What are the differences between fractions and ratios?

Fractions and ratios are both mathematical concepts used to compare quantities, but they have different interpretations and uses.

Definition:

Fraction: A fraction represents a part of a whole or a division of one quantity into equal parts. It consists of two numbers, a numerator (top number) and a denominator (bottom number), separated by a fraction bar or a slash (/). For example, 3/4 represents three parts out of four equal parts.
Ratio: A ratio represents the quantitative relationship between two or more quantities. It compares the sizes of different parts or components of a whole. Ratios are typically expressed in the form of "a:b" or "a to b." For example, a ratio of 2:5 means that the first quantity is two parts and the second quantity is five parts.
Interpretation:

Fraction: Fractions are often used to represent parts of a whole, such as portions of a pizza or shares of a quantity. They can also represent values between whole numbers, such as 1/2 or 3/4.
Ratio: Ratios compare the relative sizes or quantities of two or more values. They can represent proportions, rates, or the division of a whole into different parts. For example, a ratio of 2:5 could represent the ratio of boys to girls in a classroom.
Representation:

Fraction: Fractions are typically represented with a numerator and denominator, such as 3/4 or 5/8.
Ratio: Ratios are often represented using a colon (:) or the word "to," such as 2:5 or 2 to 5.
Simplification:

Fraction: Fractions can be simplified by dividing the numerator and denominator by their greatest common divisor. For example, 4/8 can be simplified to 1/2 by dividing both numbers by 4.
Ratio: Ratios can also be simplified, but the process is not as common as with fractions. Ratios are often kept in their original form unless there is a need for specific simplification.
Usage:

Fraction: Fractions are commonly used in mathematics, everyday measurements, cooking recipes, and financial calculations.
Ratio: Ratios are frequently used in various fields, including mathematics, statistics, finance, and scientific research. They are useful for comparing quantities, analyzing proportions, and understanding relationships between different variables.
In summary, fractions represent parts of a whole or values between whole numbers, while ratios compare the relative sizes of two or more quantities. Fractions are typically expressed as numerators and denominators, while ratios are often written as "a:b" or "a to b." Both concepts have their distinct interpretations and applications in different contexts.