ï€) = 3.142857…
- Eulerâ€™s Number (e) = 2.7182818284590452…
- âˆš2 =1.414213…

**Finding Rational Numbers Between Two Rational Numbers**

There are infinite rational numbers between any two rational numbers. You can find them by:

**Finding Equivalent Fractions**: For example, between 1/2â€‹ and 3/4â€‹, you can use 2/4 and 3/4â€‹ to identify numbers in between.**Finding the Mean**: The mean value between two rational numbers is also a rational number. Repeat this process to find more rational numbers between them.

**FAQs**

Rational numbers can be expressed as fractions with non-zero denominators, while irrational numbers cannot be written as simple fractions and have endless, non-repeating decimals.

Rational numbers can be positive or negative. Positive if both numerator and denominator have the same sign, negative if they have opposite signs.

A number is rational if it can be written as p/qâ€‹ with qâ‰ 0 and can be simplified to a decimal form.

Yes, zero is a rational number because it can be expressed as 0/1.

A rational number is a number that can be expressed as a fraction p/qâ€‹, where q is not zero.

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