Types of Fractions

The second video in the fraction series explains about different types of fractions:

1. Proper and Improper Fractions
2. Mixed Fractions
3. Equal Fractions
4. Like and Unlike Fractions

As mentioned earlier, the basic form of a fraction consists of a numerator (integer number above the stash) and the denominator ( integer number below the stash).

Proper fractions
A proper fraction represents a definite number of parts of the whole quantity of any object. Hence a proper fraction is always less than one. The example here illustrates a circle whose 3 out of 4 parts have been used, thus the proper fraction to represent its usage is \frac { 3 }{ 4 } and of the unused portion is \frac { 1}{ 4 }. Note that in a proper fraction the numerator is always smaller than the denominator because it represents a part of a bigger whole quantity.

Improper fractions and Mixed Fractions
Unlike the proper fraction in improper fractions the denominator is smaller than the numerator. For instance\frac { 9}{ 4 },\frac { 5 }{ 3 }, \frac { 7 }{ 3 } etc. Another way of writing an improper fraction is by converting it into a mixed fraction. A mixed fraction is essentially a whole number and an improper fraction connected with the mathematical operand (x). It establishes a relation between proper and improper fraction. As explained in the video,\frac { 9 }{ 4 } converts to , to and to . Illustrating the same pictorially, would be two whole parts of an object plus one –fourth part of another whole of the same object.

Equal fractions:
The concept of equal fractions is important to understand simplification of fractions. An equal fraction implies same value of a fraction irrespective of the integer values of a fraction. In equal fractions the value of the numerator and denominator of two or more fractions essentially reduces down to same fraction which have equal numeric value. For instance, 2/4 is the same as ½ as 2/4 can be simplified by cancelling 2 and 4 using 2 as the common factor. Similarly, 4/5 is the same as 12/15, as 3 can be used to reduce the latter fraction to 4/5.

Like fractions and unlike fractions:
The concept of like and unlike fractions is important to understand the working of mathematical operations on fractions. Fractions with the same denominator are termed like fractions. For intake ¼, 2/4 , ¾ etc. Such fractions can be easily added and subtracted since they have a common denominator. Let us add ¼ +2/4. Taking two circles we divide them into 4 equal parts selecting one part from the first circle (1/4) and two parts from the second circle(2/4). Denominators being the same we can simply add up the numerators to get the answer. 1+2=3, hence ¼+2/4=3/4.
Unlike fractions, on the other hand are those that do not have same denominators and therefore need to be converted into like fractions in order to add or subtract them. For instance ½ , 1/3, 3/5 etc are unlike fractions.

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