Fractions: We all had to deal with them in math class, and even today they plague us. But did you know fractions have existed for thousands of years and that the most basic math relies on them?
The Oxford Dictionary defines a fraction as a numerical quantity that isn’t a whole number. The word itself comes from the Latin term “fractio”, meaning “breaking”.
During the Middle Kingdom period of Ancient Egypt, fractions were represented by glyphs that, when combined, created the symbol we now know as the “Eye of Horus”. But Egyptian fractions are a great lesson in how we over-complicate mathematical concepts, and here’s why:
The Egyptians used addition and multiplication, but had no subtraction or division. Instead, they added and multiplied using fractions. We still do the same thing today without knowing it.
For example, 8÷2 is actually the fraction 8/2. The dots of the division symbol represent where the numbers go! So now that we see fractions aren’t as scary as we were led to believe, let’s have a look at seven different types of fraction and how we use them every day.
Note: We’ll be using two terms a lot in here, but they’re easy to grasp. Numerator is the top number and denominator (just think D for down) is the bottom number.
Types of Fractions
Here’s another bombshell already: Decimals are actually a type of fraction! Yes, you heard right. A decimal fits Oxford’s definition of a fraction, even though most of us prefer them to the traditional concept of a fraction.
To get a decimal, you’re simply solving the division problem a fraction represents. For example, 1/4 is just 1÷4, which gives us the decimal .25 when solved.
Decimals also have a sub-group known as periodicals. Pi is an example of a periodical, which is a decimal that begins repeating infinitely. We often put a line over the numbers in a decimal that will be repeating as a way to show that sequence is infinite.
2. Equivalent Fractions
These are a very useful tool in mathematics, as they’re literally multiple fractions which represent the exact same amount. For example, 1/4 is the same as 2/8 or 4/16.
When working with large fractions, we try to break it down to “the simplest terms” or “lowest common denominator” if dealing with several fractions. When we look at the fractions above, dividing 2/8 by 2 (or 2/1, which is the fraction form) and 4/16 by 4 both give us 1/4.
Breaking down a large fraction to a much simpler form makes it easier to work with. Would you rather have 1/4 or 22/88 staring up at you from the page?
3. Improper Fractions
Simply put, an improper fraction is a fraction that equals more than one. 5/4 actually equates to 1-1/4. You can easily spot an improper fraction by checking to see if the numerator is bigger than the denominator. In our example, 1-1/4 is known as a mixed number, because it pairs a whole number and a fraction.
Improper fractions are useful when dealing with a complicated math problem involving several fractions. 1-1/4 is just the equation (4/1 + 1/4) in a simpler form. Turning the mixed number into an improper fraction means working with fewer numbers.
You can then easily convert the final answer back to a mixed number if an improper fraction remains.
4. Proper Fraction
A proper fraction is the opposite of an improper fraction. The denominator will always be the bigger number. Thus, proper fractions will always represent a number less than 1 but more than zero. An archaic term for the proper fraction is “vulgar fraction”.
Fun Fact: Vulgar meant “common” in Latin and the modern meaning comes from aristocrats accusing each other of “having a vulgar tongue” i.e. “talking like a commoner”.
5. Simple Fractions
We’ve actually been using simple fractions throughout this article. A simple fraction is just a fraction where both the numerator and denominator is a whole number.
6. Unit Fractions
Unit Fractions are another good example of how words make easy things sound complicated. A unit fraction is literally any fraction where the numerator is 1. That’s it.