We start out with the only information we have â€“ Kok Yangâ€™s mass (k) expressed as a fraction of Melvinâ€™s (m):
In order to express Melvinâ€™s mass as a fraction of Kok Yangâ€™s, we need to find what m is equal at â€“ and the easiest way to do this would be to remove anything but m from that side of the equation.
Now, since we can add new operations to an existing equation â€“ the only requirement is that we have to add the same operation to both of its sides -, weâ€™ll just divide both of them by 2/7:
thus only leaving m on its side, and showing what itâ€™s equal at on the other.
Melvinâ€™s mass is 7/2 of Kok Yangâ€™s.
The ratio of Kok Yangâ€™s mass to Melvinâ€™s mass can be expressed as k:m or k/m, and can be derived in a similar manner and using the same equation as above:
except that this time we need to find what k/m is equal at. The easiest way to do this would be to once again add a new operation to both sides of the equation â€“ this time, dividing them by m:
The ratio of Kok Yangâ€™s mass to Melvinâ€™s is 2 to 7.
The ratio of Melvinâ€™s mass to the total mass (k+m) can be expressed as m:(k+m) or m/(k+m), and can be calculated by using one of the equations above. Since weâ€™re looking for ratio of Melvinâ€™s mass to something, letâ€™s choose to use m=7/2k, and calculate the total first:
Now, we look for the ratio of m to the total:
THe ratio of Melvinâ€™s mass to the total mass is 7 to 9.