Rational number
readlittle.com
Numbers written as a fraction
Rational number refers to any number that can be written as a fraction made of two integers, where the top number is the numerator and the bottom number is the denominator. The denominator cannot be zero, because division by zero is undefined. Rational numbers include many types of values used in everyday counting and measuring, such as whole numbers, negative numbers, and many decimals.
Rational numbers can appear in different forms. A simple form is a fraction, such as 1/2 or −3/4, which shows how many parts of a whole are being described. Rational numbers also include whole numbers like 5, because 5 can be written as 5/1. Many decimals are rational as well, especially if they stop (like 0.25) or repeat in a pattern (like 0.333...). These decimals can always be rewritten as fractions.
One way to understand rational numbers is to imagine dividing objects or quantities into equal parts. For example, if a pizza is divided into 8 equal slices and someone eats 3 of them, the amount eaten can be written as the fraction 3/8. This shows that rational numbers help describe parts of a whole and relationships between quantities. They are common in measurements in school, cooking, sports, and many other situations.
Rational numbers can be placed on a number line. They can appear between any two whole numbers, because you can always divide a space into smaller equal pieces. This means that between 1 and 2, there are many rational numbers such as 3/2, 5/4, or 7/6. Even between two rational numbers, there are infinitely many other rational numbers. This makes the rational number set very dense.
Rational numbers follow the same rules of addition, subtraction, multiplication, and division (except by zero) as other numbers. When adding or subtracting rational numbers, the denominators must match, and the numerators change based on the operation. When multiplying, numerators and denominators are multiplied across. Dividing rational numbers can be done by multiplying by the reciprocal, which is the flipped version of a fraction.
Rational numbers are different from irrational numbers, which cannot be written as a fraction of two integers. Irrational numbers include values like √2 or the number π. These decimals do not end or repeat. Together, rational and irrational numbers form the set of real numbers, which include all points on the number line. Understanding rational numbers helps build a foundation for learning about more advanced mathematical ideas.
Rational numbers can appear in different forms. A simple form is a fraction, such as 1/2 or −3/4, which shows how many parts of a whole are being described. Rational numbers also include whole numbers like 5, because 5 can be written as 5/1. Many decimals are rational as well, especially if they stop (like 0.25) or repeat in a pattern (like 0.333...). These decimals can always be rewritten as fractions.
One way to understand rational numbers is to imagine dividing objects or quantities into equal parts. For example, if a pizza is divided into 8 equal slices and someone eats 3 of them, the amount eaten can be written as the fraction 3/8. This shows that rational numbers help describe parts of a whole and relationships between quantities. They are common in measurements in school, cooking, sports, and many other situations.
Rational numbers can be placed on a number line. They can appear between any two whole numbers, because you can always divide a space into smaller equal pieces. This means that between 1 and 2, there are many rational numbers such as 3/2, 5/4, or 7/6. Even between two rational numbers, there are infinitely many other rational numbers. This makes the rational number set very dense.
Rational numbers follow the same rules of addition, subtraction, multiplication, and division (except by zero) as other numbers. When adding or subtracting rational numbers, the denominators must match, and the numerators change based on the operation. When multiplying, numerators and denominators are multiplied across. Dividing rational numbers can be done by multiplying by the reciprocal, which is the flipped version of a fraction.
Rational numbers are different from irrational numbers, which cannot be written as a fraction of two integers. Irrational numbers include values like √2 or the number π. These decimals do not end or repeat. Together, rational and irrational numbers form the set of real numbers, which include all points on the number line. Understanding rational numbers helps build a foundation for learning about more advanced mathematical ideas.
What We Can Learn
- Rational numbers can be written as a fraction using two integers
- Rational numbers include whole numbers, fractions, and repeating or ending decimals
- They are dense on the number line, meaning many exist between any two numbers
- Rational numbers follow rules for normal arithmetic operations
