10 Questions
¿Cuál es la propiedad que establece que el orden en que se suman o multiplican números racionales no cambia el resultado?
Asociativa
¿Cómo se suman dos números racionales?
Encontrando un denominador común y sumando los numeradores
¿Cuál es el nombre del tipo de número racional que tiene un parte entera y una parte fraccionaria?
Número mixto
¿Qué propiedad se aplica cuando se multiplican números racionales?
Asociativa
¿Qué es un número racional?
Un número que puede ser expresado como el cociente de dos números enteros
¿Cuál es la propiedad que establece que el orden de los números racionales no cambia el resultado de la suma y multiplicación?
Commutativa
¿Cómo se dividen dos números racionales?
Invertiendo el segundo número y multiplicándolos
¿Cuál es la propiedad que establece que la multiplicación de números racionales se distribuye sobre la suma?
Distributiva
¿Qué es un ratio equivalente?
Dos ratios que tienen el mismo valor
¿Cuál es el nombre del tipo de número racional que tiene el numerador mayor o igual que el denominador?
Fracción impropia
Study Notes
Definition
- A rational number is a number that can be expressed as the quotient or fraction of two integers, i.e., a/b, where a and b are integers and b ≠ 0.
Properties
- Closure: The set of rational numbers is closed under addition, subtraction, multiplication, and division (except for division by zero).
- Commutative Property: The order of rational numbers does not change the result of addition and multiplication.
- Associative Property: The order in which rational numbers are added or multiplied does not change the result.
- Distributive Property: Multiplication of rational numbers distributes over addition.
Operations
- Addition: To add two rational numbers, find a common denominator and add the numerators.
- Subtraction: To subtract two rational numbers, find a common denominator and subtract the numerators.
- Multiplication: To multiply two rational numbers, multiply the numerators and denominators separately.
- Division: To divide two rational numbers, invert the second number and multiply.
Types of Rational Numbers
- Proper Fractions: Rational numbers with the numerator less than the denominator.
- Improper Fractions: Rational numbers with the numerator greater than or equal to the denominator.
- Mixed Numbers: Rational numbers with a whole number part and a proper fraction part.
Equivalent Ratios
- Equivalent Ratios: Two or more ratios that have the same value.
- Simplifying Ratios: Finding the simplest form of a ratio by dividing both the numerator and denominator by their greatest common divisor.
Real-World Applications
- Measurement: Rational numbers are used to express measurements, such as lengths, areas, and volumes.
- Finance: Rational numbers are used to express financial ratios, such as profit margins and interest rates.
- Science: Rational numbers are used to express scientific measurements, such as ratios of chemicals and physical quantities.
Learn about the definition, properties, and operations of rational numbers, including addition, subtraction, multiplication, and division. Explore the different types of rational numbers and their real-world applications.
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