Question

Сравнить дроби 2003/2004 и 2004/2005

Answer 1

Докажем общую формулу для a>0,b>0,c>0

если a<b, то

$\frac{a}{b}$

верно!

в нашем случае

a=2003

b=2004

a<b

c=1

a+c=a+1=2003+1=2004

b+c=b+1=2004+1=2005

$\frac{2003}{2004}$

Answer 2

To compare the fractions 2003/2004 and 2004/2005, we need to find a common denominator.

We can do this by finding the least common multiple (LCM) of the denominators, which in this case is 4020.

Then, we can convert each fraction to an equivalent fraction with the common denominator of 4020:

2003/2004 = (2003 × 2010) / (2004 × 2010) = 4,022,530 / 4,040,160

2004/2005 = (2004 × 804) / (2005 × 804) = 1,611,216 / 1,617,420

Now we can compare the two fractions:

4,022,530 / 4,040,160 ≈ 0.9956

1,611,216 / 1,617,420 ≈ 0.9961

Therefore, we can see that 2004/2005 is slightly larger than 2003/2004.