Fractions: Parts, Types, Simplifications & Examples

Fractions are determined as the portion of any quantity. It identifies a specific part of a whole and the whole can be a collection or region. In ancient times, fraction was expressed in words. Later, it was represented in numerical form. In the earliest civilization, people used fractions as a mathematical solution for the equal distribution of supplies, food, and other basic needs.

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Key Terms: Fractions, Fractional Bar, Numerator, Denominator, Proper and Improper Fractions, Mixed Fractions, Equivalent Fractions

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What is Fraction?

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In mathematical terms, fractions are expressed as numerical values which help in determining the part of a whole. The whole can be a specific value, number or thing.

Fraction

The first figure shows a watermelon that is divided into 8 equal parts. Now, if we want to consider two selected parts of the watermelon, we can write it as 2/8 which shows that out of 8 equal parts, we are referring to 2 parts. Similarly, the second one shows one selected part of the watermelon out of 4 equal parts and is represented as 1/4.

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Parts of Fraction

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Fractions are separated by a horizontal bar or line called fractional bar. Every fractions have a numerator and a denominator. A denominator is placed at the lower part below the fractional bar. It represents the number of parts in which the whole has been divided into. The numerator is placed in the upper part of the fraction (above the bar). It indicates the number of sections represented or selected out of the total number of parts.

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Types of Fractions

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On the basis of the properties of denominator and numerator, fractions are classified into various types:

1. Proper Fractions: In proper fractions, the numerator is always less than the denominator. For example 7/8 is a proper fraction since the numerator is less than the denominator.
2. Improper Fractions: Here, the numerator happens to be a bigger value than the denominator. Consider 8/7, where the numerator is greater than the denominator. Hence, it is considered as an improper fraction.
3. Unit Fractions: In unit fractions, the numerator will be 1. Example, 1/7, 1/4. 1/9, etc.
4. Mixed Fractions: It is a combination of a whole number and a proper fraction. In a mixed fraction 412, 4 is the whole number and 1/2 is the proper fraction.
5. Like and Unlike Fractions: Like fractions as the name resembles are alike or same. Look at 1/2 and 2/4, mathematically, they are the same and by simplifying it, the same fractions are obtained. Unlike fractions are dissimilar, for example, 1/2 and 1/3 are not the same.
6. Equivalent Fractions: Two fractions are considered equivalent to each other if after simplification either of the fractions is equal to the other fraction. For example, 2/3 and 4/6 are considered equivalent since 4/6 = (2×2) / (2×3) = 2/3.

Types of Fraction

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Fraction on a Number Line

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The fractions on a number line represent the intervals between two integers. The fractions on a number line are represented by making equal parts of a whole. The denominator of the fraction represents the number of equal parts in which the number line is divided and marked. Consider representing 1/8 on a number line. First we should mark 0 and 1 on the two sides and divide the number line into 8 parts. First interval is marked as 1/8 and the next interval is marked as 2/8, next 3/8, and so on. The last interval represents 8/8 (which is 1). 

Fraction on Numberline

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How to Solve Fractions?

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Fractions can be solved by addition, subtraction, multiplication and division. The methods of performing different operations on fractions are given below:

Adding Fractions

Adding fractions is simple when they share a common denominator. For example 2/3 + 7/3 = (2+7) / 3 = 9/3. But if the denominators are different, one must simplify them by finding the LCM of the denominators and then make it common for both fractions.

For example, consider 2/3 + 3/4

3 and 4 are the two denominators

LCM of 3 and 4 = 12

Multiply 2/3 by 4/4 and 3/4 by 3/3

The result is: 

8/12 + 9/12 

= (8+9) / 12 

= 17/12

Subtracting Fractions

The rule for subtracting fractions remains the same as for addition. It is easy if the denominators are common. Similarly, if the denominators are different, one should simplify them by finding the LCM of denominators.

Multiplication of Fractions

When two fractions are put together for multiplication, the numerators and denominators are multiplied together. If a/b and c/d are different fractions, the multiplication will be, 

(a/b) x (c/d) = (a x c) / (b x d) = (ac / bd).

Division of Fractions

In order to perform division, one should multiply the first fraction to the reciprocal of the second fraction. Consider a/b and c/d are two fractions, the division a/b by c/d is as follows:

(a/b) ÷ (c/d) = (a/b) x (d/c) = (ad / bc)

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Things to Remember

• Fractions are represented as numerical values which help in identifying the part of a whole. 
• Fractions are separated by a horizontal bar called fractional bar. A fraction has two parts, a numerator and a denominator.
• Numerator is the upper part that represents the sections of the fraction. Denominator is the lower part that expresses the total parts in which the fraction is divided.
• Some different fractions in mathematics are proper fractions, improper fractions, like/ unlike fractions, mixed fractions, equivalent fractions.

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