# Adding Rational Numbers

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A number of the form p / q, where p and q are integers prime to each other and q≠ 0, is called a rational number or commensurable quantity; here q is taken as a positive integer and p may be a positive integer or negative integer or zero.

For example, each of the numbers 5, 2/3, 0.32, √16 etc. is a rational number. Evidently, the number 0 (zero) is a rational number.

Adding rational numbers: - Suppose there are two rational numbers
a / b and c / d. Then

a/ b + c/ d= (a d + b c) / b d                        Where  b≠ 0 and d ≠ 0

Example of adding ration numbers: -

Simplify 1 / 2 + 3 / 4

Solution: -

1 / 2 + 3 / 4 = (1 * 3 + 2 * 4)/ (2 * 4)
= (3 + 8) / 8
= 11 / 8

Simplify the following expression:-

1/ 5 + 2/ 15 + 3/ 10

Solution: -    At first we will take the least common factor of the denominators 5, 15 and 10.
L.C.M. of 5, 15 and 10 = 30
Now we will divide 30 by each denominator 5, 15 and 10 then multiply with there corresponding numerators.
Like 30 / 5 = 6 and 1* 6= 6
Similarly we will proceed for the next two rational numbers.

1/ 5 + 2/ 15 + 3/ 10= (1*6 + 2* 2 + 3* 3) / 30
= (6+4+9)/30
= 19 / 30