Compare and Order Fractions Whose Denominators Are All Multiples of the Same Number 6 - Reasoning

The task at hand involves comparing and ordering fractions with denominators that are multiples of the same number, specifically the number 6. Students are presented with a sequence of fractions and are asked to find the missing number that completes the sequence while maintaining the correct order. The sequence given is 1/4, a missing fraction, and then 5/12. To solve this, students must understand that to compare fractions effectively, the fractions must have a common denominator.

The solution to the problem is found by first converting 1/4 into twelfths, which is the common denominator shared with 5/12. Since 1/4 is equivalent to 3/12, students can then determine that the missing fraction must be greater than 3/12 but less than 5/12. The only fraction that fits this requirement is 4/12, which simplifies to 1/3. Therefore, the sequence in order, from smallest to largest, is 1/4 (or 3/12), 1/3 (or 4/12), and 5/12. The missing number, which completes the sequence, is A = 1, representing the numerator of the fraction 1/3 when it is expressed with 3 as the numerator and 12 as the denominator.