How to Identify the DIFFERENT TYPES of FRACTIONS

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

Instructions

Difficulty: Easy

Things You’ll Need:

• Pencil and
• Paper

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. 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. 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. 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. 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. 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. 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.