Introduction to rational numbers quick check
Rational numbers are a type of number that can be expressed as a fraction, where the numerator and denominator are both integers. These numbers include whole numbers, integers, and decimals that terminate or repeat.
Rational numbers can be positive or negative, and they can also be zero. They can be written in fractional form, such as 3/4 or -5/6, or in decimal form, such as 0.75 or -0.8333 (repeating).
Rational numbers are called "rational" because they can be expressed as the ratio of two integers. The word "ratio" comes from the Latin word "rationalis," which means "having to do with reasoning." Rational numbers are often used in everyday life, such as when dividing a pizza evenly among friends or measuring ingredients in a recipe.
In mathematics, rational numbers are an important concept for understanding operations such as addition, subtraction, multiplication, and division. They form a number system that is more complete than the integers alone, as rational numbers can represent more values and quantities.
In summary, rational numbers are numbers that can be expressed as a fraction or decimal, where the numerator and denominator are both integers. They are used in various mathematical operations and have practical applications in everyday life.
To introduce rational numbers, we need to understand what they are and how they differ from other types of numbers.
1. Rational Numbers: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers, and the denominator is not zero. Rational numbers include integers (such as -3, 0, 5) and fractions (such as 2/3, -7/9, 1/2).
2. Terminating and Repeating Decimals: Every rational number can be represented as either a terminating decimal or a repeating decimal. For example, 3/4 is a rational number that can be written as the terminating decimal 0.75, and 2/3 is a rational number that can be written as the repeating decimal 0.666...
3. Examples of Rational Numbers: Some examples of rational numbers include -5, 1/2, -7/9, 0.75, and 0.666...
4. Operations with Rational Numbers: Rational numbers can be added, subtracted, multiplied, and divided, just like whole numbers. The resulting answer will always be another rational number. For example, if we add 1/4 and 3/8, we get 5/8. If we multiply 2/3 and 3/4, we get 1/2.
To summarize, rational numbers are numbers that can be expressed as a fraction or a decimal and include integers and fractions. They can be added, subtracted, multiplied, and divided. Every rational number can be written as either a terminating decimal or a repeating decimal.