Denominator of Fractions

Is it true that a fraction with a small denominator is bigger than a fraction with a large denominator? If so, why?

For example, 7/2 is greater than 7/20. Why?

 

If the numerators same, fraction with the smaller denominator is the larger fraction.
There are a few ways to approach this problem. First and foremost, we could convert each fraction into an equivalent fraction with the LCD as its denominator:
the LCD of 2 and 20 is 20 so
7/2 =70/20 is greater than 7/20 because the numerator 70 is greater than 7

You often need to know when one fraction is greater or less than another fraction. Since a fraction is a part of a whole, to find the greater fraction you need to find the fraction that contains more of the whole. If the two fractions simplify to fractions with a common denominator, you can then compare numerators. If the denominators are different, you can find a common denominator first and then compare the numerators.

 

You will be surprised to know that very few students at any level know this information.