Question

Simplify $ 1\dfrac{1}{2} + \dfrac{4}{9} + 13\dfrac{1}{2} $

Answer 1

Hint: First convert the given mixed fractions in the form of simple fractions and then simplify the fractions taking the LCM (least common multiple). Mixed number is expressed as the combination of a whole number and the fraction. Fraction is the number which is expressed in the form of the numerator and the denominator. Then simplify the expression for the resultant required value.

Complete step-by-step answer:
Take the given expression: $ 1\dfrac{1}{2} + \dfrac{4}{9} + 13\dfrac{1}{2} $
Convert the given mixed fraction in the form of the simple fraction.
 $ = \dfrac{3}{2} + \dfrac{4}{9} + \dfrac{{27}}{2} $
Take the LCM (least common multiple) for the above expression, here the LCM for the denominator is $ 2 \times 9 = 18 $
Find its equivalent fraction considering the LCM
 $ = \dfrac{{3 \times 9}}{{2(9)}} + \dfrac{{4 \times 2}}{{9(2)}} + \dfrac{{27 \times 9}}{{2(9)}} $
Simplify the above expression by finding the product of the terms
  $ = \dfrac{{27}}{{18}} + \dfrac{8}{{18}} + \dfrac{{243}}{{18}} $
When denominators are same, numerators are combined
 $ = \dfrac{{27 + 8 + 243}}{{18}} $
Simplify the above expression finding the sum of the terms in the numerator of the above expression –
 $ = \dfrac{{278}}{{18}} $
Simplify for the required value and find the mixed fraction for the above expressions -
 $ = 15\dfrac{8}{{18}} $
Hence, the required solution is $ 1\dfrac{1}{2} + \dfrac{4}{9} + 13\dfrac{1}{2} = 15\dfrac{8}{{18}} $
So, the correct answer is “$15\dfrac{8}{{18}} $”.

Note: Always frame the mixed fraction into the correct fraction in mathematical expression properly since the solution depends on it only and therefore check it twice. Be good in finding the factors of the terms and remember multiples till twenty.