-486 2/2541 - (-473 1413/1694)

Question

I think I have it but I find the negative signs confusing. Please help me by showing the steps

thank you so much

Answer 1

-486 ²/₂₅₄₁ - (-473 ¹⁴¹³/₁₆₉₄)

= -486 ²/₂₅₄₁ + 473 ¹⁴¹³/₁₆₉₄

= (-486 + 473) + (-2/2541 + 1413/1694)

= (-13) + (-2/2541 + 1413/1694)

 

OK, now we need to do a lot of "prime factorization":

 

2541 = 11²*7*3

1694 = 11²*7*2

 

The LCM of these two is:

 

LCM = 11²*7*3*2

 

So ...

 

(-2/2541 + 1413/1694)

= (-2*2/11²*7*3*2 + 1413*3/11²*7*3*2)

 = (4235/11²*7*3*2)

 

Now 4235 = 11²*7*5. so ....

 

(4235/11²*7*3*2) = (11²*7*5/11²*7*3*2) = 5/6

 

So back to the original equation

 

= (-13) + (4235/5082)

= -13 + ⁵/₆

 

= -12 ¹/₆

 

Whew!