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What Are Fractions?

The term fraction is derived from the Latin word "fractio," which meaning "to break." The Egyptians, the first society to study fractions, learnt fractions to address their mathematical issues, which included the division of food and resources, as well as the absence of a gold currency.

Fractions were only written in Ancient Rome using words to express a portion of the total. Fractions were initially written in India with one number atop another (numerator and denominator), but without a line. It was only the Arabs who added the line that separates the numerator and denominator.

Parts of a Fraction

Numerator: The number above the fraction bar in a fraction; it tells how many equal parts.

Denominator: The number below the fraction bar in a fraction; it tells the total number of equal parts.

Fraction Bar: The symbol used to separate the numerator and denominator. In arithmetic, a fraction is a number stated as a quotient in which a numerator is divided by a denominator. Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A suitable fraction has a numerator that is smaller than the denominator.

If the numerator is bigger than the denominator, the fraction is termed an improper fraction, and it may also be expressed as a mixed number—a whole-number quotient with a proper-fraction remainder. Any fraction may be stated in decimal form by dividing the numerator by the denominator. The result may come to an end at some time, or one or more digits may repeat indefinitely.

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Types of Fractions

A fraction is considered to be the ratio of two numbers. The upper number is called Numerator, and the lower part is known as the Denominator. When a whole of something is divided into the number of parts, then each part is referred to as a fraction. Based on numerator and denominator, apart from these three major types of fractions, there are three more types of fractions namely like & unlike fractions and equivalent fractions.

 Hence, there are in total six types of fractions such as:

• Proper fraction
• Improper fraction
• Mixed fraction
• Like fractions
• Unlike fractions
• Equivalent fractions

How to Divide Fractions?

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed. As it turns out, the rule for dividing fractions with like denominators is derived from the general rule for dividing fractions. That is, regardless of whether the denominators are the same or not, there is a rule for dividing fractions.

To divide fractions, we must first understand how to multiply fractions. Fortunately, multiplying fractions is perhaps the simplest operation on fractions. To multiply fractions, we simply multiply their numerators and denominators together, then simplify.

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Examples on Fractions

If possible, the final step is to simplify the result. To simplify a fraction, calculate the greatest common factor (GCF) of the denominator and the numerator. The GCF is the greatest number that can be divided evenly into two numbers. In the instance of 12 and 96, 12 divides equally into 96. Divide 12 by 12 to obtain 1, and 96 by 12 to get 8. As a result, 12/96 12/12 = 1/8.

If both numbers are even, you can start by dividing them both by 2 and working your way up. 12/96 x 2 = 6/48 x 2 = 3/24 Then, because 3 divides evenly into 24, you may divide both the numerator and denominator by 3.

Multiply the numerators and denominators of the fractions and simplify your answer. Now, do the same thing you would do to multiply. If you multiply the numerators, 1 and 20, you get the result of 20 in the numerator. If you multiply the denominators, 2 and 18, you get 36 in the numerator. The product of the fractions is 20/36. 4 is the largest number that is evenly divisible by both the numerator and the denominator of this fraction, so divide each by 4 to get the simplified answer. 20/36 ÷ 4/4 = 5/9.

How do we add or subtract mixed fractions?

As you may recall, a mixed number consists of an integer and a proper fraction. Any mixed number can also be written as an improper fraction, in which the numerator is larger than the denominator. If the sum of the fractions is an improper fraction, then we change it to a mixed number. Here's an example. The whole numbers, 3 and 1, sum to 4. The fractions, 2/5 and 3/5, add up to 5/5, or 1. Add the 1 to 4 to get the answer, which is 5.

Well, as it turns out, this rule for dividing fractions with like denominators actually comes from the rule for dividing fractions in general. That is, there is a rule for dividing fractions regardless of if their denominators are the same or not. To divide fractions, we need to know how to multiply fractions. Thankfully, multiplying fractions is probably the easiest operation to perform on fractions. To multiply fractions, we simply multiply their numerators together and multiply their denominators together, then simplify.

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How do you write algebraic fractions in simplest form?

Adding to that, it could be seen that Algebraic fractions are extremely complex at first glance and might be intimidating to the inexperienced student. It's difficult to know where to start with a jumble of variables, numbers, and even exponents. Fortunately, the same laws that apply to conventional fractions, such as 15/25, also apply to algebraic fractions. Review how to solve simple fractions. These are the exact same steps you will take to solve algebraic fractions. Take the example, 15/35. In order to simplify a fraction, we need to find a common denominator. In this case, both numbers can be divided by five, so you can remove the 5 from the fraction