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Question Number 192477 by Shrinava last updated on 19/May/23
Find: ((((25)/(42)) − (5/(16)) + ((10)/9) − (2/3))/((3/8) + (4/5) − (5/7) − (4/3))) = ?
$$\mathrm{Find}:\:\:\:\:\:\frac{\frac{\mathrm{25}}{\mathrm{42}}\:−\:\frac{\mathrm{5}}{\mathrm{16}}\:+\:\frac{\mathrm{10}}{\mathrm{9}}\:−\:\frac{\mathrm{2}}{\mathrm{3}}}{\frac{\mathrm{3}}{\mathrm{8}}\:+\:\frac{\mathrm{4}}{\mathrm{5}}\:−\:\frac{\mathrm{5}}{\mathrm{7}}\:−\:\frac{\mathrm{4}}{\mathrm{3}}}\:=\:? \\ $$
Answered by Tomal last updated on 19/May/23
=(((((25)/(42))−(5/(16)))+(((10)/9)−(2/3)))/((((315+672−600−1120)/(840))))) =(((((200−105)/(336)))+(((10−6)/9)))/(−((733)/(840)))) =((((95)/(336))+(4/9))/(−((733)/(840)))) =(((285+448)/(1008))/(−((733)/(840)))) =((733)/(1008))×((840)/(733))×(−1) =−((840)/(1008)) =−(5/6)
$$=\frac{\left(\frac{\mathrm{25}}{\mathrm{42}}−\frac{\mathrm{5}}{\mathrm{16}}\right)+\left(\frac{\mathrm{10}}{\mathrm{9}}−\frac{\mathrm{2}}{\mathrm{3}}\right)}{\left(\frac{\mathrm{315}+\mathrm{672}−\mathrm{600}−\mathrm{1120}}{\mathrm{840}}\right)} \\ $$$$=\frac{\left(\frac{\mathrm{200}−\mathrm{105}}{\mathrm{336}}\right)+\left(\frac{\mathrm{10}−\mathrm{6}}{\mathrm{9}}\right)}{−\frac{\mathrm{733}}{\mathrm{840}}} \\ $$$$=\frac{\frac{\mathrm{95}}{\mathrm{336}}+\frac{\mathrm{4}}{\mathrm{9}}}{−\frac{\mathrm{733}}{\mathrm{840}}} \\ $$$$=\frac{\frac{\mathrm{285}+\mathrm{448}}{\mathrm{1008}}}{−\frac{\mathrm{733}}{\mathrm{840}}} \\ $$$$=\frac{\mathrm{733}}{\mathrm{1008}}×\frac{\mathrm{840}}{\mathrm{733}}×\left(−\mathrm{1}\right) \\ $$$$=−\frac{\mathrm{840}}{\mathrm{1008}} \\ $$$$=−\frac{\mathrm{5}}{\mathrm{6}} \\ $$$$\:\cancel{\underline{\underbrace{ }}} \\ $$
Answered by Frix last updated on 19/May/23
=((((25)/(2×3×7))−(5/2^4 )+((10)/3^2 )−(2/3))/((3/2^3 )+(4/5)−(5/7)−(4/3)))= =(((600−315+1120−672)/(2^4 ×3^2 ×7))/((315+672−600−1120)/(2^3 ×3×5×7)))= =((N/(2×3))/((−N)/5))=(1/6)×(5/(−1))=−(5/6)
$$=\frac{\frac{\mathrm{25}}{\mathrm{2}×\mathrm{3}×\mathrm{7}}−\frac{\mathrm{5}}{\mathrm{2}^{\mathrm{4}} }+\frac{\mathrm{10}}{\mathrm{3}^{\mathrm{2}} }−\frac{\mathrm{2}}{\mathrm{3}}}{\frac{\mathrm{3}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{4}}{\mathrm{5}}−\frac{\mathrm{5}}{\mathrm{7}}−\frac{\mathrm{4}}{\mathrm{3}}}= \\ $$$$=\frac{\frac{\mathrm{600}−\mathrm{315}+\mathrm{1120}−\mathrm{672}}{\mathrm{2}^{\mathrm{4}} ×\mathrm{3}^{\mathrm{2}} ×\mathrm{7}}}{\frac{\mathrm{315}+\mathrm{672}−\mathrm{600}−\mathrm{1120}}{\mathrm{2}^{\mathrm{3}} ×\mathrm{3}×\mathrm{5}×\mathrm{7}}}= \\ $$$$=\frac{\frac{{N}}{\mathrm{2}×\mathrm{3}}}{\frac{−{N}}{\mathrm{5}}}=\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{5}}{−\mathrm{1}}=−\frac{\mathrm{5}}{\mathrm{6}} \\ $$

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