Question

simplify the following :-
$6 \frac{1}{8} - 2 \frac{1}{12} - 5 \frac{1}{10} + 3 \frac{7}{25}$
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Answer 1

Simplify the following :-

• $\sf 6 \dfrac{1}{8} - 2 \dfrac{1}{12} - 5 \dfrac{1}{10} + 3 \dfrac{7}{25}$

Solution

$\\{~~~~~:~~\implies\sf 6 \dfrac{1}{8} - 2 \dfrac{1}{12} - 5 \dfrac{1}{10} + 3 \dfrac{7}{25} }$

• Convert Mixed into Proper Fraction

${~~~~~:~~\implies\sf \dfrac{(8 \times 6) + 1}{8} - \dfrac{(12 \times 2) + 1}{12} - \dfrac{(10 \times 5) + 1}{10} + \dfrac{(25 \times 3) + 7}{25} }$

${~~~~~:~~\implies\sf \dfrac{48+ 1}{8} - \dfrac{24 + 1}{12} - \dfrac{50+ 1}{10} + \dfrac{75 + 7}{25} }$

${~~~~~:~~\implies\sf \dfrac{49}{8} - \dfrac{25}{12} - \dfrac{51}{10} + \dfrac{82}{25} }$

• Taking LCM of 8,12,10,25 = 600

$\\{~~~~~:~~\implies\sf \dfrac{(49 \times 75) - (25 \times 50) - (51 \times 60) + (82 \times 24)}{600} }$

${~~~~~~~~~~:~~\implies\sf \dfrac{3675 - 1250 - 3060+ 1968}{600} }$

${~~~~~~~~~~~:~~\implies\sf \dfrac{5643 - 4310}{600} }$

${~~~~~~~~~~~~~~~:~~\implies\sf \dfrac{1333}{600} }$

${~~~~~~~~~~~~~~~~~~~~\sf or \: \: \: \: 2\dfrac{133}{600} }$