3 ms·
Watch out for negative numbers The mediant inequation is: a/b < (a+c)/(b+d) < c/d If a=1, b=2, c=-1, d=-1 1/2 < 0/1 < -1/-1 1/2 < 0 is obviously wrong If y
by GuB-42 4y ago
Watch out for negative numbers
The mediant inequation is: a/b < (a+c)/(b+d) < c/d
If a=1, b=2, c=-1, d=-1
1/2 < 0/1 < -1/-1
1/2 < 0 is obviously wrong
If you remove negative signs in the denominators by multiplying by -1/-1, it works
1/2 < 2/3 < 1
- dxbydt 4y ago> The mediant inequation is: a/b < (a+c)/(b+d) < c/d The equality is more fun & shows up frequently on the Nationals. It states: a/b = c/d => a/b = c/d = (a+c)/(b+d) For example - On the AIME 2023 this Tuesday (Feb 7), Problem 12 was literally this equality. (see solution 2 below) https://artofproblemsolving.com/wiki/index.php/2023_AIME_I_Problems/Problem_12 https://artofproblemsolving.com/wiki/index.php/2023_AIME_I_P...