What is a proper fraction?

A proper fraction is a fraction where the numerator is less than the denominator.

In a proper fraction, the value of the fraction is always less than 1. For example, in the fraction 3/4, the numerator (3) is smaller than the denominator (4), making it a proper fraction. This is different from an improper fraction, where the numerator is equal to or greater than the denominator, such as 5/4 or 7/7.

Proper fractions are commonly used in everyday situations, such as measuring ingredients in a recipe or dividing a pizza into slices. They are easy to recognise because the top number (numerator) is always smaller than the bottom number (denominator). This means that the fraction represents a part of a whole, rather than a whole number or more.

When working with proper fractions, you might need to simplify them by finding the greatest common divisor (GCD) of the numerator and the denominator. For instance, the fraction 6/8 can be simplified to 3/4 by dividing both the numerator and the denominator by their GCD, which is 2.

Understanding proper fractions is essential for solving various mathematical problems, including addition, subtraction, multiplication, and division of fractions. They also form the basis for understanding more complex concepts like mixed numbers and improper fractions. By mastering proper fractions, you build a strong foundation for further studies in mathematics.