Fractions

The concept of fractions, though a simple one, can be often confused. Having not solved questions based on this simple concept, students often tend to confuse the problems. These questions can throw up the occasional challenge and it makes sense to practice these questions from this area.

Definition: Technically, fraction is defined as part of the whole. The most common example of a fraction that comes to mind is half. When we say give me half of something, we are essentially demanding ½ part of it, in other words, ½ is the fractional representation for half.

Fractions are nothing else than the numerator divided by denominator, that is they occur in the form X/Y where X is the numerator and Y is the non-zero denominator.

Remember:

The numerator represents how many parts of that whole are being considered. To remember simply, numerator is the top number of the fraction that represents the numbers of parts that are to be chosen. The denominator represents the total number of parts created from the whole, in other words it is the bottom number representing the total number of parts created.

Example of Fractions : ½, 2/3, 3/4, are the numbers which are in the form of x/y where y is non zero.

Types of Fractions:

Proper Fraction: When Numerator< Denominator, then the fraction is called as proper fractionFor example: 2/3, 4/5, 6/7 etc

Improper fraction: When Numerator >Denominator, then the fraction is called as improper fraction. For example: 5/3, 7/5, 19/7 etc

Mixed fraction: When a natural number combines with a fraction that is called a mixed fraction.

For Example: 21/2 ,34/etc. In other words, the mixed fractions are improper fractions

Tooltip: Properties of fractions

Property 1: If we multiply the numerator and denominator by same quantity, the basic value of fraction will never change. For example:4/5 x 5/5 = 20/25 = 4/5

Property 2: If there are two fractions a/b and c/d then a/b=c/d when ad=bc. For example 3/4 = 12/16 because 3 x 16 = 4 x 12

Property 3: A fraction with zero as the denominator is not defined.

Property 4: If the numerator of the fraction is zero, then the fraction equals to zero.

Property 5: If the numerator and denominator of the fraction are equal, then the fraction is equal to one.