Explain how you know that 7/12 is greater than 1/3 but less than 2/3

To compare, all denominators must be the same. So, find the common denominator for 12,3&3, which is 12 (12x1=12, 3x4=12). Whatever you do for the bottom you must also do for the top. So, 7x1/12x1= 7/12, 1x4/3x4=4/12, and 2x4/3x4=8/12. Therefore 7/12 is greater than 1/3 (AKA 4/12) but less than 2/3 (AKA 8/12).