Fraction Facts: A Deep Dive Into Numerators & Denominators

Fractions are a big part of our everyday lives, but how much do we really know about them?

Like whole numbers, fractions can be added, subtracted, divided, and multiplied. They are numbers in their own right, but are simply broken down pieces of a whole.

In this article, we will take a deep dive into numerators and denominators. We'll discuss what these terms mean, provide examples of fractions with both numerators and denominators, and show you how to simplify fractions. Stay tuned, it's going to be a fraction-tastic journey!

History Of Fractions

A fraction refers to a number that represents a portion of another number in Mathematics. The top number in the fraction is the numerator and tells how many parts are being represented. The bottom number in the fraction is called the denominator and tells what size each part is.

The word fraction comes from the word 'fractus', which is Latin for 'broken'.

Fractions have been used by humans for thousands of years to help with mathematical calculations. They were originally developed to help people divide things up evenly, such as when sharing food or land. Fractions can be used to represent any division of a whole, including divisions that are not equal.

Early civilizations like the Egyptians, the Greeks, and the Ancient Indians used fractions to express parts of a whole object. Though their methods were slightly different from what we learn in school nowadays, they were able to use mathematical operations on these fractions and receive similar answers to how we can today!

The Egyptians used a form of fractions called unit fractions, meaning they split each object into equal portions obtaining a number of portions equal to 1/n, where n is the number of portions the object was split into. So, if a piece of land was split into 10 parts, they regarded each split portion as 1/10.

Today, fractions are still widely used in mathematics and other sciences. In particular, fractions are often used when working with ratios and proportions. Additionally, fractions can be helpful when trying to understand and solve problems.

Fractions can be a bit tricky to learn at first, but with a little practise, they are easy to use and understand.

Fractions consist of three types: proper fractions, improper fractions, and mixed fractions.

Proper fraction: a number that is less than one and can be written as a part of a whole number. The numerator of the fraction is always smaller than the denominator.

If the number is converted into a decimal number, the result will always be less than one. For example, 2/5 is a proper fraction denoting two out of five equal portions of a whole.

Improper fraction: a number that is greater than one and can be written as a fraction. It is usually not a whole number and the numerator is greater than the denominator. For example, 7/5 is an improper fraction.

Mixed number: a number that is more than one and can be written as a combination of an integer and a proper fraction. The numerator is still the total amount being divided and the denominator is still how many pieces it's been divided into.

However, in this case, the integer part is written before the fractional part. An improper fraction can be written as a mixed fraction by dividing the numerator by the denominator.

The quotient will be the integer and the remainder upon the divisor gives us the fraction part of the number. Taking the example above of an improper fraction, 7/5 can be written as a mixed number, 1 2/5.

Multiplying Fractions

Multiplying fractions is extremely easy. In fact, it's much easier than adding or subtracting fractions! Unlike addition or subtraction, where both numbers need to have a common denominator, fractions can be multiplied no matter what the denominator is.

To multiply a fraction, you simply multiply the two numerators together and then the two denominators. Once this has been done, simplify the fraction by dividing both numerator and denominator by common factors.

For example, if you are multiplying 3/4 and 2/8, the steps for multiplication will be:

Multiply numerators i.e. 3 x 2 = 6

Multiply the denominators i.e. 4 x 8 = 32

You then get the fraction 6/32. This fraction can be simplified further. Both 6 and 32 are divisible by 2 so we can divide them both by 2.

By doing so, we get 3/16, which is our final answer!

Here, 3/16 is just a simplified version of 6/32, which makes them equivalent fractions, as they are the same number!

Dividing Fractions

Dividing fractions can be tricky at first, but it's extremely similar to the multiplication of fractions.

In multiplication, we multiply the fractions with each other as they are, by multiplying both the numerators with each other, as well as the denominators.

In division, we multiply the numerator of the first fraction with the denominator of the second fraction and vice versa i.e. with its reciprocal.

In simpler words, we invert the second fraction i.e. flip the numerator and denominator, and then simply multiply both numbers. The flipped fraction is called the reciprocal of the original fraction.

For example, if we are dividing 3/4 by 6/9, the steps will be as follows:

We have 3/4 ÷ 6/9

To proceed, we need to cross multiply numerators and denominators. We can do this by inverting the second fraction

So, we now have 3/4 x 9/6

Following fraction multiplication, we get 3 x 9 upon 4 x 6, giving us 27/24

Both the numerator and the denominator here are divisible by 3 which is the highest common factor, so we can simplify it to 9/8, which is our final answer.

And so there you have it, that's how you divide fractions!

Decimals Vs Fractions

When it comes to fractions and decimals, there are a few things that you need to know. Firstly, fractions can be expressed as decimals by dividing the numerator (top number) by the denominator (bottom number).

For example, if you have the fraction 3/4, this can be written as the decimal 0.75, simply by dividing 3 by 4.

Secondly, when converting decimals to fractions, you just need to remember that anything after the decimal point is moved over to the numerator. For example, if you have the decimal 0.12, this would be written as 12/100 or simply 12 ÷ 100.

Lastly, when adding or subtracting fractions with different denominators, it's best to first convert them all to equivalent fractions with the same denominator. This can be done by multiplying the numerators and denominators of all the fractions by the same number (the least common denominator).

For example, if you were trying to add 3/4 and 1/2, first convert them both to fractions with a denominator of 4, which is the least common multiple of the denominators, so 1/2 would become 2/4. Then add the numerators together and put the result over 4 again.

3/4 + 1/2

3/4 + 2/4

The final answer would be 5/4 or simply 5 ÷ 4. You can then easily convert the answer into a decimal number, which here is 1.25.

You can also simply convert the fractions into decimals and add them this way if you find it easier.

For the above example, you can convert 3/4 to 0.75 and 1/2 to 0.5.

0.75 + 0.5 = 1.25

So when it comes to fractions vs decimals, just remember these few tips!

FAQs

What are the three types of fractions?

The three types of fractions are proper fractions, improper fractions, and mixed fractions.

What three things can a fraction represent?

Fractions can be used in a wide variety of ways to represent a portion of a whole, ratios, and can also be used to represent the division of then numerator by the denominator.

What is fraction math?

Fractions can undergo the same basic operators as whole numbers. We can add, subtract, multiply and divide many fractions with each other by applying these basic operations.

How are fractions used in real life?

Fractions are quite useful in real life. They can be used to divide an object into a number of equal parts.

For example, to determine how to divide profit among investors in the ratio of the capital they put in. As one investor may have put in more capital than the other, he will receive more profit as well. Using fractions helps make the division process much easier.

Why is learning about fractions important?

Fractions are extremely important as they help us understand how to divide wholes into portions. It can help a person understand how much of something they should take or give.

What grade are fractions taught?

Simple fractions are usually taught to children once they understand the basic operations of whole numbers, so in around the second or third grade.