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10 Amazing Facts About Fractions That Will Blow Your Mind

Fractions represent a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, fractions describe how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters. From the ancient civilizations that employed fractions for measuring land and goods to the modern world where they underpin mathematical calculations and engineering designs, fractions have played an integral role in shaping our understanding of the world.

The ability of fractions to represent parts of a whole, proportions, and ratios makes them indispensable tools for problem-solving across various fields, from dividing a pizza into equal slices to calculating the area of a complex shape. Let’s delve into 10 amazing facts about fractions that will blow your mind, from revealing their historical significance, practical applications, and the awe-inspiring power they hold in solving everyday problems.

1. Fractions are older than you think

The earliest recorded use of fractions dates back to the ancient Egyptians around 1800 BC where they were used to measure land and goods. About 4000 years ago, Egyptians divided with fractions using slightly different methods. 

They used least common multiples with unit fractions. Their methods gave the same answer as modern methods. The Egyptians also had a different notation for dyadic fractions in the Akhmim Wooden Tablet and several Rhind Mathematical Papyrus problems.

2. The word fraction comes from the Latin word fractus, which means broken

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A fraction, from Latin: fractus, broken represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters. 

3. Fractions represent a division of a whole into equal parts

In a fraction, the number of equal parts being described is the numerator, and the type or variety of the parts is the denominator.  As an example, the fraction 8/5 amounts to eight parts, each of which is of the type named fifth. In terms of division, the numerator corresponds to the dividend, and the denominator corresponds to the divisor.

Informally, the numerator and denominator may be distinguished by placement alone, but in formal contexts, they are usually separated by a fraction bar. The numerator indicates how many parts are considered, and the denominator indicates the total number of equal parts.

4. Common fractions can be classified as either proper or improper

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When the numerator and the denominator are both positive, the fraction is called proper if the numerator is less than the denominator, and improper otherwise. The concept of an improper fraction is a late development, with the terminology deriving from the fact that fraction means a piece, so a proper fraction must be less than 1.

In general, a common fraction is said to be a proper fraction, if the absolute value of the fraction is strictly less than one that is, if the fraction is greater than −1 and less than 1. It is said to be an improper fraction, or sometimes a top-heavy fraction, if the absolute value of the fraction is greater than or equal to 1. Examples of proper fractions are 2/3, −3/4, and 4/9, whereas examples of improper fractions are 9/4, −4/3, and 3/3.

5. The reciprocal of a fraction is another fraction with the numerator and denominator exchanged

The reciprocal of 3/7, for instance, is 7/3. The product of a fraction and its reciprocal is 1, hence the reciprocal is the multiplicative inverse of a fraction. The reciprocal of a proper fraction is improper, and the reciprocal of an improper fraction not equal to 1 is a proper fraction.

When the numerator and denominator of a fraction are equal, for example, 7/7, its value is 1, and the fraction therefore is improper. Its reciprocal is identical and hence also equal to 1 and improper. Any integer can be written as a fraction with the number one as the denominator. For example, 17 can be written as 17/1, where 1 is sometimes referred to as the invisible denominator. Therefore, every fraction or integer, except for zero, has a reciprocal. For example. the reciprocal of 17 is 1/17.

6. Fractions can be converted to decimals, and vice versa

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To change a common fraction to a decimal, do a long division of the decimal representations of the numerator by the denominator, and round the answer to the desired accuracy. For example, to change 1/4 to a decimal, divide 1.00 by 4, to obtain 0.25. 

Decimal numbers, while arguably more useful to work with when performing calculations, sometimes lack the precision that common fractions have. Sometimes an infinite repeating decimal is required to reach the same precision. Thus, it is often useful to convert repeating decimals into fractions.

7. Fractions are used to represent ratios and division

Other uses for fractions are to represent ratios and division. Thus the fraction 3/4 can also be used to represent the ratio 3:4 the ratio of the part to the whole, and the division 3 ÷ 4 three divided by four.

8. Fractions can be represented visually

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Fractions are used in many different fields of mathematics, science, and engineering. For example, fractions are used to represent probabilities, calculate rates of change, and measure angles.

Fractions can be represented visually with pie charts or number lines, making them easier to understand.

9. Prime factorization is useful for simplifying fractions

Breaking down the numerator and denominator into their prime factors can help simplify fractions effectively. Dividing the numerator and denominator of a fraction by the same non-zero number yields an equivalent fraction: if the numerator and the denominator of a fraction are both divisible by a number, called a factor greater than 1, then the fraction can be reduced to an equivalent fraction with a smaller numerator and a smaller denominator.

10. We use fractions in everyday life

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Fractions are used in various everyday activities, such as cooking, measuring, and calculating discounts.

We equally use fractions all the time, without even realizing it. For example, when we talk about half an hour, or three-quarters of a pizza, we are using fractions. 

Despite their fundamental nature, fractions often get a bad rapport for being difficult to understand. However, with a bit of understanding and practice, their versatility and usefulness become apparent. So next time you think fractions are boring or useless, think again! Fractions are a fascinating and versatile tool that can be used in many different ways.