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How to Identify the DIFFERENT TYPES of FRACTIONS

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By Z-MATH
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The DIFFERENT NAMES given to a FRACTION can be very confusing. This Article will Identify the TYPE of FRACTIONS with their respective NAMES.

Difficulty: Easy
Instructions

Things You'll Need:

  • Pencil and
  • Paper
  1. Step 1

    A FRACTION is also called a RATIONAL NUMBER, since it is the RATIO of two INTEGERS. IF we compare the Integer ( 5 ) to the Integer ( 7 ) we can write that comparison in three different ways. One way, is ...
    " 5 to 7 ", a second way is ... " 5 : 7 ", and the third way is...
    " 5 / 7 ". The third way is the one mostly used when working with fractions.

  2. Step 2

    The first Integer ( 5 ) is called the NUMERATOR, and the second Integer ( 7 ) is called the DENOMINATOR. It is very IMPORTANT to know which Integer is the NUMERATOR or the DENOMINATOR, since ( 5 / 7 ) is not equal to ( 7 / 5 ). That is, " 5 to 7 " is not the same ratio as
    " 7 to 5 "

  3. Step 3

    If the NUMERATOR is less than the DENOMINATOR, that is ( 5 ) less than
    ( 7 ) and it is written in the form of a FRACTION ... ( 5 / 7 ) this fraction is called a PROPER FRACTION.

  4. Step 4

    If the NUMERATOR is greater than or equal to the DENOMINATOR, that is if ( 7 ) is the NUMERATOR and ( 5 ) is the DENOMINATOR, or ( 7 ) is both the NUMERATOR and the DENOMINATOR and these ratios are written in the form of a FRACTION ... ( 7 / 5 ) also ( 7 / 7 ) these fractions are called IMPROPER FRACTIONS.

  5. Step 5

    All positive integers can be called improper fractions since they can be considerd NUMERATORS to the DENOMINATOR ( 1 ). That is every number is understood to be divided by the number ( 1 ).

  6. Step 6

    An IMPROPER FRACTION in which the NUMERATOR is greater than the DENOMINATOR, can be changed to a WHOLE NUMBER with a PROPER FRACTION,
    or stated another way ... An IMPROPER fraction can be changed to
    a MIXED-FRACTION...a WHOLE NUMBER ' mixed ' with a PROPER FRACTION.

  7. Step 7
     

    So the IMPROPER FRACTION ( 7 / 5 ) can be changed to 1 and ( 2 / 5 )
    that is ...we divide ( 7 ) by ( 5 ) to get the quotient ( 1 ) and
    remainder ( 2 ), we then write the ( 2 ) and the divisor
    ( 5 ) as the PROPER FRACTION besides the WHOLE number ( 1 ). Please click on the above Image to the left.

Tips & Warnings
  • If the answer to an Equation in Algebra is in the form of an IMPROPER FRACTION, it is advisable to leave it in that form rather than changing it to a MIXED-FRACTION. The reason being, if one wants to check if the answer to the equation is correct and they have the answer in MIXED-FRACTION form the answer has to be changed back to an IMPROPER FRACTION form in order to do the checking.
  • For e.g., solve the following equation for p; 5p = 7, then check your answer.
  • the answer can be expressed as shown in the Image of STEP #7, in the IMPROPER form or in the MIXED form.
  • To check the answer, substitute ( 7 / 5 ) for ( p ) in the equation 5p = 7, that is 5 x ( 7/ 5 ) = 7.
  • now check the answer, by substituting ( 1 and 2 / 5 ) for p in the equation 5p = 7, that is 5 x ( 1 and 2 / 5). it is more convient to change the mixed-fraction to an Improper form then check the equation.
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