Egyptian fraction facts for kids

A unit fraction is a special kind of fraction where the top number, called the numerator, is always 1. Think of it like cutting a pizza into equal slices and taking just one slice. For example, 1/2, 1/3, or 1/7 are all unit fractions. An Egyptian fraction is a way to write any fraction as a sum of different unit fractions. This means you add up several unique unit fractions to get your original fraction. For instance, the fraction 3/4 could be written as 1/2 + 1/4. The ancient Egyptians used this method to work with fractions.

What are Unit Fractions?

A fraction has two main parts: the numerator (the top number) and the denominator (the bottom number). The denominator tells you how many equal parts something is divided into. The numerator tells you how many of those parts you have.

In a unit fraction, the numerator is always 1. This means you are talking about just one single part of a whole.

• 1/2 means one part out of two equal parts.
• 1/5 means one part out of five equal parts.
• 1/100 means one part out of one hundred equal parts.

Unit fractions are the basic building blocks for Egyptian fractions.

Why "Egyptian" Fractions?

These special fractions are called "Egyptian fractions" because the ancient Egyptians used them thousands of years ago. They had a unique way of writing fractions. Instead of using fractions like 3/5 or 2/7, they preferred to break them down into sums of unit fractions.

For example, if we wanted to write 3/5 today, the Egyptians would write it as 1/2 + 1/10. They almost always made sure that all the unit fractions in their sum were different. So, they wouldn't write 2/3 as 1/3 + 1/3. Instead, they would write it as 1/2 + 1/6.

How Ancient Egyptians Used Them

The ancient Egyptians were skilled mathematicians. They used Egyptian fractions for many practical things in their daily lives. This included dividing food, land, or other goods fairly among people.

One of the most famous examples of their math is found in the Rhind Mathematical Papyrus. This ancient scroll, written around 1650 BC, contains many mathematical problems and solutions. It shows how the Egyptians worked with fractions and often expressed them as sums of unit fractions. This papyrus is a key source for understanding how they thought about numbers.

Examples of Egyptian Fractions

Let's look at some examples of how common fractions can be written as Egyptian fractions:

• 1/2 is already a unit fraction, so it's simple.
• 2/3 can be written as 1/2 + 1/6.
• 3/4 can be written as 1/2 + 1/4.
• 4/5 can be written as 1/2 + 1/4 + 1/20.

It's important to remember that there can be more than one way to write a fraction as an Egyptian fraction. For example, 1 could be 1/2 + 1/3 + 1/6.

Why are they important today?

Even though we use a different system for fractions now, Egyptian fractions are still studied by mathematicians. They are a fascinating part of the history of numbers. They also show us how people in ancient times solved mathematical problems with the tools they had. Studying them helps us understand the different ways humans have thought about and used numbers throughout history.

Images for kids

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  The Rhind Mathematical Papyrus is an ancient Egyptian mathematical text.

See also

In Spanish: Fracción egipcia para niños