Question

Evaluate the given equation\[\dfrac{5}{6} + \dfrac{7}{9}\]?

Answer 1

Hint:For solving fraction addition you should about lowest common multiplication(L.C.M) rule, this rule states that find the L.C.M of the denominators of the fractions given then divide the L.C.M obtained with each of the denominators for each fraction and then the divisor thus obtained would be multiplied with the numerator for each given fraction.

Formulae Used:
L.C.M rule, that is for any given fraction \[\dfrac{a}{b},\dfrac{c}{d}\]
L.C.M of the fraction in summation or subtraction states that
\[ = \dfrac{{(a)(c) \pm (c)(d)}}{{(b)(d)}}\]

Complete step by step solution:
In the given fraction \[\dfrac{5}{6} + \dfrac{7}{9}\]
Lets first find the L.C.M of the denominators, for which you have to factories the denominator and thus the factorization of both denominator thus obtained would be our L.C.M
We get, Factors of the denominators are:
\[6\,and\,9 = (1,2,3)\,and\,(1,3,3\]
Common factor is \[3,1\]
L.C.M formulae state that common factor product the rest of the factors, applying it we get:
\[3 \times 1 \times 2 \times 3 = 18\]
Now on solving further when the L.C.M is divided by the respective denominators divisor obtained are:
\[\dfrac{{18}}{6} = 3,\dfrac{{18}}{9} = 2\]
Now on solving further we get:
\[
= \dfrac{{(5 \times 3) + (7 \times 2)}}{{18}} \\
= \dfrac{{15 + 14}}{{18}} \\
= \dfrac{{29}}{{18}} \\
\]
So the summation of the above fraction is \[\dfrac{{29}}{{18}}\] which is the least possible fraction, that is not any common factor in the fraction.

Note: Adding or subtracting a fraction only needs to be careful while finding L.C.M, and the rest divisor can easily be obtained and further solution can be done. In order to check your L.C.M you can see the outcome from L.C.M divisible by the denominators and it always gives a perfect divisor. The solution obtained after should be always given in the least smallest fraction.