Why is it that when the denominator gets larger in a fraction, its value gets smaller? Well, if you look at it this way, it is like cutting a pie. First you have it as one whole. Then you could cut it into halves, thirds, fourths, etc. That one piece you have will remain the same, but the whole just gets smaller. This analogy has help me understand this concept better.
When the denominator gets larger in a fraction, the value gets smaller because it is seperated into more smaller parts, such as 1/5, 1/6, 1/7, etc. So 1/3 would be greater than 1/5 because the larger the denominator is, the smaller the value gets. 1/5 may seem larger but it's not. Because one out of five is not greater than one out of three.