Question

Find the sum and difference between the greatest and smallest fraction given below.
$2\frac{5}{7},\frac{18}{7},\frac{5}{8},\frac{43}{14},2\frac{7}{8}$

Answer 1

First we will convert all the given fractions in (a/b) form if they are not in the same form.
$2\frac{5}{7}=\frac{2\times 7+5}{7}=\frac{19}{7}2\frac{7}{8}=\frac{2\times 8+7}{8}=\frac{23}{8}So,thefractionsare,\frac{19}{7},\frac{18}{7},\frac{5}{8},\frac{43}{14},\frac{23}{8}L.C.Mof7,8,14=56$
Converting all the given fractions into equivalent fractions.
$\frac{19\times 8}{7\times 8}=\frac{152}{56}\frac{18\times 8}{7\times 8}=\frac{144}{56}\frac{5\times 7}{8\times 7}=\frac{35}{56}\frac{43\times 4}{14\times 4}=\frac{172}{56}\frac{23\times 7}{8\times 7}=\frac{161}{56}\frac{35}{56}<\frac{144}{56}<\frac{152}{56}<\frac{161}{56}<\frac{172}{56}$
Therefore,
The sum of the greatest fraction and smallest = $\frac{35}{56}+\frac{172}{56}=\frac{35+172}{56}=\frac{207}{56}$
The difference between the greatest and smallest fraction
$=\frac{172}{56}-\frac{35}{36}=\frac{172-35}{56}=\frac{137}{56}$