Compare and Order Fractions Whose Denominators Are All Multiples of the Same Number - Reasoning

The statement in question is a common misconception when comparing fractions. Tia suggests that the fraction 13/6 is greater than 12/5 simply because the numerator 13 is larger than 12, and the denominator 6 is larger than 5. However, this reasoning is incorrect when it comes to fractions. To accurately compare the two fractions, one must consider the value of the fractions as a whole, not just the individual numerators and denominators.

The correct approach to compare the fractions is to express them with a common denominator, which in this case is 30, since both 6 and 5 are multiples of 30. By converting 13/6 into an equivalent fraction, we get 65/30. Similarly, converting 12/5 gives us 72/30. Now, it is clear that 65/30 is less than 72/30, which means that 13/6 is actually less than 12/5, not greater. Therefore, the initial claim is false, and it is important to understand that in fractions, a larger numerator or denominator does not necessarily indicate a larger overall value.