Fractions, Study Notes, Material - Super TET, DSSSB & KVS

By Komal|Updated : July 1st, 2022

In this article, we should read related to the Fractions Important for the Super TET.

A fraction can simply be defined as the symbol that tells about how many parts of a whole (single object) or parts of a set (a group of objects). You may also term it as a portion or division or section of any quantity.

TYPES OF FRACTIONS

  • Proper Fractions
  • Improper & Mixed Fractions
  • Equivalent Fractions
  • Unlike Fractions

What is a Fraction?

A fraction can simply be defined as the symbol that tells about how many parts of a whole (single object) or parts of a set (a group of objects). You may also term it as a portion or division or section of any quantity. Fractions are represented as,

both the numerator & denominator are integers & Denominator 0

1.The numerator denotes the number of parts considered.
2.The denominator denotes the total number of parts.
3.The line separating the two numbers is called a fraction bar.
  • If the numerator = denominator, then the fraction is said to become a whole i.e 1.
  •  Example: Imagine you divide a cake into 8 pieces & eat 3 of them. You can represent it in the form of a fraction. Where 3 is the number of the pieces you ate & 8 is the total number of pieces of the cake.
  • And if you were hungry & ate all the 8 pieces, it would be  = 1. (Whole)
  • Note: All integers can be expressed as a form of a fraction because the total numbers of parts of an undivided whole are 1

Proper Fractions

  • A proper fraction is a number that represents part of a whole hence these fractions are always lesser than 1. Such fractions always have a smaller numerator than the denominator and they denote how many parts of a whole are considered.

    Example

    Example : , , , , etc.



  • A group of proper fractions where each fraction represents a whole that is divided into an equal number of parts (with the same denominators) are called like fractions.
  • Example:, (All the fractions share a common denominator hence they are like fractions.)

 

Comparison of Like Fractions

  • To compare like fractions all you have to do is to compare the numerators, A fraction with a smaller numerator is always lesser than the one containing a bigger one.
    Example :

Improper & Mixed Fractions

         1. The fractions considering parts of more than a whole are called improper fractions, i.e. >1. Hence the numerator is always greater than the denominator. Thus, ,, are improper
         fractions.
         2. Example: Imagine you have 6 oranges that you have to split between 5 friends including you. The value of each share would be 65, i.e.
         3. It also means that all five of you are going to get 1 full orange and an additional one-fifth of the extra orange. So the value of each share can also be written as 1 +. i.e 1 that equals to.
         4. Such a fraction, 1 containing both a whole and a part is called a mixed fraction.
         5. You can express all improper fractions in the form of mixed fractions by dividing the numerator by its denominator to find the quotient & the remainder. The mixed fraction will be represented as.

         Example: Express, as mixed fractions.

         Solution: Divide the numerators with their respective denominators to obtain the quotient & the remainder. The above fractions can be written as the following mixed fractions:

                              ● = 4 (4 whole and more)
                              ● = 4 (4 whole and more)
                              ● = 5 (5 whole and more)
         Similarly, all mixed fractions can be expressed as improper fractions by adding the whole number and the part. Thus, putting any mixed fraction into this formula will give you an improper fraction.

         Example: Write an improper fraction for 2 and 3. Example: Write an improper fraction for 2 and 3.

         Solution: Add the whole to the parts to obtain improper fractions of the following mixed fractions.
                      ● 2 = + = + = =
                            And
                     ● 3 = + = + ==

Equivalent Fractions

    1. The fractions that are proportional to each other are called equivalent fractions. They represent the same part of a whole with different fractions such that, = =... and so on.

   2. Example: ==.
   3. To obtain an equivalent fraction of any fraction, you may multiply or divide both the numerator and the denominator of the given fraction by the same number.=, =, =, =and more.
         Or
   4. =, =, = etc.

Unlike Fractions

 1. Two fractions are said to be unlike if they have different denominators.
 2. Example: and are unlike fractions. Also, and are unlike too.

Comparison of Unlike Fractions

  • If the fractions have a common numerator.
  • When two proper fractions have the same numerator, the fraction that has a smaller denominator is always greater than the other.
  • Example: In, we divide the whole into two equal parts and take one. Similarly,  shows the whole is divided into three equal parts & you take one.
  • In, the whole is divided into a smaller number of parts hence, the equal part we take in will be larger than that of the part in.
  • Therefore,
  • If the fractions have different numerators.
  • When two proper fractions have different numerators, the fractions have to be converted into like fractions (same denominator) in order to compare which one is greater using equivalent fractions so that their value remains the same.
  • You can obtain the equivalent fractions with a denominator that’s a common multiple of denominators of both the fractions by finding the LCM of the two denominators and multiplying the given fraction with a number such that you obtain the LCM as the denominator.
  • Example: Compare and.
  • Solution: The above fractions are unlike hence to compare the following we need to find their respective equivalent fractions.

This article tends to be beneficial for the following exams - REETUPTETCTETSuper TETDSSSBKVS etc.

        

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