* If a cake is cut into five pieces and three pieces are taken out of five pieces, then these three pieces are known as .
* Thus the relation to represent some part to the whole part is known as fraction.
* The upper part of the fraction is called Numerator and the lower part is called Denominator.
* For example in the fraction , 4 is the numerator and 7 is the denominator.
* Fraction is always represented in its lowest terms.
* To reduce a fraction to its lowest term, both numerator and denominator are to be divided by the highest common factor.
* For example 3 is the highest common factor of the numerator and denominator of . When both 6 and 9 are divided by 3, the fraction becomes .
Comparison of Fractions:
When comparing two or more fractions, the following points are to be remembered.
* When the denominators of the fractions are same, the fraction having largest numerator is the largest of all the fractions.
* When the numerators of the fractions are same, the fraction having smallest denominator is the largest of all the fractions.
* When neither numerators nor denominators of the fractions are same then they are converted into equivalent fractions of the same denominator by taking the LCM of the denominators of the given fractions and then compared.
* If the difference of the numerators and denominators of each of the given fractions be same then the fraction of the greatest numerator is the greatest and the fraction of the least numerators is the smallest.
* For example,
the difference between the numerator and the denominator of all the fractions is same which is 3 in numerator, 11 is the biggest and 4 is the smallest
Therefore, is the biggest and is the smallest fraction.
Cross multiplication Method:
* Two fractions can be compared with this method.
* The numerator of the first fraction is multiplied by the denominator of the second fraction and the numerator of the second fraction is multiplied by the denominator of the first fraction.
* For example,
are to be compared then
5 × 7 = 35 and 4 × 9 = 36
since 36 is greater than 35 and in 36 the numerator 0f is included.