A simple example of fraction would be a rational number of the form p/q, where q ≠ 0. In fractions also we come across different types of them. The two fractions 3/4 and 1/4 are like fractions and the fractions 2/5 and 6/7 are unlike fractions. That is, fractions whose denominators are same are referred to as like fractions and the fractions like 2/5 and 6/7 are called unlike fractions as their denominators differ. Further when the numerator in a fraction is lower than the denominator, that fraction is referred to as proper fraction and the fraction in which the numerator is greater than the denominator, is referred to as improper fraction. Also a fraction like is referred to as mixed fraction as it consists of an integer 3 and a fractional part 2/5.
Addition of Like Terms: While adding like fractions the denominator will have the same term as that present in the individual quantities, while the numerator will be the sum of numerators present in the individual fractions.
We take an example.
Example
Add 2/5 and 7/5.
Subtraction of Like Fractions: This will be similar to addition of fractions. Only that the plus symbol should be replaced by the minus symbol. The subtraction operation for the above fractions will be
Multiplication of Like Fractions: The multiplication of fractions will be much simpler. We multiply the numerators and the denominators respectively and express the product as a fraction. For the fractions 2/5 and 7/5, the product will be
Division of Like Fractions: If we have to divide one fraction with the other, we multiply the first one with the reciprocal of the second. For the fractions 2/5 and 7/5, the quotient will be:
Addition of Unlike Fractions: This can be better understood with the help of an example only. Add 2/5 and 7/3. We begin by taking the LCM of the terms present in the denominators of the given fractions. In our case the LCM will be 5 x 3 = 15/15. We write that as shown below.
Now we divide the LCM by the denominator of the first fraction. We obtain 15/5 = 3. In the numerator, the product of this term (3) and the term in the numerator of the first fraction (2), that is 2 x 3 = 6 is stated. It is shown below.
We repeat the same procedure for the second fraction also. On division we obtain 15/3 = 5. Then we multiply 5 with the term in the numerator of the second term. We obtain 5 x 7 = 35 and write this term as shown below. The sum of these two terms gives us our required result.
Subtraction of Unlike Fractions: This is identical to what we have seen above except that the symbol has to be replaced. In our case it will be
Multiplication of Unlike Fractions: This will be similar to multiplication of like terms we have seen before. For the fractions, 2/5 and 7/3, the product will be
Division of Unlike Fractions: This will be similar to what we have seen in like terms. The quotient of the fractions 2/5 and 7/3 will be
Reducing the Fractions to Lowest Terms: By 'reducing a fraction to its lowest terms' we understand that the numerator and the denominator of the fraction being reduced to lowest terms by dividing the numerator and the denominator by the same term. This we do repeatedly until it becomes clear that we cannot do it any further. This should be clear if we look at an example.